introduction to the teacher - western cape
TRANSCRIPT
Inte
rmed
iate
Pha
se
Teac
her’s
Gui
de
Grade
6
Mathematics
INTRODUCTION TO THE TEACHER’S GUIDE
Accompanying the work schedule is this teacher’s guide, which gives more detail on the work schedule. The following information will be found in this teacher’s guide:
1. Core concept/s
2. Resources
3. Integration
4. Ideas of Methodology with Activities and Examples
5. Consolidation of Concepts
6. Homework/Reflection on Learning
7. Extended Activities
8. Assessment
9. Approved Software List for Mathematics
Results from the WCED Grade 6 Diagnostic Tests show that the mathematical competencies of the learners in a class vary greatly. (In some instances from Grade 1 competency to Grade 6 competency.) This requires differentiated teaching in the majority of the mathematics’ classes. It is with this in mind that the WCED recommends that when starting a new concept the teacher first starts with the concrete, i.e. the actual concrete representation, then moves to the semi-abstract, i.e. diagrammatic representation, and then to the abstract, which is the use of numbers and symbols only. This method has been expounded under the heading ‘Ideas of Methodology with Activities and Examples’ in the teacher’s guide.
A daily 10-minute mental mathematics time has been allocated. It is recommended that the mental mathematics flipbooks be used during this time. Teachers should supplement this with regular repetition of number combinations and times tables.
It is during the Intermediate Phase that the foundations for algebra and geometry are laid (i.e. LO 2, 3 and 4). Learners must experience the concepts in these learning outcomes through a practical and investigative approach, e.g. learners must spend time investigating the dimensions and common characteristics of shapes and objects, so that their properties can be formulated. The same is required for measurement. Learners must discover the formula for area etc. through investigation. It is only in the Senior Phase that they will be expected to use the formula.
Built into the work schedule and teacher’s guide is time for consolidation of the concepts. Learners must be given enough time in class to practise the concepts. Homework must be given daily so that these concepts practised in class can be consolidated. Learners will not be able to consolidate mathematical concepts without doing homework.
Ideas for formal assessment have been given. Exemplar assessment tasks which could be used with this work schedule will be distributed to schools in January 2009. This should further assist in the standardisation of assessment in the WCED.
The WCED hopes that these work schedules and teacher’s guides will assist in reducing the load on teachers with regard to planning. Time can now be spent on the actual planning of the lesson.
- 1 -
MATHEMATICS GRADE 6 TEACHER’S GUIDE
DAILY ROUTINE At least one hour must be spent on Mathematics every day TIME ALLOCATION 10 min Oral and written Mental work 10 min Review and Correct homework of previous day 20 min Teacher introduces the concept of the day 15 min Problem solving – Application and Reflection of the day’s work 5 min Homework tasks are given and explained by the teacher REVISION OR BASELINE ASSESSMENT (refer to work schedule) Formal written activity must be completed individually by learners and assessed by teachers. All baseline assessment must be kept as part of learners’ portfolios. Problem areas must be identified and strengthened before continuing. MENTAL MATHEMATICS must be done during the first 10 minutes of every period covering those Assessment Standards already covered. Possible activities from mental mathematics flipbook is given in work schedule for every week. MENTAL MATHS STRATEGIES 1. COUNTS FORWARDS AND BACKWARDS - Counts forwards and backwards in steps
from a certain number. 2. REARRANGE – Numbers change places e.g. 9 + 27 = 27 + 9 3. RENAME: MULTIPLES OF 10 AND 100 – Breaking down of numbers in 100’s, 10’s, 1’s.
e.g. 236 + 45 = 230 + 40 = 270 + 10 + 1 = 281 4. RENAME: BRIDGING USING MULTIPLES OF 10 - Breaking down numbers and rounding
to the nearest multiple of 10. e.g. 47 becomes 50 – 3, 27 + 5 = 30 + 2, 18 + 9 = 20 + 7
5. RENAME: COMPENSATING - Helps with + and – of numbers closer to multiples of 10.
The number that gets added, is rounded off to the nearest 10, where after the difference is +/-
e.g. 27 + 18 = 25 + 20, 27 – 18 = 27 –20 -2 6. RENAME: USING ALMOST DOUBLES - When learner is comfortable using doubles, they
can use this information when calculating close numbers: e.g. 8 + 7 = 8 + 8 – 1 = 15, 9 + 13 = 9 + 9 + 4 =22 7. RENAME: BRIDGING BY USING OTHER NUMBERS THAN 10
Bridging numbers other than 10. e.g. Time: learner learns that bridging with 10 and 100 is not always the correct strategy e.g. 09:59 + 2 min, is read as 10:01 and not 09:61
8. MULTIPLICATION TABLES TO 10 – Repeated addition and subtraction of numbers in
counting patterns.
- 2 -
9. MULTIPLES OF 10 - X10: add a 0, X 100 add 00. Establishing place value focusing on
powers of 10. e.g. 7 x 10 = 70, 67 x 100 = 6 700 10. DOUBLING AND HALVING - Doubling and halving of numbers (even and uneven). e.g. 7 + 7 = doubling 7, 14 x 5 = 14 x 10 ÷ 2 11. X AND ÷ SINGLE DIGIT NUMBERS ; X AND ÷ 2 DIGIT NUMBERS - Breaking down
numbers to primitive ways to solve. e.g. 9 x 8 = 9 x (3 + 5) = 9 x 3 + 9 x 5 12. FRACTIONS: DECIMALS AND PERCENTAGES - Relation between fractions,
percentages and decimal fractions. All are the same, represents same fraction e.g. = 50% = 0,5. 13. GAMES: Use games to make mental mathematics fun e.g. Divide a pack of cards between 2. Hold the cards upside down. Each person turns over the top card and adds the two numbers. The first one with the correct answer gets the cards. Start again – the person with the most cards will be the winner. Decide beforehand what numbers the King, Queen and Jack will represent. PROBLEM SOLVING AND APPLICATIONS The strategies stated in 6.1.10 and 6.1.11 must be practised daily whilst teaching LO1 and LO4 mainly.
o 6.1.10. Techniques to perform written and mental calculations with whole numbers in the above number range:
- adding, subtracting and multiplying in columns - long division - building up and breaking down numbers - rounding off and compensating - using a calculator.
o 6.1.11. Use a range of strategies to check solutions and judges the reasonableness of solutions.
- 3 -
TERM 1
WEEK 1 CORE CONCEPT Calculators Basic calculations Use of brackets RESOURCES Gr 6 Text books WCED Illustrative examples Calculator Poster Internet Web sites INTEGRATION Technology, EMS, IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Use of the calculator (6.1.10)
Activities o Using the calculator Experiment and learn how to use the following:
- RM Recall memory - M+ Plus memory - Minus memory - CM Clear memory - clear the display before starting a calculation; - CE Cancel entry - change an accidental wrong entry by using the [clear entry] key;
o Use the memory and select the correct key sequence to carry out calculations involving more than one operation including brackets: for example, (23 + 41) x (87 + 48); or 8 x (37 + 58);
o Constant facility
Use a calculator to add the following:
1 467 + 1 467 + 1 467 + 1 467 + 1 467 + 1 467 + 1 467 = ?
How did you do this?
Did you key in the number every time?
How many times did you key in the number?
Can you think of a shorter method?
MATHEMATICAL VOCABULARY calculator, display, key, enter, clear, constant... recurring, cancel, memory keys; operations:
- 4 -
o Key in the following:
What do you notice?
How many times did you press ?
What is the answer to 5 x 6?
Can you do this with bigger numbers?
LO and ASs
Multiple operations on whole numbers with or without brackets (6.1.8) Commutative, associative and distributive properties. (6.1.12) Use a range of techniques ( 6.1.10)
Activities
o Use the calculator for order of operations: (BODMAS - brackets; off; division; multiplication; addition; subtraction)
- Calculate the following: (Where there are brackets, always do the operation inside the brackets first.)
6 x 5 + 7 (6 x 5) + 7 6 x (5 + 7) Which one of the above is different? Why do you think this is so?
- Do the same kinds of exercises, using combinations of +; -; x; and ÷ Allow the learners to reflect on the answers and relate these to the order of operations.
o Use a calculator to solve problems e.g.
- Every day a machine makes 100 000 paper clips which go into boxes. A full box has 120 paper clips. How many full boxes can be made from 100 000 paper clips?
- Each paper clip is made from 9.2 cm of wire. What is the greatest number of paper clips that can be made from 10 metres of wire?
- 2753 people go to a sports event. Each person pays R120.00 for a ticket. What is the total amount of ticket money collected?
- Calculate 24% of 525. - Find two consecutive numbers with a product of 1332. - Find three consecutive numbers which add up to 171
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Teacher lead activity interpret a rounding error such as 6.9999999 as 7; Have a feel for the approximate size of an answer, and check it by performing the inverse calculation or by clearing and repeating the calculation.
5 + = = = = = =
=
- 5 -
Codebuster – Work out the sums, find the letter, crack the code! 1. 57 ÷ 3 / 64 +24 / 66 ÷ 3 / 31 – 9 / 456 – 437 / 3 x 10 138 ÷ 6 / 800 ÷ 100 / 12 – 6 / 930 –
911 / 89 – 47 2. 19 + 4 / 128 ÷ 16 / 104 – 98 / 361 ÷ 19 / 126 ÷ 3 96 ÷ 12 / 11 x 2 120 ÷ 4 / 373 – 365 / 408
÷24 / 644 – 631 / 800 ÷ 100 / 306 ÷ 18 3. 96 – 89 / 736 ÷ 32 / 9 x 2 / 529 ÷ 23 / 11 x 4 / 388 – 369
34 – 26 / 596 – 574 6 x 5 / 399 – 311 / 196 ÷ 14 / 784 – 765 / 23 + 19 / 276 ÷ 12 / 188 – 145
ASSESSMENT Informal: observation ______________________________________________________________________________ WEEK 2 CORE CONCEPT Whole numbers Number system different to own Place value Rounding off RESOURCES Gr 6 Text books WCED Illustrative examples MST (Maths Science Technology) Kit Calculator Place value tables 100 chart Poster Internet Web sites INTEGRATION Technology, SS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Number systems different to own (Range 1-10 000) (6.1.2).
LANGUAGE – NEW TERMINOLOGY ones, tens, hundreds, thousands… ten thousand, hundred thousand, million… digit, one-digit number, two-digit number, three- digit number, four-digit number, numeral, place value
- 6 -
Activities
o Discuss ways of counting in the past, e.g. notches in sticks, counting stones, scratches on cave walls, knots in rope, etc.
o Convert between number systems of Egyptian numeral system to own e.g.
- The ancient Egyptians represented:
one with this symbol: │ 10 with this symbol: ∩ 100 with this symbol: פ What is the total value of the number represented here? It didn’t matter in which order you arranged the symbols.
o Convert between number systems of Roman numeral system to own e.g. - The ancient Romans wrote
1 like this: I 5 like this: V 10 like this: X 100 like this: C 1 000 like this: M
- What numbers do these symbols represent?
XVII XIX MCCCXIV MMXC
- Explain, in your own words, how the Roman system works. - Can you think of any disadvantages of the Roman system?
LO and ASs
Recognise, represent, describe and compare: whole numbers to at least 9-digit numbers. Start with 6-digit and build up to 9 digits. (6.1.3)
Activities o Read, say and write 9-digit numbers. Start with 6-digit and build up to 9-digit.
Convert from numbers to words and words to numbers.
- Shade in the number two million, three hundred and eighty-five thousand seven hundred and forty-nine in the grid below:
- Find the card with: ‘sixty-two thousand, six hundred and twenty’ on it ‘six hundred and forty-five thousand and nine’ on it ‘fifty-six thousand and seventy-six’ on it.
2 859 784 745 879 2 849 857
87 459 3 278 495 2 385 749
5 447 859 2 385 479 249 785
2179 584 859 478 378 945
│││││ ∩ ∩ ∩ ∩ פ פ פ פ פ
│││ ∩ ∩ פ פ
- 7 -
- Say the following numbers aloud:
2 758 432 5 861 972 750 580 001
- Respond to oral or written questions such as: Read these: 3 010 800, 342 601, 630 002, 2 489 075…
- Write down the following numbers: ten million, four thousand and two
seven hundred and seventy-nine thousand
nine hundred million - Put in your calculator display: ninety-nine thousand, five hundred and two; two hundred and fifty-two thousand and forty. - Write in figures: twenty million, ninety thousand and fifty. - Write the number that is equivalent to: five hundred and forty-seven thousands, four
hundreds, nine tens and two ones (units). - Write in words: 207 001, 594 090, 5 870 300, 10 345 602…
LO and ASs
Recognise, represent, describe and compare: prime numbers to at least 100. (6.1.3)
Activities
A prime number is a number that only has the factors 1 and the number itself.
o Which of the following numbers are prime numbers?
2 7 9 13 21 467
Make a list of the first 20 prime numbers. A 100 square can be used.
LO and ASs Recognise the place value and value of whole numbers to at least 9-digit numbers. (6.1.4)
(1st term could be just 7-and 8-digit numbers).
Activities o Use place value tables.
- Distinguish between numeric value and place value
HM TM M HTh TTh Th H T U 4 6 8 9 7 3 2 1 5
e.g. the numeric value is the value of the digit in the number. The 8 is 8 000 000. The place value is the place it takes in the number e.g. place of the 8 is millions.
- What is the place value of the underlined digit in each of the following numbers?
12 594 672 10 987 890 258 955 675 100 508 256
- What does the digit 3 in 305 642 represent? and the 5? and the 6? and the 4? and the 2?
- What is the numeric value and place value of the digit 7 in the number 79 451? And the 9?
- 8 -
LO and ASs Build up and break down numbers (6.1.10)
Activities Expanded notation of numbers.
- Practice writing 6-7 digit numbers in expanded notation e.g. 6 682 347 = 6 000 000 + 600 000 + 80 000 + 2 000 + 300 + 40 + 7.
- Fill in the missing number and give a reason why: 5967 = 5000 + ……. + 60 + 7 4529 = 4000 + 500 + …. + 9
LO and ASs Estimate, calculate, solve problems by rounding off to the nearest 5, 10, 100 or 1 000. (6.1.8).
Activities o Use concept in basic operations Rounding off to :
5 Look at last digit More than 2
21
- units must be one more
10 Look at last digit More than 5 – tenths must be one more 100 Look at last 2 digits More than 50 - hundreds must be one more
1000 Look at last 3 digits More than 500 - thousands must be one more
o Use concept in problem solving - Estimate the number of learners in your class. - Estimate the number of learners in your school. - Can you estimate the number of people who live in your town, city or suburb? - In your group/class, see who can estimate the answer of the following sum in one
minute. (Do not try to accurately calculate the answer.) 454 595 731 389 88 783 1 012 044 59 132 478 897 + 9 813 575 __________ Now use a calculator to find out the exact answer. Whose estimation was closest to the correct (accurate) answer? What method of estimation did they use? (Let them explain it to the whole class.) Who rounded off to the nearest 10; 100; or 1 000? CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving.
- 9 -
EXTENDED ACTIVITY Which is less: 4 thousands or 41 hundreds? What needs to be added/subtracted to change: 47 823 to 97 823; 207 070 to 205 070? Use your calculator. Make the change in one step. Make the biggest/smallest integer you can with these digits: 8, 3, 0, 7, 6, 0, 2. Write your number in words. ASSESSMENT Informal: observation ______________________________________________________________________________ WEEK 3 CORE CONCEPT Whole numbers Addition Subtraction RESOURCES Grade 6 text book Illustrated Examples Number board Flard cards Base 10 blocks, Mental Maths flipbook Concrete material e.g. counters; number lines; thousand chart Calculators INTEGRATION EMS, Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Addition of whole numbers: - revise addition within number range 1 – 100 000
- solve problems in context. (6.1.8) Uses a range of techniques to perform written and mental calculations with whole numbers including: adding and subtracting in columns; building up and breaking down numbers; rounding off and compensating; using a calculator. (6.1.10)
Activities o Follow the following sequence:
- Estimate answer by rounding off. - Explore different techniques emphasise the addition in columns. Where calculations are
set out in columns, know that units should line up under units, and so on… - Check answer with calculator. - Discuss the methods used.
MATHEMATICAL VOCABULARY Whole number, place value, inverse operation, difference between, sum of, add, subtract
- 10 -
o Solve problems by using the above sequence e.g. - The following spectator tickets were sold at the Olympics. 1 625 407 for gymnastics; 68
945 for weightlifting; 2 165 001 for athletics; 770 239 for swimming. How many tickets were sold altogether? How many more tickets were sold for athletics than for swimming?
- Sipho buys the following: milk for R11,50; bread for R4,30; washing powder for R7,89; oil for R4,40; and eggs for R9,70. Without doing any calculations on paper, can you quickly tell if R30 will be enough to buy all of this? How do you know? Add amounts with a calculator. Compare your estimated answer with the answer on the calculator. o Examples of the different techniques:
- Method 1: Adding the most significant digits first e.g.
6584 + 5848
11000 add the thousands 1300 add the hundreds 120 add the tens 12 add the units 12432
- Method 2: Compensating (add too much, take off).
6467 + 2684 9467 (6467 + 3000) –316 (2684 – 3000) 9151
- Method 3: Working in columns. (Emphasise this method.) Continue to develop an efficient standard method that can be applied generally. For example: using ‘carrying’. 111 111
7648 6584 +1486 +5848 9134 12432 5 634 098 989 342 + 1 623 998 Extend method to numbers with any number of digits. Using similar methods, add several numbers with different numbers of digits.
TD D H T E 1 2 2 2 4 5 3 6 9 7 5
2 6 0 9 8 1 7 9 4 3 4 9 5 5 2
- 11 -
o Use the method you like best to calculate the following: 1 582 457 + 2 719 043 + 1 689 885 = 8 117 023 + 6 914 590 = 681 233 970 + 367 564 856 = Compare your methods with other learners in the class. Did everybody’s work? Did anybody show you a method that you prefer? Who had the quickest method?
LO and ASs 0 in terms of its additive property (6.1.3).
Activities o Make the learners aware that when we add nought to a number, the answer is always
that number, for example: 23 + 0 = 23 679 + 0 = 679 0 + 52 = 52
LO and ASs
Subtraction of whole numbers: - revise subtraction within number range 1 – 100 000 - solve problems in context. (6.1.8)
Uses a range of techniques to perform written and mental calculations with whole numbers including: subtracting in columns; building up and breaking down numbers; rounding off and compensating; using a calculator. (6.1.10)
Activities o Follow the following sequence:
- Discuss subtraction and addition as inverse operations - Estimate answer by rounding off - Explore different techniques emphasise subtraction in columns. Where calculations are
set out in columns, know that units should line up under units, and so on… - Check answer with calculator or check answer by doing inverse operation - Discuss the methods used.
o Solve problems by using the above sequence e.g.
o Examples of the different techniques:
- Method 1: By counting up (complementary addition)
6467 – 2684 +16 (2700) +300 (3000) +3467 (6467) 3783 (add the 3 numbers together)
- Method 2: By compensating (take too much, add back)
6467 – 2684 3467 (6467 – 3000) +316 (since 3000 – 2684 = 316) 3783
- 12 -
- Method 3: By decomposition 5 13 16
6467 – 2684 3783
- Methods 4: Work in columns. (Emphasise this method) Continue to develop an efficient standard method that can be applied generally. For example: Subtract numbers with different numbers of digits. For example, find the difference between: 782 175 and 4387. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Use larger digit range. ASSESSMENT ASSESSMENT TASK 1: ACTIVITY 1.1. e.g Tutorial on work covered in weeks 1-3) ______________________________________________________________________________ WEEK 4 CORE CONCEPT Whole numbers Multiplication RESOURCES Gr 6 Text books WCED Illustrative examples MST (Maths Science Technology) Kit Poster Internet Web sites Number board Flard cards Base 10 blocks Mental Maths Flipbook Concrete material, e.g. counters; number lines; thousand chart Calculators
TD D H T E 7 9 13 15 8 10 4 5 9 2 9 7 6 6 5 0 6 9 3
MATHEMATICAL VOCABULARY Factors, product, multiples, multiply, times
- 13 -
INTEGRATION Technology, EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognise, describe, use multiples and factors of at least any 2-digit and 3-digit whole number. Know time tables - practice regularly up to 12 x12. (6.1.9)
Activities o Practise these type of examples:
- I count in multiples of 16, up to 160. Will I count the number 32? Will I count the number 104? Will I count the number 144? - Complete this pattern:
256; 512; 1 024; _____ ; _____; _____ These numbers are multiples of : ______
- Which two numbers, when multiplied together, will give me 24? This question has a host of correct answers. The whole number pairs that learners use to get the answer 24, are called the factors of 24.
So the factors of 24 are: 1; 2; 3; 4; 6; 8; 12; and 24 itself. The factors of 10 are 1; 2; 5; and 10. The possibility of there being many possible answers to a question can be a powerful tool in problem solving where learners realise that there does not always have to be only one correct answer. This is also an effective way in which to introduce the concept of prime numbers, where the only factors are 1 and the number itself.
LO and ASs
Multiply at least any 4-digit by 3-digit whole number (6.1.8). Uses a range of techniques to perform written and mental calculations with whole numbers including: multiplying in columns (6.1.10).
Activities o Follow the following sequence:
- Estimate answer by rounding off. - Explore different techniques emphasise multiplication in columns. Where calculations
are set out in columns, know that units should line up under units, and so on… - Check answer with calculator. - Discuss the methods used.
o Solve problems by using the above sequence e.g.
- A farmer can pack 2 139 oranges into a crate. How many oranges can be packed into 428 crates.
- Use the method you like best to calculate the following: 6 384 X 165 7 876 X 393 Compare your methods with other learners in the class.
- 14 -
Did everybody’s work? Did anybody show you a method that you prefer? Who had the quickest method? o Examples of the different techniques:
- Method 1: Building up and breaking down numbers / partitioning e.g. Example 1 How many bottles of cooldrink are there in 237 boxes? One box can hold 24 bottles. 24 x 237 = 24 x 200 + 24 x 30 + 24 x 7 If I think.24 x 200 = 20 x 200 + 4 x 200. This gives me 4 000 + 800 So 24 x 30 = 20 x 30 + 4 x 30. This gives me 600 + 120 And 24 x 7 = 20 x 7 + 4 x 7 which gives me 140 + 28 Finally 24 x 237 = 4 000 + 800 + 600 + 120 + 140 + 28 = 5 688. Example 2 Approximate first. 4346 x 8 is approximately 4500 x10 = 45 000. 4346 x 8 = (4000 + 300 + 40 + 6) x 8 = 32 000 + 2 400 + 320 + 48 = 34 768 or Short multiplication: Th H T U x U 4346 x 8 is approximately 4500 x 10 = 45 000. 4346 4346 x 8 x 8 4000 x 8 32000 leading to 34768 300 x 8 2400 40 x 8 320 6 x 8 48 34768 Long multiplication: HTU x TU (Columns) 352 x 27 is approximately 350 x 30 = 10 500. 352 x 27 352 x 20 7040 352 x 7 2464 9504 - Method 2: Grid method (ThHTU ´ U and HTU ´ TU)
e.g. 5 469 x 187 =
M HTh TTh Th H T U
5 4 6 9
1 8 7
3 8 2 8 3 X 7
4 3 7 5 2 0 X 80
5 4 6 9 0 0 X 100
1 0 2 2 7 0 3
- 15 -
LO and ASs Revise 1 in terms of its multiplication property. (6.1.3)
Activities o Make the learners aware that when we multiply any number by 1, the answer is always that number, for example: 7 x 1 = 7 458 x 1 = 458 1 x 75 = 75 CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: observation. _____________________________________________________________________________ WEEK 5 CORE CONCEPT Whole numbers Division RESOURCES Gr 6 Text books WCED Illustrative examples MST (Maths Science Technology) Kit Poster Internet Web sites Number board Flard cards Base 10 blocks Mental Maths Flipbook Concrete material, e.g. counters; number lines; thousand chart Calculators INTEGRATION EMS, Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognises, describes and uses: divisibility rules for 2, 5, 10, 100 and 1 000. (6.1.12) Multiples and factors of any 2- and 3-digit numbers. (6.1.3)
MATHEMATICAL VOCABULARY share, group, divide, divided by, divided into, divisible by, factor, quotient, remainder, inverse… and the division signs ÷ or /, divisor, dividend.
- 16 -
Activities o Revise multiples e.g. 7;14;21;28;……
- Complete this pattern: 256; 512; 1 024; _____ ; _____; _____
These numbers are multiples of : ______
o Which two numbers, when multiplied together, will give me 24? This question has a host of correct answers. The whole number pairs that learners use to get the answer 24, are called the factors of 24. So the factors of 24 are: 1; 2; 3; 4; 6; 8; 12; and 24 itself. The factors of 10 are 1; 2; 5; and 10. The possibility of there being many possible answers to a question can be a powerful tool in problem solving where learners realise that there does not always have to be only one correct answer.
o While learners may be able to ‘spot’ divisibility by these numbers, it can be advantageous for them to try to discuss and formulate rules by inspecting number relationships, for example:
- All even numbers are divisible by 2. Also, because 10 is an even number, all multiples of 10, and subsequently of 100 and 1 000, are also divisible by 2.
- Numbers ending in 5 are all divisible by 5 and, because 10 is also a multiple of 5, all multiples of 10, and subsequently of 100 and 1 000, are also divisible by 5.
- Numbers ending in a 0 are divisible by 10. This therefore includes those numbers ending in 00 and 000 and so on.
- Numbers ending in a 00 are divisible by 100. This therefore includes thos numbers ending in 000 and 0 000 and so on.
- (This could be practised during mental mathematics too).
LO and ASs Division of at least whole 4-digit by 3-digit numbers. (6.1.8)
Activities o Division (Mental division: practice regularly turning the tables i.e. doing the inverse operation.
e.g. 5x8=40 → 40÷8=5 40÷5=8 o Follow the following sequence:
- Estimate answer by rounding off - Discuss multiplication and division as inverse operations - Long division in columns with and without remainders - Explore different techniques emphasise long division. Where calculations are set out in
columns, know that units should line up under units, and so on… - Check answer with calculator or check answer by doing the inverse operation e.g.
7x8=56 56÷7=8 56÷8=7. - Discuss the methods used and respond to oral or written questions, explaining the
strategy used. For example: Share 108 between 9.
Divide 112 by 7. Divide 15 into 225. How many groups of 16 can be made from 100? What is the remainder when 104 is divided by 12? How many lengths of 25 cm can you cut from 625 cm? Is 156 divisible by 8? How do you know? What are the factors of 98?
Tell me two numbers with a quotient of 0.5.
- 17 -
o Solve problems by using the above sequence e.g. - I have to pack 4 902 apples into 129 boxes, how many apples will there be in each
box? Decide what to do after division, and round up or down accordingly. Make sensible decisions about rounding down or up after division. For example: 1000 ÷ 265 = 3.8, but whether the answer should be rounded up to 4 or rounded down to 3 depends on the context. - Examples of rounding down. Dad has saved R5000. An airfare to Bloemfontein is R865. 5000 ÷ 865 is 5.780 346 on my calculator. He can buy 5 tickets. I have 5 metres of rope. I need lengths of 865 cm. I can cut off 5 lengths. - Examples of rounding up. I have 5000 sheets of paper. A box holds 865 sheets. I will need 6 boxes to hold all 5000 sheets. 5000 football fans have tickets for a match. Each stand seats 865 people. They can all sit in 6 stands.
o Examples of the different techniques:
- Method 1: By using multiples of the divisor. HTU ÷ TU 977 ÷ 36 is approximately 1000 ÷ 40 = 25. 977 ÷ 36 977 – 360 10 x 36 617 – 360 10 x 36 257 – 180 5 x 36 77 72 2 x 36 5 Answer: 27 rem 5 - Method 2: By long division HTU ÷ TU 972 ÷ 36 is approximately 1000 ÷ 40 = 25. 27 36) 972 36) 972 – 720 20 x 36 – 72 252 252 – 252 7 x 36 – 252 0 0 Answer: 27
- 18 -
- Method 3: By using the grid method e.g. 436028 ÷ 23 HD TD D H T E 1 23 1 8 9 5 7 remain
der 17 2 46
23 4 3 6 0 2 8 3 69 23 Divisor - 2 3 4 92 2 0 6 5 115 436 028
Dividend - 1 8 4 6 138 2 2 0 7 161 18 957 rem 17
Quotient - 2 0 7 8 184 1 3 2 9 207 - 1 1 5 10 230 1 7 8 1 6 1 1 7
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT ASSESSMENT TASK 1: Activity 1.2 e.g. Test (Work covered in weeks 1-5) WEEK 6 CORE CONCEPT Geometric patterns Numeric patterns RESOURCES Gr 6 Text books WCED Illustrative examples MST (Maths Science Technology) Kit Poster and Pictures Internet Web sites Mental Maths Flipbook Concrete material, e.g. counters; number lines; thousand chart Calculators Beads Matches
MATHEMATICAL VOCABULARY match squares, geometric patterns, numeric patterns, investigate, recognise, describe, rule/relationship, input, output, term number, term value
- 19 -
INTEGRATION Arts and Culture, Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Investigates and extends numeric and geometric patterns looking for a relationship or rules. (6.2.1)
Activities (The whole idea of this assessment standard is to see patterns and to explain how patterns are repeated and extended. This requires a lot of practice.) Method:
o Step 1 : Packing shapes Learners should investigate and expand patterns by using beads, matches, etc. Teaching should not only be teacher driven, but learners should also explore their own physical forms by making their own squares and triangles out of paper, sticks, matches, caps, buttons etc.
o Step 2: Draw Learners now draw what has been physically packed out.
o Step 3 : Learners expand and complete their drawn patterns. - Draw the next 5 beads in the string (Colored beads can be used for the activity):
(Notice how this activity can be grouped with LO3. i.e. 6.3.4 and 6.3.5)
- Complete this number pattern. Use beads, matches or blocks as aids.
5; 7; 9; ……; …….; …….
- How many matches are needed to make the 4th shape?
NOTE: Once learners can easily solve the squares problem, get them to solve similar matchstick problems with hexagons, octagons, etc. Do they see the relationship between the number of sides of each polygon and the number of matchsticks needed to make each new shape?
- Can you expand the marble pattern?
- Expansion of patterns does not have to be limited to a series with constant differences of relationships.
3; 7; 12; 18; ……; ……; …… 1; 1; 2; 3; 5; ……; ……; ……
- 20 -
o Step 4 : Describe patterns Describe(to your friend) in your own words, how the pattern was formed and how it’s repeated.
NOTE: Once learners can easily solve the squares problem, get them to solve similar matchstick problems with hexagons, octagons, etc. Do they see the relationship between the number of sides of each polygon and the number of matchsticks needed to make each new shape? Rule: Learners write patterns in own words for e.g. add 2 matches every time
o Step 5 : Design own pattern - Learners take physical objects e.g. squares, triangles; matches etc. and physically pack
out the patterns. Reinforce the names of the 2D shapes (LO3). - Draw own patterns on paper. - Design your own pattern without physical objects (Homework assignment).
Example: Design patterns for the use of a skirt, shirt, gift paper or for a gift bag by using circles triangles, squares and rectangles.
o Step 6 : Find patterns in own environment (Homework task): - Look for patterns in your classroom, home, nature, painting of traditional huts, Persian
rugs etc. Bring examples or pictures to school. - Draw and describe the patterns in own words. Tell the class, describe to the class and /
or write in workbooks Steps 1 to 6 can easily integrate with A&C (visual art), Technology (structures), Languages (advertisements and oral description of patterns.)
o Step 7 : Number patterns NB: Mental maths – Consolidation on daily basis: counting in multiples e.g. Count in 3’s forwards and backwards from certain numbers; also in higher number ranges.
- Use the patterns that were packed in Steps 3 to 6 and write down the number patterns. - Number patterns are taught in the same sequence from step 1-6 as for geometric
patterns. They can be integrated with geometric patterns step-by-step or geometric patterns step 1-6 can be taught first and then number patterns step 1-6 next.
- Remember that number sequences:
Could have constant patterns e.g. x3 each time(3,9,27,…), +2 each time (10,12,14), divide by 4 each time (64,16,4,1) or
- 21 -
Could have non-constant patterns, e.g. Fibonacci-patterns(1,1,2,3,5,8,etc.) i.e. the sum of the 2 previous consecutive numbers, (1,2,4,7,11,16,etc.) add 1 to the 1st number, 2 to the 2nd number, 3 to the 3rd number etc.
o Step 8: Create own pattern, friend completes and describes the pattern verbally and/or in writing.
- Create your own numeric pattern (Make sure you understand how your pattern grows).
Clue : Think of a calculation (or two) which could be transferred to numbers-the calculation has to stay the same; you cannot change it halfway through the numeric pattern. Start with 1 and relate the calculation to that, move on to 2, then to 3 and so on. Example follows: My rule is: number x 2 and than +1 for every number… 1 x 2 = 2 and than +1 is equal to 3 2 x 2 = 4 and than +1 is equal to 5 3 x 2 = 6 and than +1 is equal to 7 My number pattern is : 3;5;7;…(can you work out the rest?)
- You must provide at least 3 numbers to enable your friend to complete the rest of the pattern.
- Challenge your friend to extend your pattern. - Can your friend explain how it grows?
o Step 9: Develop tables from rule.
- (Tables presented in more detail only in 6.2.3- don’t do in detail-only introduction) - Look at the matches example in Step 1 and write the number pattern: 4;7;10;13;…,etc.
find the rule, discuss with a friend and try to complete the table.
How many matches are needed to make the 4th shape? And the 10th shape?
(Until now it was easy to get the next number in the pattern (by adding 3 each time), but what if you want to determine the 100th number/term in the row? A table is now the next logical step. Take note: number the top row of the table individually and find a rule/pattern/formula to get the 100th number of matches completing the table). How does a table work? How will you determine the bottom rows numbers (in other words, the amount of matches) by only using the number of squares to determine the amount of matches? Think vertically not horizontally. What do you do with the top number to get the bottom number?
No. of squares 1 2 3 4 5 10 20
No. of m/sticks needed
4 7 10
- 22 -
Remember the rule has to stay the same for the whole table. In this table the rule is square x 3 + 1 to determine the amount of matches.
- This is a reasonably difficult example-start with easier examples, e.g. 1 2 3 4 5 6 3 6 9 12 15 18 This formula is number (number in top row) x3 determine the bottom number.
- How many marbles are needed to complete the fourth shape? And the fifth? And the tenth shape? And the twentieth?
Pattern 1 2 3 4 10 20 Marbles 1 4 9 ? ? ?
- Find number patterns in:
100 blocks – colour in sequential numbers e.g. every 5 or 7 number. calendar – find patterns in weeks, every fortnight, multiplication table - colour in sequential numbers – multiples, tables, explore patterns.
LO and ASs Describe observed relationships or rules in own words (6.2.2).
Activities o (Extend geometrical shapes to hexagons, octagons, etc.). o Repeat steps for 6.2.1 but in grade 6 put the emphasis on the learner’s own verbal
description. The learner should be able to explain why he/she describes the pattern in a certain manner.
o Pose questions which require insight e.g.
- Explain how the pattern grows. - How did you know which numbers to fill in? - Explain how you worked out how many matches were needed - Will ___(number) also be part of pattern?
- Draw the following 5 beads in the necklace Can you describe the pattern the necklace makes?
- Complete the following number pattern. Explain how the pattern grows? 5; 7; 9; ……; ……; ……
- Calculate how many matches you will need for the fourth shape. Explain how you calculated the amount of matches needed.
- 23 -
- Can you complete the number pattern? How did you know which numbers to fill in? 3; 7; 12; 18; ……; ……; …… 1; 1; 2; 3; 5; ……; ……; ……
- Sipho counts as follows: Will the number 1020 also be part of the pattern? How do you know this?
LO and ASs Determines output values for given input values using verbal descriptions of flow diagrams and tables. (6.2.3)
Activities
o Step 1: Verbal Descriptions:
- Teacher presents visual patterns and learners should continue or complete the pattern – at first orally in their groups to develop confidence.
- Then they need to support their decisions. This can be explained by the following example which could be written:
Using the matches challenge as the example: How many matches would be used to complete the first figure? How many matches would be used to complete the second figure? How many matches would be used to complete the third figure? How many matches would be used to complete the fourth figure? How many matches would be used to complete the tenth figure? How many matches would be used to complete the twentieth figure?
- Describe how the pattern grows. - Illustrate by using a table how the pattern grows. - Use a table to show the growth pattern. - NOTE: Once the learners have solved the square figure, it can be extended to
hexagons, octagons etc. Do the learners see the relationship between the number of sides of the polygon and the matches needed to complete an extra figure? Is there a relationship between the sides and the rule?
- Describe in your words how the pattern grows. “I take the number of squares, multiply it by 3 and then add 1.” OR “I take the top number and multiply it by 3 then add 1.”
o Step 2: Flow diagram
- Consult a variety of sources for different forms of flow diagrams e.g. The flow diagram of the matches’ example could possibly look like: 1 2 3 x3 +1 10 20
- 24 -
- Consolidate the following concepts: Input values, Output values, function, operation/rule (two operations are allowed at grade 6 level.), term number and term value.
- Begin by using a simple example, e.g.
1 ? 2 +2 ? 3 ?
- Rotate the flow diagram vertically so that it resembles a table – this will facilitate the introduction of a table – the input values are represented at the top – rule or operation in the middle – and output value below, e.g.
1 2 3 n+2 3 4 5
- Ensure that learners are exposed to the reverse/inverse operation by requesting the input result from the output values.
? 3 ? +2 4 ? 5
- Even removing the middle operation can be done, which the learners then need to formulate.
1 3 2 ? 4 3 5
o Step 3: Table
- Learners are given an incomplete table which they complete after finding the rule/function.
- Also give learners the opportunity to do the reverse function where they have to calculate the input value from the output values using the reverse operation.
- Teachers can give the geometric figure and learners should complete their own table and find the rule.
- There should be a definite relationship between the number rows, table, flow diagram and number sentence.
The table of the “match squares” could look like:
Squares 1 2 3 4 10 20 Matches 4 7 10 13 ? ?
o The important aspect of this assessment standard is to show that the same rule can be
represented by using verbal descriptions, flow diagrams or tables. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept.
- 25 -
HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Pascal's Triangle
This pattern is named after the French mathematician Blaise Pascal (1623-62) who brought the triangle to the attention of Western mathematicians (it was known as early as 1300 in China, where it was known as the "Chinese Triangle").
The triangle itself is made by arranging numbers. Each number in the triangle is the sum of the pair of numbers directly above it (to the above left and above right). The first four rows are as follows (the 1 at the top is considered to be Row 0):
The worksheet here shows the above triangle, and then ask the learners to try and work out how the triangle is made. They are then required to complete the next five rows of the triangle, which are as follows:
When the learners have completed all of the triangle, they should look for patterns. The questions at the bottom of the worksheet focus the learner's attention on different aspects of the triangle (e.g. even and odd numbers, diagonal lines, total of the numbers in each row).
- 26 -
Triangular Numbers
Triangular numbers are those numbers that can be formed by counting the number of objects used in making a triangle.
1) Ask the learners to make these triangles using Unifix cubes or other suitable equipment. They should note down the number of cubes it took to build each triangle.
2) Discuss the numbers of cubes needed and explain that the number of cubes in each triangle is called a triangular number.
3) Ask them to look for any patterns in their work. How many cubes do they need to add to the bottom of each triangle to make it larger?
4) Is there a way of predicting how many cubes will be needed to build each triangle? How many cubes would be needed to make a triangle which has a base of 100 cubes?
5) You could also try the above activity, using triangles which only have sides (i.e. no middles). What is significant about the numbers in this case?
The Mathemagician's Seven Spells The great spell has to be broken! It has seven parts. Two children, Anna and David, must break it, but you can help...
The Maths magician stands by his immense cauldron, flames dancing round. He stares hard at the cauldron and then at the two children.
- 27 -
"Tell me the next two numbers in each of these seven minor spells, "chanted the Maths magician, "and the great spell will crumble away! Watch the smoke to see the spells."
Spell the first:
Spell the second:
Spell the third:
Spell the fourth:
Spell the fifth:
Spell the sixth:
- 28 -
Spell the seventh:
Anna and David managed to break the spell, did you?
ASSESSMENT Informal: observation + marking of classwork. ______________________________________________________________________________ WEEK 7 CORE CONCEPT Space and shape RESOURCES Illustrated Examples Mental Maths Flipbook Grade 6 text book MST Kit e.g. cubes, dice prisms, triangular prisms, spheres (balls), cylinders, dowels. INTEGRATION Technology, NS, Arts and Culture IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognise, visualize, and name 3D objects in natural and cultural forms and geometric settings:
-similarities and differences between tetrahedrons and other pyramids (6.3.1).
Activities o Collect a large number of 3D objects which learners can sort and group according to their
own criteria. o What do the following shapes all have in common?
What is different between them?
MATHEMATICAL VOCABULARY tetrahedrons pyramids, rectangles, faces, parallelograms, vertices edges; cubes, dice prisms triangular prisms, spheres (balls), cylinders, dowel
- 29 -
NOTE: It’s extremely important for the learners to discover and discuss the differences between the pyramids, and then come up with their own (sensible) reasons for similarities and differences.
The first figure is called a tetrahedron, and the second is called a square-based pyramid (the one we are most familiar with). The other two are pentagon-based and hexagon-based pyramids respectively. Learners can try making heptagon and octagon-based pyramids themselves.
Learners can count the faces on each of the pyramids, possibly linking this to LO2.
There are quite a few interesting questions and subsequent investigations that arise when looking at pyramids. While a tetrahedron can be made from four equilateral triangles, and a square-based pyramid can have four equilateral triangles as its faces, at what point will you have to stop using equilateral triangles?
LO and ASs Recognise, visualize, and name 2-D shapes in natural and cultural forms and geometric settings: - Similarities and differences between rectangles and parallelograms. (6.3.1)
Activities
o Sort the following shapes into groups: similarities and differences between rectangles and parallelograms.
Explain why you think they belong together in these groups. What do these shapes have in common? (Their sides? The angle size of the corners?)
(Angles can be looked at practically here and done in more detail in Term 4, Week 1)
Note that squares, rhombuses and a trapezium appear among these examples. This is to help the learners to develop the properties of especially the rectangles and parallelograms.
Interesting questions may be posed:
Is a rectangle a parallelogram? (Does it possess all the properties of a parallelogram?)
Can a parallelogram be a rectangle? If you consider the squares and rhombuses, you can start including these for consideration.
LO and ASs Describe and classify 3-D objects and 2-D shapes in terms of:
-faces, vertices and edges -length of sides -angle size of corners.(� = � 900) (6.3.2)
A
B
C
D
E
F
H
G
I
- 30 -
Activities o One way of handling this assessment standard is to give the learners an assortment of
found objects which you will have to choose carefully – examples of cubes (dice, blocks), rectangular prisms (boxes, wooden blocks), triangular prisms (wooden wedges, fancy chocolate boxes), spheres (balls), pyramids (wooden or plastic), cylinders (toilet rolls, pens, dowel sticks), cones (party hats, ice cream cones). It may be a good idea to throw in one or two irregular or semi-irregular objects (stones, shells) to provoke discussion. Let the learners sort these objects into groups. (Don’t specify how many at first, and DON’T give them any criteria for classification.)
They must explain the criterion for each grouping. Grade Six learners should come up with more sophisticated criteria than Grade Fives. You can use this type of activity to help gauge the level that your learners are at. Later you can reduce the number of groupings to 3 or 4.
- Faces, vertices and edges
Make sure the learners have a firm grasp of what these three terms refer to.
- The learners must progress towards using these (faces, vertices and edges) as criteria.
VERTEX
FACE EDGE
FACE
CURVED SURFACE
EDGE
- 31 -
They may start placing all those objects having (flat) faces together. They may group those that have both faces and curved surfaces together, and finally group those that have only curved surfaces.
One the other hand, they may decide to group the objects in terms of edges – those with straight edges only together, those with curved edges together, etc.
Learners can also group objects according to the shapes of the objects’ faces. e.g. those having faces that are rectangular or square (These are cuboids.).
- Length of sides Regular and irregular polygons can be introduced in this manner.
When sorting 2-D shapes, learners can use this as a criterion. What you will be looking for, is the development of the properties of polygons. So the learners, through the teacher’s questions, should move towards making a group of triangles, quadrilaterals, pentagons, hexagons, and so forth. Remember that these polygons can be either regular or irregular.
Remember that, ideally, the learners should come up with their own criteria for comparing and sorting. The teacher’s job is to guide them towards this point, by challenging them, and making them justify their groupings.
Learners can also be led toward grouping shapes that have all sides equal (regardless of the number of sides). This will lead to understanding and defining regular polygons as opposed to irregular polygons.
• Is a square a regular polygon?
• Is a rectangle a regular polygon?”
Try to let the learners sort shapes that are printed or drawn on sheets of paper. Do not cut the shapes out, as they will become 3-dimensional.
- 32 -
- This activity can also be linked to 6.3.1, where learners explore and develop an understanding of the differences and similarities between parms (parallelograms) and rectangles.
This also creates an opportunity to further discuss the differences between rectangles and squares, and parms and rhombuses.
Teachers can initiate debates around whether a square is, in fact, a rectangle or not. (Considering that a square’s opposite sides are equal in length, and all its corners are 90 degrees)
- Angle size of corners Sort the following in terms of their angles:
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. EXTENDED ACTIVITY Further classification of 2-D shapes and 3-D objects. This must be done through investigation. e.g. 3-D objects Classify solids according to properties such as: • the shapes of the faces • the number of faces, edges, vertices • whether or not any face is right-angled • whether the number of edges meeting at each vertex is the same or different. 2-D shapes Recognise properties of rectangles such as: • all four angles are right angles • opposite sides are equal and parallel • the diagonals bisect one another. Name and classify triangles. Know some of their properties. For example: • in an equilateral triangle all three sides are equal in length and all three angles are equal in size • an isosceles triangle has two equal sides and two equal angles • in a scalene triangle no two sides or angles are equal • in a right-angled triangle one of the angles is a right angle.
- 33 -
Know properties such as: • a parallelogram has its opposite sides equal and parallel • a rhombus is a parallelogram with four equal sides • a rectangle has four right angles and its opposite sides are equal • a square is a rectangle with four equal sides • a trapezium has one pair of opposite parallel sides • a kite has two pairs of adjacent sides equal. Begin to know properties such as: • the diagonals of any square, rhombus or kite intersect at right angles; • the diagonals of any square, rectangle, rhombus or parallelogram bisect one another Group the figures that you think belong together. In each case give a reason for the way you
grouped them:
A B C D E
F G H
J K
L M N P Q
R S T U V
W X Y Z
- 34 -
ASSESSMENT TASK 2: ACTIVITY 2.1 e.g. Investigation on patterns or shapes (week 6-8) ____________________________________________________________________________
WEEK 8 CORE CONCEPT 2-D shapes 3-D objects RESOURCES Illustrated Examples Grade 6 text book Straws Grid paper Glue INTEGRATION Technology, NS, Arts and Culture IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Practical exploration: Investigate and compare 3-D Objects
-make 3-D models (according to geometric properties listed) using: -drinking straws to make a skeleton -nets provided by the teacher.
Activities
o Make these shapes using drinking straws. (Learners can also attempt making skeletons of the pyramids that they investigated in 6.3.1.)
o Open boxes (3-D objects) to investigate their nets.
MATHEMATICAL VOCABULARY Skeleton Pentominoes compasses
- 35 -
o Fold these nets into 3-D objects.
LO and ASs Practical exploration: Investigate and compare 2-D shapes
-draw shapes on grid paper. (6.3.3)
Activities o These shapes are called pentominoes. A pentomino is a shape made from 5 squares of the
same size. These squares must touch along the length of at least one side. How many more different pentomino designs can you make on the grid paper?
o Using different kinds of graph paper, make designs for fancy boxes or gift containers.
(This can be integrated with the Technology Learning Area.)
LO and ASs
Use a pair of compasses to draw patterns in circles Use a pair of compasses to draw patterns with circles. (6.3.3)
Activities o Allow the learners to practice and explore using compasses.
- 36 -
Using circles, make a decorative design for a bookmark or wrapping paper. (Integrate with Arts and Culture)
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise the 4 basic operations. EXTENDED ACTIVITY
Make these models.
Tetrahedron Cube Octahedron
Dodecahedron Icosahedron
- 37 -
Fold these nets into 3-D objects - nets provided by the teacher. ASSESSMENT ASSESSMENT TASK 2: ACTIVITY 2.1 e.g. Investigation on patterns or shapes (week 6-8) ______________________________________________________________________________ WEEK 9 CORE CONCEPT Time RESOURCES Analogue watch Digital watch Stop watch Illustrated Examples Grade 6 text book Internet INTEGRATION Technology, SS, LO IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Describes and illustrates ways of representing time in different cultures throughout history. (6.4.4)
Activities o Years ago, in Africa, people used to measure time by judging the lengths of their shadows.
Arrangements for meetings would be made in terms of shadow length. If you were to meet somebody at a time when your shadow was short, you would meet that person close to midday.
MATHEMATICAL VOCABULARY Analogue time watch / clock with hour, minute, second hand) digital, hour
- 38 -
o Other methods are the hourglass and the candle clock. The hourly markings must be made on the candle the day before. Similar candles can be used on subsequent days to measure time.
Learners can make 3-minute or 5-minute timers using bottles and sand. This activity can be integrated with the Technology Learning Area. (Check if learners did this in grade 4 or 5).
LO and ASs
Read, tell and write (to at least the nearest minute and second) Analogue time (watch / clock with hour, minute, and / or second hand) Digital (notation e.g. 03:45am/pm) 24-hour time (07:45 ; 19:45). (6.4.1)
Activities o Write the time 21h35 in
Analogue time (as on a watch face)
Digital time (say whether a.m. or p.m.)
What are you usually doing at this time? Tell the class.
o Using a watch or clock that has a second hand, get the learners to tell time accurately to the second. Each learner must be able to use an appropriate method to signal the time correctly and accurately - learners can do this using 24-hr time as well.
e.g. “When you hear the signal, the time will be eighteen-thirty, and twenty seconds, exactly.”
o Using a stopwatch, play “reflex” games: seeing who can start and stop the timer the fastest.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise flow charts and development of rules. EXTENDED ACTIVITY: None ASSESSMENT ASSESSMENT TASK 2: ACTIVITY 2.2 e.g. Test on work covered in weeks 1-9 ______________________________________________________________________________
- 39 -
WEEK 10 CORE CONCEPT Time RESOURCES Analogue watch Digital watch Stop watch Illustrated Examples Grade 6 text book Internet Map International Time table INTEGRATION Technology, SS and LO
LO and ASs Solves problems involving calculations and conversions between appropriate time units including time zones and differences. (6.4.2)
Activities
o Conversions: Complete the following:
5 minutes = _______ seconds
17 hrs = _______ minutes
4 hours = _______ seconds
1 week = _______ minutes
o Conversions: Know and use:
1 millennium = 1000 years 1 century = 100 years 1 decade = 10 years 1 year = 12 months or 52 weeks or 365 days 1 leap year = 366 days 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds and the rhyme: 30 days hath September...
o Estimate or measure, suggesting suitable units
- Suggest things you would estimate or measure in: weeks, months, years, decades, centuries... - Suggest a unit to estimate or measure, for example: how long it takes from planting a daffodil bulb to when it flowers;
the age of an old pine tree. - Suggest how to measure, for example:
how long it takes for a runner bean to grow... how long until your birthday...
o Estimate, using standard units, for example: the hours of darkness in December… in June… how long it takes to run a marathon… the time each week you spend sleeping... eating...
MATHEMATICAL VOCABULARY Analogue time watch / clock with hour, minute, second hand) digital,hour
- 40 -
o A man leaves Cape Town at 10:30 p.m. and arrives in London at 6:45 a.m. the next day. How long did the flight take?
o If you watch TV for 45 minutes every day, how much time will you spend watching TV in 6 weeks?
o How many decades to go until the year 2150?
o Answer questions on time zones. Understand different times around the world.
- If Caracas is 6 hours behind Cape Town, what time will it be in Caracas when it is 2:00 a.m. in Cape Town? (This kind of activity can be integrated with Human and Social Sciences – Geography, time zones.)
- Use a world time chart to answer questions such as: If it is 12:00 noon in London. What time is it in Delhi, Tokyo, Hawaii, San Francisco…?
- If it is 4:36 am in Sydney. What time is it in New York? CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Give practice in time zone questions. ______________________________________________________________________________
- 41 -
TERM 2
WEEK 1 CORE CONCEPT Whole numbers Properties of operations RESOURCES Illustrated Examples Number board Flard cards Base 10 blocks Mental Maths Flipbook Concrete material, e.g. counters; number lines; thousand chart Calculators Grade 6 text book INTEGRATION Technology, EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs 0 in terms of its additive property 1 in terms of its multiplicative property (6.1.3) Recognises, describes and uses the commutative, associative and distributive properties of whole numbers (not necessarily know the names).(6.1.12)
Activities o Properties of operations
- Revise
Make the learners aware that when we add nought to a number, the answer is always that number, for example:
23 + 0 = 23 679 + 0 = 679 0 + 52 = 52
- Revise
Make the learners aware that when we multiply any number by 1, the answer is always that number, for example:
7 x 1 = 7 458 x 1 = 458 1 x 75 = 75
- Revise Comparing number sentences when the numbers are rearranged: When the order of the numbers matters: (commutative)
Is 45 + 39 the same as 39 + 45? Is 45 - 39 the same as 39 - 45? Is 9 x 7 the same as 7 x 9? Is 20 ÷ 5 the same as 5 ÷ 20?
- Revise Associative properties : order of operations: 7 + 6 + 3 = 13 + 3 = 16 7 + 6 + 3 = 7 + 9 = 16 5 - 3 + 4 = 2 + 4 = 6 5 - 3 + 4 = 5 - 7 = -2? (Is this incorrect?)
MATHEMATICAL VOCABULARY Number sentence
- 42 -
20 ÷ 5 x 3 = 4 x 3 = 12 20 ÷ 5 x 3 = 20 ÷ 15 = 1 1/3! (Is this incorrect?)
- Revise Distributive properties : apply an operation to two or more numbers: e.g. 2x(4 + 5) = (2 x 4) + (2 x 5) = 8 + 10 = 18 2(4 + 5) = 2 x 9 = 18
These above examples do not show progression regarding the number ranges appropriate for the grade. Larger numbers (appropriate to the grade) may cloud the issue of investigating these operational properties. Once learners are familiar with these properties, they must start working with larger numbers appropriate to the grade.
LO and ASs Multiple operations on whole numbers with or without brackets. (6.1.8)
Activities o Revise: Calculate the following: (Where there are brackets, always do the operation inside the brackets first.) 6 + 5 x 7 (6 + 5) x 7 6 + (5 x 7) Which one of the above is different?
Why do you think this is so? o Do the same kinds of exercises, using combinations of +; -; x; and ÷. o Allow the learners to reflect on the answers and relate these to the order of operations:
- Using combinations of +; -; x; and ÷ - Reflect on the answers - Relate these to the order of operations.
Use brackets: know that they determine the order of operations, and that their contents are worked out first. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: observation + mark classwork. ______________________________________________________________________________
- 43 -
WEEK 2 CORE CONCEPT Number sentences Verbal descriptions Flow diagram Tables RESOURCES Illustrated Examples Number board Flard cards Base 10 blocks Mental Maths Flipbook Concrete material, e.g. counters; number lines; thousand chart Calculators Grade 6 text book INTEGRATION IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Writes number sentences to describe a problem situation within the learner’s life experience. (6.2.4)
Activities o Step 1 : Word problems and number sentences.
Write number sentences to solve and describe a problem.
- Learners are given an easily understood word problem within the learner’s experience which he/she should be able to reduce to a number sentence e.g.
Write these word problems as number sentences. A farm worker earns R45 per day. How much will he/she earn in: 6 weeks (working 6 days a week) Do you think it is a living wage (salary that can sustain a person)?
- Note the different ways of writing the same number sentence: Number sentence: 10 + 7 = 7 + 10 = = 7 + 10 or = 10 + 7 or 7 + 10 = or 10 + 7 = The instruction to learners must be clear and will depend on the teacher if he/she would require the number sentence and/or if the answer will also need to be given.
o Step 2 : Own word problems Learners create their own word problems based on number sentences.
- The opposite to the above where the learners are given the number sentence and the learners must make up ‘number stories’ to reflect statements like:
MATHEMATICAL VOCABULARY Inspection, Solution flow diagrams, number sentences, tables.
- 44 -
27 x - = 728.73 For example: 27 compact discs cost R728.73. How much will one cost?
- Give a word sum for the following number sentence: 247 x 34 Possible solution - I pack 247 oranges into a crate. How many oranges do I pack into 34 crates?
LO and ASs Solve number sentences and complete. (6.2.5)
Activities (You can use a letter / symbol as e.g. c,d g as a place holder and not always a square)
o Step 1 : Inspection Inspection implies that a learner must guess an answer, test it; try another if necessary until they find the correct number that will solve the problem. Do not just try any number. Think carefully about the answer, estimate and look for patterns and relationships. Usually you can start with 1. e.g. Solve the following problem: 3 x y + 6 = 39 Start by replacing y with 1. This will be 3 x 1 + 6 = 9. Not enough!! Replace y with 10. It becomes 3 x 10 = 36. Much closer to the answer! Add 1 and it becomes 11. 3 x 11 + 6 = 39 Solves or completes number sentences e.g. □ ÷ 4 =12 12 ÷ □ = 4 12 ÷ 3 = □
o Step 2 : Control Teach learners to estimate answers. Test answers by fitting the number into the number sentence. That will indicate the correctness of the answer. e.g. Test by substitution: 42 ÷ 6 = 7 of 6 x 7 = 42. Never just accept that your answer is correct. NB: Lots of exercise on a daily basis is needed to consolidate these concepts. These concepts can also be integrated during the Mental Maths session, e.g. 3 + what is 7?
LO and ASs Determine equivalence (similarities) between different descriptions of the same rule. (6.2.6)
Activities
o Revise verbal descriptions, flow diagrams and number sentences from Term 1, Week 6. e.g.
- Verbal description on the ‘squares pattern’ made with matches –from Term 1, Week 6.
- Flow diagram Learners are given an incomplete flow diagram which has to be completed.
- 45 -
Squares Matches 1 2 3 x3 +1 10 20
or
- Number sentence Rewrite the flow diagram in the form of number sentences which can be written below each other. 1 x 3 + 1 = 4 2 x 3 + 1 = 7 3 x 3 + 1 = 10 10 x 3 + 1 = 31 20 x 3 + 1 = 61
- Table Learners must draw reflecting the rule or pattern.
Squares 1 2 3 10 20 Matches 4 7 10 31 61
NB: This assessment standard is similar to 6.2.3. The outcome is to allow learners to observe the relationship between different or alternative strategies/ presentations (orally, flow diagrams, tables and equations/ number sentences). It is also vital to encourage discussions when and where possible strategies/ presentations are most applicable. Discussions surrounding the effectiveness can be held. This can be dealt with when 6.2.3 is covered.
The example illustrates how assessment standards can be grouped and similarly allows the educator to cover more than one assessment standard during a lesson or activity.
o Further examples e.g.
Alwyn wants to find out how many small squares he will need if he wants to make more patterns. Can you help him by completing the table?
Pattern number 1 2 3 4 5 6 7 10 23 n
No. of small squares 1 4 9
1
2
3
10
20
x 3
+ 1
- 46 -
Explain in words how you find the number of squares in any pattern. Can you find a rule to work out the number of squares for any pattern number? Write your rule in the “n- block” in the table. Zonia decided to make tessellations using an equilateral triangle. She starts with one triangle and each time adds one more to make the next pattern. Can you help her to complete patterns number 4 and 5? Pattern 1 Pattern 2 Pattern 3
Pattern 4 Pattern 5 Zonia wants to find out how many sides there are in each pattern. Can you help her to complete the table below for each pattern?
Pattern number Number of sides
1 3
2 5
3 7
4
5
6
9
21
n
Can you find a rule to calculate the number of sides for any pattern number? Write your rule in words. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept.
- 47 -
HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. ASSESSMENT ASSESSMENT TASK 3: ACTIVITY 3.1 e.g. Tutorial on work covered in week 1 and 2. ______________________________________________________________________________ WEEK 3 CORE CONCEPT Fractions RESOURCES Mental Maths Flipbook Base 10 blocks, number lines Number rods Illustrated Examples Fraction wall, fraction circles Calculators Grade 6 text book INTEGRATION IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognise and represent common fractions including tenths, hundreds and percentages in order to describe and compare them. ( 6.1.3)
Activities o Common Fractions (Number range: Number range: denominators 1 – 100). o Follow the following sequence when teaching fractions:
- Explore concretely by using fraction walls, number rods and fraction circles then proceed to diagrams and number lines.
- Recognize common fractions - Represent common fractions - Describe.
o Examples:
- Write the following values in the correct places on the number line:
21
108
54
1101
1011
MATHEMATICAL VOCABULARY Whole number, numerator, denominator, equivalent forms, cancel, percentage
0 1
- 48 -
- Look at the Fraction Wall below and answer the questions.
11
or 1 whole
21
21
31
31
31
41
41
41
41
51
51
51
51
51
61
61
61
61
61
61
71
71
71
71
71
71
71
81
81
81
81
81
81
81
81
91
91
91
91
91
91
91
91
91
101
101
101
101
101
101
101
101
101
101
- Make a list of all the fractions that fall onto the half line. - How many of each fraction does it take to reach the half line?
- How many 41
s make 21
?
- How many 61
s make 21
?
- Make a list of all the fractions that fall onto the 31
line.
- How many 61
s make 31
? - How many 9
1 s make 31 ?
- What do you notice about the denominators of these fractions?
LO and ASs
Recognises and uses equivalent forms of the numbers listed above, including: common fractions with 1-digit or 2-digit denominators. (6.1.5)
Activities o Compare common fractions. Try the following methods:
- Method 1: Compare by looking on the fraction wall. (example on previous page). Or use fraction circles or number rods.
- Method 2: Compare by finding equivalent fractions. Step1: Start off with fractions where the denominators are the same:
86*
83
83
<86
Step 2: Now use denominators where they are multiples. Change the denominators so that it is the same.
- 49 -
52*
103
104
52
103
103
== and
So: 103
<104
So: 103
<52
o Further examples - Complete the following:
43
= 100
?
?4
= 108
31
= 6?
= ?3
24?
= 7239
- Fill in : > ; < of =
42
* 83
53
* 105
84
* 21
o Method 3:
A fraction such as 103
can be changed to an equivalent fraction 10030
by multiplying both
numerator and denominator by the same number.
e.g. 10010
3= =
10030
or
431
43
=x (1 times any number stays the same)
So 1=33
And 129
3433=
xx
or 129
33
43
=x
So 129
43= (The value is the same but it looks different)
- 50 -
- Further examples. Complete the following:
a) 43
= 80
b) 65
= 12
c) 257
= 100x
d) 83
= 15
e) 53
= 25x
f) 169
= y
36
g) 32
= 27
h) 127
= 35
i) 75
= 28a
Method 4:
A fraction such as 205
can be reduced to an equivalent fraction 41
by dividing both
numerator and denominator by the same number (cancel); always write a fraction in its smallest form)
e.g. 420
5= =
41
205=
2051
205
=÷ (Any number divided by 1 stays the same)
Because 1=55
so 41
52055=
÷÷
or 41
55
205
=÷
So 41
205= (The value is the same but it looks different)
- Further examples. Write the following in the smallest form:
2016
3624
- Method 5: mixed numbers A mixed number can be written as a fraction:
7
16722 =
722
722 +=
=1 + 1 + 72
=7
1672
77
77
=++
- 51 -
In short:
7
2)72(722 +=
x
=7
16
- Further examples.
Write the following mixed numbers as fractions
325
629
Method 6: A fraction can also be written as a mixed number
523
517
=
52
55
55
55
517
+++=
=1 + 1 + 1 + 52
523
523 =+
In short:
5175
17÷= (Any fraction is a division sum)
17÷ 5= 3 remainder 2 (The 2 must still be divided by 5)
=523 (3 units and two fifths)
- Further examples. Write the mixed number as a fraction
742
855
LO and ASs Write a fraction as a percentage. (6.1.5)
e.g. ===10060
106
53
60%
Activities o Match fractions to a percentage.
- 52 -
- Use straight lines to match the fraction with the correct percentage and/or decimal fraction (decimals can be filled in later in 3rd term).
1001
75% 0,01
105
12,5% 0,5
10075
50% 0,75
1000125
1% 0,125
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: classwork. ______________________________________________________________________________ WEEK 4 CORE CONCEPT Fractions: part of a whole Percentages RESOURCES Mental Maths Flipbook Base 10 blocks Number lines Counters, marbles Illustrated Examples Fraction wall Fraction circles Number rods Grade 6 text book INTEGRATION Technology, EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Find a fraction of the whole number. (6.1.8)
MATHEMATICAL VOCABULARY Whole number, numerator, denominator, equivalent forms, cancel, percentage mixed numbers
- 53 -
Activities o Find fractions of a whole number by doing it concretely first e.g. Number rods and base 10 blocks can also be used. Method 1: Step 1 : Use easy fractions: Do it practically e.g. Peter had 20 marbles and lost half of them. How many marbles does he have left? Divide the marbles in 2 groups: He lost 10 and has 10 left. Step 2:
Peter had 20 marbles and lost 51
of it. How many marbles does he have left?
Divide the marbles into 5 groups: He lost 4. Step 3:
Peter had 20 marbles and lost 53
of it. How many marbles does he have left?
Divide the marbles in 5 groups. Take away 3 groups – you are left with 2 groups which equals 8 marbles. He lost 12 and has 8 left. o Once learners can do the above activities concretely learners can do similar activities with
drawings (like the above ones instead of the concrete items. i.e. more the semi- abstract stage.
o The last stage would be when learners can do it abstractly i.e. just using the numbers and
symbols e.g.
- 54 -
Method 2:
=2052 of ?
Work out one part: 42051
=of (20 ÷5)=4
Now work out 2 parts: 8422052
== xof
Method 3
Or: 2483 of
= 3 x ( )2481 of
=3 x 3 =9 Method 4 In short:
=2483 of ?
24 ÷ 8 x 3= 9 - Examples. Find the following:
32
of 87 81
of 1000 52
of 570
LO and ASs Solve problems in context using equivalent fractions. (6.1.8).
Activities
o Examples.
- There are 820 learners at a school. 52
of the learners are absent. How many
learners are absent? (First try to estimate how many of them were absent. Was it less than half? More than a quarter?)
LO and ASs
Find percentage of whole numbers. (6.1.8).
Activities o Possible methods to use to find the percentage. Method 1: 20% of 50=?
- 55 -
Write the percentage as a fraction:
20% =51
102
10020
==
Find the fraction of the whole:
=5051 of
50 ÷ 5 x 1=10 Method 2: Try to do this on the calculator using the method above Can you find another method by using the calculator? Method 3: 24% of 2000
= 200010024 of
= 24 x )2000100
1( of (Work out one percentage and multiply it with 24)
= 24 x 20 = 480
o Examples.
- Mrs Kader earns R8 460 per month. At the end of the year, her boss gives her a 10% increase. What is her new salary?
- Calculate the following: 25% of R260 50% of 1kg
o Train learners to estimate the answer before starting a calculation and then reflect and discuss the method they used to solve the problem.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY More difficult problem-solving activities. ASSESSMENT Informal: classwork. _____________________________________________________________________________
- 56 -
WEEK 5 CORE CONCEPT Addition of fractions RESOURCES Mental Maths Flipbook Concrete material, e.g. counters Base 10 blocks Number lines Illustrated Examples, Fraction wall Number rods Grade 6 text book INTEGRATION Technology, EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Estimate, calculate and solve problems using addition and subtraction of common fractions with denominators which are multiples of each other and whole numbers with common fractions (mixed numbers. (6.1.8)
e.g. 86
82
21
=+
-mixed numbers
e.g. 833
412
811 =+
Activities (Number range: denominators 1 – 100)
o Revise counting backwards and forwards in fractions. This can be done mentally. e.g.
- Fill in the missing values: 4 3⅔ 3⅓ _____ _____ _____
- Fill in the next fractions
51
; 52
; ____ ; ____ ; ____ ; ____ ; ____ ; ____
7101
; 7 ; ____ ; ____ ; ____ ; ____ ; ____
41
; 21
; 43
; 1 ; ____ ; ____ ; ____ ; ____
o Revise addition - denominators the same.
Step 1: Do it practically with 2 fractions with the denominators the same. Make use of a fraction wall.
e.g. Peter eats 81
of a cake and his bigger brother eats 84
of it. How much did they eat
together?
MATHEMATICAL VOCABULARY Whole number, numerator denominator, equivalent forms, cancel, percentage mixed numbers
- 57 -
?84
81
=+
85
84
81
=+
NB (You do not count the denominators, only the numerators, when the denominators are the same)
Do this: 41
+ 42
+ 43
=
o Addition of fractions where the denominators are multiples of each other. Step 2:
Use two fractions where the denominators are multiples of each other.
?21
81
=+
e.g. Peter eats 81
of a cake and his bigger brother eats 21
of it. How much did they eat
together? Notice that this is the same as the previous one in step 1. Why? We made use of equivalent forms of fractions.
85
21
81
=+ (84
21= )
=85
84
81
=+
Always make the denominators the same You cannot add 2 fractions if the denominators are not the same. Always use the bigger one of the denominators as the new denominator. Do this without the fraction wall.
54
+ 102
=
107
+ 201
=
- Further examples. Calculate the following:
52
+ 103
32
+ 61
21
+ 43
o Addition of 3 fractions where the denominators are multiples of each other.
- 58 -
Step 3: Add 3 fractions:
e.g. At the Pizza-place John ate 31
of a pizza, Karel ate 21
and Andy ate 125
. How much did
they eat together?
125
21
31
++
=125
126
124
++ or 12
564 ++
=1215
=1231 (Write as a mixed number)
=411 cancelling (
41
123= )
- Further examples. Do the following:
124
+ 126
+ 122
=
21
+ 43
+83
=
o Add mixed numbers.
Step 4: Add 2 mixed numbers:
e.g. Kyle and Hennie had to run around a track. Kyle ran 212 laps before he got tired and
Hennie ran 413 before he stopped. How far did the two boys run together?
?413
212 =+
First count the 2 whole numbers: 2+ 3=5 and then the fractions.
=4
125 + or
41
4232 +++ (Make the denominators the same.)
=435
- Further examples. Calculate:
441
+ 1121
254
+ 1153
- 59 -
o Train learners to estimate the answer before starting a calculation and then reflect and discuss the method they used to solve the problem.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Use examples where the denominators are not multiples of each other.
ASSESSMENT Informal: classwork. ______________________________________________________________________________ WEEK 6 CORE CONCEPT Fractions: subtraction RESOURCES Mental Maths Flipbook Concrete material, e.g. number rods Base 10 blocks Number lines Fraction wall INTEGRATION IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Estimate, calculate and solve problems using subtraction of common fractions with denominators which are multiples of each other and whole numbers with common fractions (mixed numbers). (6.1.8)
e.g. 41
82
82
21
==−
-mixed numbers
e.g. 812
411
833 =−
Activities o Subtract fractions- (Number range: denominators 1 – 100). o Revise subtraction - denominators the same.
Step 1: Do it practically with 2 fractions and the denominators the same. Make use of a fraction wall or number rods or fraction circles.
e.g. Peter eats 81
of a cake and his bigger brother eats 84
of it. How much more did his
brother eat?
MATHEMATICAL VOCABULARY Whole number, place value Interval, even number, odd number, multiple
- 60 -
?81
84
=−
83
81
84
=−
NB (You do not count the denominators, only the numerators, when the denominators are the same).
- Further example. Do this
127
- 125
=
o Use two fractions where the denominators are multiples of each other.
Step 2: Two fractions where the denominators are multiples of each other.
?81
21
=−
e.g. Peter eats 81
of a cake and his bigger brother eats 21
of it. How much more did his
brother eat?
You will notice that this is the same as the previous one in step 1. Why? We made use of equivalent forms of fractions.
83
81
21
=− (84
21= )
=83
81
84
=−
Always make the denominators the same. You cannot add 2 fractions if the denominators are not the same. Always use the bigger one of the denominators as the new denominator.
- Further examples. Do this without the fraction wall.
54
- 102
=
107
- 201
=
- 61 -
Calculate the following:
43
- 83
=
5015
10057
−
o Subtract 2 mixed numbers.
Step 3: Subtract 2 mixed numbers.
e.g. Kyle had to run 921
times around a track. Kyle could only run 417 laps before he got
tired. How far must he still run to complete the race?
?417
219 =−
First subtract the 2 whole numbers: 9 - 7=2 and then the fractions.
=4
122 − or
41
422 − (Make the denominators the same.)
=412
o Subtract 2 mixed numbers.
Step 4 Subtract 2 mixed numbers but the second fraction is bigger than the first one.
?437
219 =−
First subtract the 2 whole numbers: 9 – 7 = 2 and then the fractions.
=4
322 − or
43
422 − (Make the denominators the same.)
=4
3241 −+ or 1 +
43
42
44
−+
=143
- Further examples. Calculate:
361
- 1125
7104
- 154
o Train learners to estimate the answer before starting a calculation and then reflect and
discuss the method they used to solve the problem. o Always let learners move from the concrete (use of number rods etc) to semi-abstract (use
of fraction wall and diagrams) to abstract (just the fractions and symbols- like in step 4)
- 62 -
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Use examples where the denominators are not multiples of each other. ASSESSMENT ASSESSMENT TASK 3: ACTIVITY 3.2 e.g. Tutorial on fractions. ______________________________________________________________________________ WEEK 7 CORE CONCEPT Data handling RESOURCES Mental Maths Flipbook Data Handling in the GET Band Statistics from websites and newspapers INTEGRATION Social Science, Natural Science IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Critically reads and interprets data presented in a variety of ways (including own representations, representations in the media – words, graphs, pie graphs) to draw conclusions and make predictions sensitive to the role of: context (e.g. rural or urban, national or provincial) • categories within the data (e.g. age, gender, race) • other human rights issues. (6.5.7)
Activities o Interpret data and graphs in media or other contexts (e.g. rural or urban, national or
provincial). Choose relevant and topical data.
o For example.
The results of a survey could be on the number of vehicles passing the school between 07h30 and 08h00 during one week in February and June . In terms of the results of the traffic volume survey, one can draw the learners’ attention to the possibility that while high traffic volume poses a problem to them in terms of road safety, learners in rural settings do not encounter problems with traffic in this sense. Their issue will rather be the lack of frequent vehicular traffic and the subsequent lack of transport. An ideal survey to run in a rural setting could be to find out the distances that learners have to travel to school, and what their mode of transport is. A purpose for this type of information gathering would be to motivate for funding for transport from the provincial education department or from local business.
MATHEMATICAL VOCABULARY Critically read, interpret, media, human rights issues, Interval, scale equally likely, equal chance, even chance, fifty-fifty , chance, biased, random, certain, impossible, not likely.
- 63 -
Double Bar Graph showing traffic volume during one week in February and one week in June.
(Drawing of double bar graphs is only in the 4th term, but the interpretation can be introduced in the 2nd term)
- Look at the graph. The traffic flow seems lighter in February than in June. Why do you think this is so?
- Look at newspaper reports supplemented with graphs on a regular basis and interrogate the data. Try to ascertain if the data has been used to anybody’s advantage.
o Interpret data relating to e.g. age, gender, race issues. e.g. We need to buy cooldrink for the school’s interclass netball competition. What were the
most popular flavours among the girls? o Critically interpret data relating to other human rights issues. e.g. The graph below shows how people from a township near Cape Town get their water.
How people get water
Walk > 100mWalk < 100mTap inside propertyTap inside house
Volume of Traffic
0
20
40
60
80
100
Mon Tues Wed Thur Fri
Days of the Week
No. o
f Veh
icle
s
FebJun
- 64 -
How do the most people get water? Why do you think so few people have taps inside their houses?
LO and ASs Predicts the likelihood of events in daily life based on observation, and places them on a scale from ‘impossible’ to ‘certain’. (6.5.8)
Activities o Rate predictions e.g.
- Rate the following events using: Certain (C) Possible (P) Impossible (I)
It will rain tomorrow. You will breath in air. You will speak to somebody this afternoon. Your teacher will praise you for your school work. You will flap your arms and fly home this afternoon. You will marry somebody in your class.
LO and ASs
Lists possible outcomes for simple experiments (including tossing a coin, rolling a die, and spinning a spinner) (6.5.9) Counts the frequency of actual outcomes for a series of trials (6.5.10)
Activities o Do simple experiments e.g.
- List possible outcomes for simple experiments (including tossing a coin, rolling a die, and spinning a spinner).
- Test the possible outcomes using one die. Decide on a limited number of throws. Be realistic, if one die has six faces, you will need to throw the die enough times to give each face ample chance to come up. Assume we settle for 42 or 60 throws. (Choose a sizeable multiple of 6, thus giving each number an equal amount of chances to come up.) Let one learner throw, and one record the number that comes up each time. Once the pre-decided number of (fair) throws is reached, stop recording and count the number of times each number has been thrown. Theoretically, each number has a one in six chance of being thrown (coming up). The learners can work out their own method to see which numbers were thrown the most in reality. Different groups can compare results. It is also important that groups run a second experiment using the same dice, same number of throws, and the same throwers/rollers. Results must be compared again, this time with the first round. - A similar experiment can be conducted tossing/flipping a coin.
o Learners must record the results of the above experiments. These results are compared to the predicted outcomes. For example, each of the sides of a die has the same chance of coming up as the next. Its chance is 1 in 6 of being thrown, but do the recorded results show this?
o Further experiments can be done after the tests/examinations have been written.
- 65 -
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Use, read and write, spelling correctly, the vocabulary from the previous year, and extend to: equally likely… equal chance, even chance, fifty-fifty chance… biased, random… Discuss events which might have two equally likely outcomes. For example: a new baby is equally likely to be a boy or a girl if I drop a picture postcard there is an even chance it will land picture side up if I roll a dice I am just as likely to roll an even number as an odd number… Discuss events with two or more equally likely outcomes. For example: Consider a 1 to 6 dice. What is the probability of: rolling a 4 rolling an even number rolling a number greater than 2 rolling zero rolling a number lying between 0 and 7? Place each probability on this scale. Discuss the difference between the theory of outcomes and the actual, experimental results. For example: Discuss outcomes when a coin is tossed. How many heads and how many tails might turn up if a coin is tossed 10 times, 20 times, 30 times...? Work in pairs and record results on squared paper. In 20 tosses, did heads and tails each come up 10 times? What happens when you combine your results with another pair? Discuss whether the results would be the same if the experiment were repeated. Test a hypothesis by drawing and discussing a bar chart where (discrete) data are grouped: for example, to check predictions of the most common number of: lengths that will be swum in a sponsored swim peas in a pod scores in a tables test… We think that most of the class will get more than 30 marks in the test. Discuss questions such as: What was the most common score in the test? How many children took the test? Estimate how many of them got fewer than half marks. Begin to interpret simple pie charts, such as those showing the data in a computer database. Answer questions such as: What fraction (percentage) of the population of Ham is 16 or under? 60 or over? Why do you think there are more people aged 16 or under than aged 60 or over living in Ham? ASSESSMENT Informal: classwork.
- 66 -
WEEK 8 REVISION ______________________________________________________________________________ WEEK 9 ASSESSMENT TASK 4: EXAMINATION ______________________________________________________________________________ WEEK 10 INTERVENTION + more probability experiments. ______________________________________________________________________________
- 67 -
TERM 3 WEEK 1 CORE CONCEPT Decimal Fractions Place value RESOURCES Illustrative Examples Textbooks Base 10 Blocks Blackboard and blank paper Fraction wall INTEGRATION Technology, EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognise and represent decimal fractions to at least 2 decimal places. (6.1.3) Count forwards and backwards in decimals. (6.1.1)
Activities o Oral exercises: Count forwards and backwards in decimals e.g.
- Count backwards (aloud) in ones from 25,5 to 5,5. Count forwards and backwards in tenths up to 1.
Count forwards from 1 to 2 in tenths. Count backwards from 2 to 1 in tenths.
- Fill in the missing values on the number line:
- Fill in the missing values: 4; 3⅔; 3⅓; _____; _____; _____;
LO and ASs Recognise the place value of digits in: decimal fractions to at least 2 decimal places. (6.1.4)
Activities o It is important that the teacher revise notation and place value tables. Learners must know that numbers in front of the comma are whole numbers and numbers after the comma are fractions. It is also important that learners know that the comma can also be a point like on the calculator. o Use diagrams and a fraction wall and read, say and write up to 2 decimals.
MATHEMATICAL VOCABULARY decimal places, decimal fractions, value, place value, positive decimals, notation
0 0,5 1,25
- 68 -
o Example
ONE WHOLE ONE
ONE HALF 0.5 Naught comma five / zero comma five.
ONE QUARTER 0,25 Naught comma two five / zero comma two five.
23,75 is read as twenty three comma seven-five.
0,05 is read as naught comma naught five / zero comma zero five.
o Convert from words to numbers and number to words e.g. two tenths =102
o Practice the use of notation (e.g. 101 = 0,1)
o Place value of decimals. - Use place value table- (t / h / th ) 975318642,345 (see work schedule)
HM TM M HTH
TTH TH H T U t h th
9 7 5 3 1 8 6 4 2 3 4 5 (The assessment standards says 2 decimal places but in measurement they will be exposed to 3 decimal places). - Distinguish between numeric value and place value.
o Solve problems in context. e.g. During the long jump event at an athletics meet, the girls jumped the following:
• Phumla: 4m • Alice: 3,95m • Joan: 4,02m • Khadija: 4,4m • Khwezi: 4,19m Who came first? Who came second? Who came third?
- 69 -
o What is the value of the 3 in each of the following numbers? You can also name the place value.
5,39 23,59 7,53
o Decimal fractions: Teacher Information The most common test is the question “Which number is bigger? “0.650 or 0.65”. Most learners will give the wrong answer “0,650 is greater than 0,65”. Surprisingly most will get this question right “Are these two numbers the same? 0345 and 345”. Why the zeros before the whole part and the zeros after the decimal part of a decimal number do not matter?
000000000000345,65000000000000000 Decimal numbers are written according to some rules. The decimal rules are also consistent with normal whole numbers. A decimal number can be thought of as two numbers put together. The first number is the whole part, and the other one is the decimal part. Therefore 3,45 is 3 plus with ,45 The leading zeros Let’s look at a normal whole number: 345
Hundreds Tens Units(ones)3 4 5
We can break the number up to see how the number 345 is constructed. The construction of the number 345 actually means: 3 of 100s + 4 of 10s + 5 of ones. Now imagine extending this number 345 to show some hidden numbers. These numbers have been taken away because they have no real value at all.
Thousands Hundreds Tens Units(ones)0 3 4 5
Similarly the construction of the number 0345 is: 0 of 1000s + 3 of 100s + 4 of 10s + 5 of ones.
We can see that 0 of 1000s means zero. So we do not count the number of 0s leading a number. The trailing zeros after the decimal part of a decimal number. Let’s look at this number 0,650.
Decimal comma Tenths/10th Hundredth/100th Thousandth/1000th , 6 5 0
- 70 -
The construction of this decimal part of a decimal number means:
6/10 + 5/100 + 0/1000 We can see that 0 out of 1000 is nothing. So we can ignore this 0. What it means is that 0,65 is the same as 0,650 Similarly 0,6500 is the same as 0,65 because it means:
6/10 + 5/100 + 0/1000 + 0/10000
o The concept of decimals is best taught through the context of measurement or money.
o Example
Hanna’s pencil is twelve and a half centimetres long.
We can write it as ________ mm.
We can also write it as12 21 cm.
It can be written as 12,5 cm.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Counts forwards and backwards in decimal intervals and in integers for any intervals. Work with decimals to at least three decimal places, fractions and percentages. Equivalent forms of common fractions, decimals and percentages. ASSESSMENT Informal: classwork. ______________________________________________________________________________
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 71 -
WEEK 2 CORE CONCEPT Equivalent forms of numbers
RESOURCES Illustrative Examples Textbooks Base 10 blocks Fraction wall INTEGRATION EMS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Decimal fractions: Recognise and use equivalent forms of decimal fractions to at least 2 decimal places. (6.1.5)
Convert from common fractions to decimals –equivalence. (e.g. 105
= 0,5)
Activities o Let learners investigate practically by using fraction walls etc. and find out that 2
1 = 0,5 =
50%. Lead them to the awareness that the first number is written as a common fraction, the second number is written as a decimal and the third one is written as a percentage but that they are also fractions, they are just recorded differently (different notation). So 0,5 means 10
5 , which is equal to a 21 and 50% means 50 out of 100, which is equal to
21 of the total.
Ask the learners to give practical examples where decimals and percentages are used in daily life.
o Activities must include the following: - Write fractions as decimals - Write decimals as fractions - Write decimals as percentages. e.g. - Use straight lines to match the fraction with the correct percentage and/or decimal
fraction:
100
1 75% 0,01
105 12,5% 0,5
10075
1% 0,125
1000125
50% 0,75
MATHEMATICAL VOCABULARY Notation, place value
tenth 101
hundredth 100
1
equivalent
- 72 -
- Write:
0,25 as a common fraction
83 as a decimal fraction
0,5 as a common fraction 54 as a decimal fraction
- Convert the following decimals to fractions in their simplest form.
0,6 0,04 0,5 0,025 e.g. 0,6 = 10
6 = 53
0,04 = 100
4 = 502 = 25
1
0,5 = 10
5 = 21
0,025 = 1000
25 = 2005 = 40
1
- Write the decimal fraction equivalent to:
two tenths five hundredths nine thousandths eight and seven thousandths ; sixteen and twenty-nine thousandths.
o Solve problems in context. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: classwork. ______________________________________________________________________________
- 73 -
WEEK 3 CORE CONCEPT Money Buying, selling, profit and loss Budgets RESOURCES Textbooks Illustrative examples Money games Examples of South African notes and coins Examples of money from other countries (optional) Base 10 blocks INTEGRATION Economic and Management Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Solves problems in context: financial (including buying and sellilng, profit and loss, simple budgets, reading and interpreting accounts and discounts. (6.1.6). Addition and subtraction of positive decimals with at least 2 decimal places. (6.1.8)
Activities o Revise the concept of money
- notation e.g. R34,69. - read, say and write money notation. - convert from money to words and words to money. - convert from cent to rand and inverse e.g. R3,25 = ___ 2 555c = ___ - exchange of coins for rand. - rounding down (5c and 10c).
o Addition and subtraction of positive decimals with at least 2 decimal places.(This will be
practised further through the context of money and measurement.)
- When adding decimal fractions, a strategy learners may use is to change the decimal to a common fraction. So 0,3 + 0,24 is 10
3 + 10024 is 100
30 + 10024 = 100
54
If there are whole numbers involved the learners simply add up as normal. e.g. 1,1 + 1,42 = 2 + 100
52 = 2 10052 = 2,52
Only start with the algorithm or adding up in columns when the learners understand the concept well. (If learners have grasped the concept of place value in decimals and can add whole numbers in columns, adding decimals should be easy!)
- Examples to be practised:
3,23 + 5, 62 26,57 + 37,78 1,35 + 0,46 0,382 + 0,003
13,23 - 5, 62 86,57 -37,78
467,02 – 389,8 Subtract in columns. Check answer with e.g. calculator.
MATHEMATICAL VOCABULARY Buying, selling, profit, loss, budget, discount, expenses, salary, expenditure, price, sell, income, bond.
- 74 -
Design written questions for number sentences involving decimals, for example: n + 2,56 = 5,38 9,1 + n + 4,8 = 15,6
o Solve problems in financial context buying and selling, profit and loss e.g.
- Mrs Zungu buys a melon for R3,45, and sells it for R5,50, how much money did she make for selling the melon? (This is called profit.)
How much profit can she make if she sells 67 melons? If she has to sell the 15 melons for R2,95 each. What would her loss be? Profit is the difference between the buying and selling price. This is when you gain money. Loss is also the difference between the buying and selling price, but this is when you lose money.
- A clothing shop sells items for the following prices: Jeans @ R120 T-shirts @ R40 Shoes @ R240 Jackets @ R490 If you had R1 000 to spend in the shop, draw up a list of the things you would buy. If the shop has a sale with a 10% discount on all the goods, what would the new selling prices be on each item? How much would you save if you bought the clothing on the sale instead? Draw up another list showing the extra items you can buy if you purchase clothing on the sale.
o Solve problems relating to simple budgets e.g. This is Mrs September’s budget for a month:
Monthly expenses Amount Monthly income Amount Living Expenses
Rent
Electricity
Telephone
Water
School fees
Groceries
Transport
Insurance
Craft market stall rental
R 1 400,00
R 200,00
R 325,00
R 60,00
R 83,00
R 497,00
R 210,00
R 324,00
R 300,00
Salary R 3 345,00
Entertainment expenses
Movies
Games
TV channel subscription
Restaurants
R 75,00
R50,00
R237,00
R 200,00
Rental (tenant) R 300,00
Personal expenses
Clothing
Toiletries
R 175,00
R 50,00
Craft market income (beadwork)
R 657,00
Total expenses for month Total income for the month
- 75 -
- What is the total of Mrs September’s expenses for the month? - What is her total income? - What are her monthly living expenses? - What is Mrs September doing to supplement her salary? - What is the balance at end of the month?
Balance is the difference between the total income and the total expenditure. NOTE: Allow learners to use their calculators during this exercise, as the focus is on understanding how the budget works.
- Every family should plan their budget (the way they spend their monthly income) carefully. It is a skill you develop over time.
Apollis family monthly expenses Bond R4 350,00 Electricity R720,00 Food R2 500,00 Clothes and other items R3 000,00
- Use the information above and solve these problems. - How much does the Apollis family pay on their bond in 12 months? - Approximately how much do they pay for electricity in 7 months? - What is their total monthly expenditure? - Approximately how much do they spend on food in a year? - What is the difference between their bond payment and their food expenses in a
month?
o Reading and interpreting accounts and discount. e.g. - Collect copies of different accounts e.g. water and electricity, rates, telephone, clothing
store accounts, furniture store accounts. Let learners work in groups answering set questions which assists them in interpreting the accounts. Include accounts where a discount is allowed for early payment of the account.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Financial: more difficult examples of accounts and discounts e.g. medical accounts. Measurements in Natural Sciences and Technology contexts. ASSESSMENT ASSESMENT TASK 5: ACTIVITY 5.1. e.g. Tutorial or investigation within the context of money and decimals. ______________________________________________________________________________
- 76 -
WEEK 4 CORE CONCEPT Ratio RESOURCES Textbooks Illustrative examples Calculator Base 10 blocks INTEGRATION Economic and Management Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Solves problems comparing two or more quantities of the same kind (ratio). (6.1.7)
Activities o Complete accounts and discounts from week 3 if more time is required. o Teach Ratio by referring to fractions. One way of comparing things is to write them down as a ratio. We usually write a ratio as simply as we can using the lowest whole numbers possible. In a hospital there are 5 very ill patients out of every 10 patients. The ratio of very ill patients to the total number of patients is 5 to 10. Written as 5:10. We may also write the ratio as a fraction. Very ill patients 5 Total number of patients 10 o Solve problems comparing two or more quantities of the same kind (ratio) e.g.
There are 1 295 spectators at a soccer match. There are four times as many adults as there are children. How many are children and how many are adults? Can you solve this problem? Work in a group and show how you worked out the answer.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Solve problems with ratio. Use more difficult numbers and examples. ______________________________________________________________________________
MATHEMATICAL VOCABULARY Problem solving, ratio rate, estimate, quantities
- 77 -
WEEK 5 CORE CONCEPT Rate Multiplication Division RESOURCES Textbooks Illustrative examples Calculator Base 10 Blocks INTEGRATION Economic and Management Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Solves problems comparing two quantities of different kinds (rate, e.g. wages/day). (6.1.8)
Activities o Rate can only be taught through a context e.g.
- John works in a hospital. He is paid at a rate of R54.00 per hour. How much does he
earn when he has worked for 4 hours? To find out, multiply R54,00 by 4. John will earn R276,00.
- A car travels at 120 km per hour. How far will it travel in
1 hour? 5 hours? 12,5 hours?
- Peter has a part-time job as a packer in a supermarket. He earns R 4,50 for one hour of work. If a working day is 8 hours, how much will he earn in a week?
- The rand – dollar exchange rate is quoted at R 3,67 to the dollar. How much in rands is the $35 your aunt in New York sent you? (This is expanded on in Grade 7.) o Train learners to do the following when problem-solving:
- Estimate answer by rounding off - Check answers with e.g. calculator - Reflect method used.
o Revise long multiplication (4-digit by 3-digit number) and division (4-digit by 3-digit number). Use columns.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving.
MATHEMATICAL VOCABULARY Compensate, revise building up, breaking down
- 78 -
EXTENDED ACTIVITY More difficult examples of problem-solving involving rate. ASSESSMENT ASSESSMENT TASK 5: ACTIVITY 5.2 e.g. Investigation on rate. _____________________________________________________________________________
WEEK 6 CORE CONCEPT Measurement Length Mass RESOURCES Textbooks Illustrative examples MST – kit Measuring instruments e.g. rulers, bathroom scales etc. INTEGRATION Natural Sciences Technology Human and Social Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for: Measurement: -Length using millimetres (mm), centimetres (cm), metres (m) and kilometres (km) (6.4.5). Use appropriate measuring instruments: using rulers, metre sticks, tape measures and trundle wheels to measure length. (6.4.7) Solve problems involving measurement in Natural Sciences and Technology contexts. (6.1.6)
Activities o It is important that learners explore length and use instruments to measure length.
- To measure a curved line or a round object, you can use a piece of string. - Show ways how measuring was done in the past. - Estimate length in learners’ experience. - Measure length using rulers, metre sticks, tape measures and trundle wheels. - Choose the appropriate SI unit mm, cm, m and km.
o Examples:
- Estimate the lengths of the following objects: your pen or pencil your Maths book/file your teacher (height) the school building.
- Write down your estimated lengths. - Now measure these objects using a tape measure.
What units did you use to measure each of the objects? Why? What unit would you use to measure the distance from your school to the city centre/the next town?
MATHEMATICAL VOCABULARY millimetre mm length centimetre cm metre m kilometre km gram g, mass, kilogram kg
- 79 -
Bring the learners’ attention to instances where distance is measured using the odometer of a car or taxi.
- Let the learners look at a map of South Africa. If the distance from Cape Town to
Knysna is about 500 km, what is the distance from: Johannesburg to Durban? Cape Town to Kimberley? Beaufort West to Bloemfontein? Cape Town to Beit Bridge?
(This activity can be integrated with Human and Social Sciences.)
- Do calculations using mm, cm, m and km ( +, -, x) 3,24m + 1,236m = _______m 3,54m – 0,7m = _______m
- Convert mm ↔ cm and m ↔ km (note the 3 decimal places) 140mm = _______m 7 002m = _______km 4,521m = _______mm 1,85km = _______m
- Choose a measuring instrument in B to measure each object, person or aspect in A:
LO and ASs Estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for: Measurement: - mass – using grams (g) and kilograms (kg ) (6.4.5). Use appropriate measuring instruments: using bathroom scales, kitchen scales and balances to measure mass (6.4.7). Solve problems involving measurement in Natural Sciences and Technology contexts. (6.1.6)
Activities o It is important that learners explore mass and use instruments to measure mass.
- Show ways how measuring was done in the past. - Estimate mass in learners’ experience. - Measure mass using bathroom scales, kitchen scales and balances. - Choose the appropriate SI unit g and kg.
o Examples - Allow the learners to lift an object of 500g or 1 kg in their hands. Let them guess the
mass of other objects, which can be heavier or lighter than the “benchmark” mass. (Learners need to have a point of reference when estimating). Again, record the class’s responses for later data handling lessons/activities. Measure the mass and let the learners see who was closest.
- Do calculations using g and kg. ( +, -)
2,04kg + 6,261kg = _______kg 4,3kg – 1,186kg = _______kg
A B Distance around a netball field A measuring jug 1 kg of sand Stop watch Time Odometer An athlete running Measuring tape The amount of water in a jug Scale (mass meter) The distance from one town to another Watch or clock Temperature Thermometer
- 80 -
- Convert g ↔ kg
1 250g = _______kg 4,698kg = _______g 1,462kg = _______g 2847g = _______kg
- Use bathroom scales, kitchen scales and balances to measure mass after estimating e.g.
Allow learners to estimate each other’s mass, then allow them to measure their mass on a bathroom scale. Learners may be sensitive to their mass so use a suitcase or any other every day object. Allow them to measure relatively light objects on a bathroom scale so that they can see how inappropriate it is. Measure the mass of objects and substances of different sizes and densities. Let the learners observe if there is a correlation between size and mass. o Whilst measuring and calculating make learners convert between decimal and common
fractions e.g. 21
kg = 500g = 0.5kg, 5.5 kg = 5500g = 521
kg
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: classwork. ______________________________________________________________________________ WEEK 7 CORE CONCEPT Measurement - Capacity Temperature RESOURCES Textbooks Illustrative examples MST – kit Measuring instruments e.g. thermometers, measuring jugs INTEGRATION) Natural Sciences Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
MATHEMATICAL VOCABULARY Measure, capacity, temperature, volume, convert, SI unit
- 81 -
LO and ASs Estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for: capacity – using millilitres (ml) and litres (l) (6.4.5). Use appropriate measuring instruments: using measuring jugs (6.4.7). Solve problems involving measurement in Natural Sciences and Technology contexts. (6.1.6)
Activities o It is important that learners explore capacity and use instruments to measure capacity.
- Show ways how measuring was done in the past. - Estimate capacity in learners’ experience. - Measure capacity using measuring jugs. - Choose the appropriate SI unit (ml) and (l).
o Examples - Display these items in front of the classroom: a litre bottle, a 250ml container, a
500ml container and a 2 litre bottle. Arrange them from smallest to the largest. Inform learners that they will explore capacity and use instruments to measure it.
- How much water will a kettle hold? 20 litres 2 litres 500 ml
- How many cups of juice can you pour from a 5-litre container? Estimate your answer. Now find out by measuring.
How much water/cooldrink does one cup normally hold?
- Do calculations using ml and l ( +, -) 2,899l + 1500 ml = _______l 3 150ml – 1,024l = _______l
- Convert ml ↔ l 1 300ml = _______l 95ml = _______l 5,007l = _______ml 4,750l = _______ml
- Solve problems involving measurement in Natural Sciences and Technology contexts.
Choose the item that best matches each capacity measure below: Draw lines to match. Soda bottle 5ml Cup 1l Teaspoon 340ml Cool drink can 250ml
- Look at the beaker below and answer the questions.
How much water (in ml) is in this beaker?
How much water can the beaker hold?
How much more water can be added to the beaker?
- 82 -
How many of these beakers would you need to fill a 1,5-litre cooldrink bottle?
- 250 ml of energy concentrate makes 1 litre of energy drink. How much concentrate do I need to make 1,5 litres of energy drink? How much concentrate do I need to make 5 litres of energy drink?
LO and ASs Estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for: temperature using degree Celsius scale (6.4.5). Use appropriate measuring instruments: using thermometers (6.4.7). Solve problems involving measurement in Natural Sciences and Technology contexts. (6.1.6)
Activities o This unit of measurement, like all others, is best introduced in a practical manner. Pictures
and drawings will not bring across the concept effectively enough. - Using a normal thermometer, allow the learners to check their body temperatures
(please ensure hygienic practice) by placing the thermometer under their tongues, or under their armpits. If any learner in the class is ill, use the opportunity to compare this learner’s temperature with the temperatures of the others in the class. Let the learner explain how he/she feels.
o Examples. - Estimate temperature in learners’ experience.
Inform the learners that they will investigate daily temperatures in order to compare them. Ask the learners to estimate the temperature of today. Ask the learners whether they consider today as hot, warm, cool or cold. Demonstrate how to use the thermometer to measure the temperature. Place the thermometer outside the class and ask a learner to read the temperature for the day. Record the temperature on the board. Learners can complete the chart.
Estimated temperature (degrees Celsius)
Measured temperature (degrees Celsius)
Difference between estimated and measured temperatures
Tap water Add hot water Add cold water Add hot water Add hot water Add cold water Add cold water Add hot water
25 ml
- 83 -
- Choose the appropriate SI unit degree Celsius.
Choose the appropriate temperatures from the list below to complete the statements. 0°C 4°C 180°C 6000°C -60°C 12°C 34°C 4000°C 37°C -20°C 100°C 40°C
1. My body temperature when I am fit and healthy is _______
2. My body temperature when I am feeling ill and have a fever is _______
3. The temperature when water freeze _______
4. The temperature when water boils is _______
5. The temperature on a hot day in summer in SA _______
6. The temperature on a cold day in winter in SA _______
7. The temperature in a fridge _______
8. The temperature in a freezer _______
9. The temperature at the South Pole _______
o Solve problems involving measurement in Natural Sciences and Technology contexts. Integrate with these learning areas as far as possible.
- Make reference to the daily temperatures as predicted in the weather forecasts.
Ask questions such as: What temperatures do you consider to be hot weather? What is just right / comfortable? When would you need to wear a jersey? Is 10°C cold or warm? Ask learners to estimate the temperature outside. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY Extend investigations to more unusual contexts. ASSESSMENT Informal: classwork. ______________________________________________________________________________
- 84 -
WEEK 8 CORE CONCEPT Measurement Perimeter
RESOURCES Textbooks Illustrative examples MST - kit String Metre ruler, tape measure INTEGRATION Natural Sciences Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Investigates and approximates (alone and/or as a member of a group or team): • perimeter using rulers or measuring tapes. (6.4.8)
Activities o Practically investigate Perimeter.
- Estimate distance around e.g. book, desk, class, etc. - Explore by using body e.g. hand, fingers, etc.(This can be left out if they did it in
Grade 4or 5). - Explore length outside e.g. walk, steps, run, etc. - Explore by using a piece of string for irregular shapes. - Select and use appropriate measuring instrument and SI unit.
o Use rulers, measuring tapes to find perimeters (approximate).
- Draw round the edge of a rectangle with your pencil. - How far did your pencil travel? Measure the distance. - Estimate then measure the perimeter of the classroom… the top of your desk… a piece of A4 paper… a regular hexagon…
o Allow the learners to participate in an activity that lets them experience distance in terms of perimeter. e.g. Walk or run around the edge of the playground. End up where you started from. How far did you walk/run? How many steps/paces did you take? How long is each step/pace? Measure the distance using a measuring tape or trundle wheel.
o Develop methods to determine perimeter of different shapes.
- How long is the perimeter of: a 5 cm by 5 cm square... a 4 cm by 7 cm rectangle. a triangle whose sides are 10 m, 20 m, and 24 m?
- The perimeter of a square is 28 cm. What is the length of one side? Draw two rectangles with the same perimeter as the square. Draw different rectangles with a perimeter of 24 cm. Which has the largest area?
Find a short way to work out the perimeter of a rectangle.
MATHEMATICAL VOCABULARY Perimeter, distance, shapes, squares, rectangles, formula
- 85 -
o Investigate and approximate (alone and/or as a member of a group or team): perimeter using rulers or measuring tapes. From this investigation, develop the formulae for perimeters of squares and rectangles (do not use formula) Initially, it is important not to stress the finding the perimeter of rectangles and squares explicitly (so as to hurriedly arrive at the formula). It is a good idea to start off by letting the learners experience the perimeters of more irregular shapes.
What is the distance around the edge of these shapes?
Hint: You can use a piece of string and a ruler.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY ASSESSMENT Informal: classwork. __________________________________________________________________________
- 86 -
WEEK 9 CORE CONCEPT Area RESOURCES Text books Illustrative examples MST kit: shapes 1 cm Square grid paper 2 cm Square grid paper Scissors String, tracing paper INTEGRATION Technology, Natural Science IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES REVISION Rounding off to the nearest: 10, 100, and 1000.
LO and ASs Practically investigate: Area: (SI units-mm², cm², m², km²) of polygons (using square grids) to develop rules for calculating area of squares and rectangles. (6.4.8) Select and use appropriate measuring instrument and SI unit. (6.4.7)
Activities o Use the following method to investigate area:
- Use cut out squares (hint: 3cm x 3cm squares to tile an area, e.g. text book, desk, table, etc.
- Use the squares to build any shapes - Pack out the same shape on grid paper (1cm x1cm) and draw the outline - Count number of covered squares on grid paper - Colour in given drawings on grid paper - Determine area of different polygons on grid paper (include half blocks).
o Practically investigate area. - Use cut-out squares (e.g. 3cm x3cm) to tile an area of a shape e.g. textbook or any
other square or rectangular shapes. - Find out which of two or more things has the greatest area by covering with, say, 5-cent
coin, cubes, postcards, sheets of A4 paper, sheets of newspaper. Then count the number of 5-cent coins etc. which are required to cover the shape. e.g. Find out which of two greetings cards has the greatest area by tracing on centimetre squared paper or by covering with a transparent centimetre grid.
- Count the number of covered squares on the grid paper. - After a number of examples have been done get learners to explain a rule for working
out area of squares and rectangles. (Do not use the formulae for calculations.)
o Examples: - Area of polygons (using square grids and tiling) in order to develop an understanding of
square units.
MATHEMATICAL VOCABULARY Investigate, covers, surface, square, square millimetre square centimetre square metre
- 87 -
How many squares do each of these shapes cover?
LO and ASs Investigate relationships between the perimeter and area of rectangles and squares. (6.4.10)
Activities o Use the following method to investigate the relationship between perimeter and area in a
number of square and rectangular shapes: - Colour in given drawings on grid paper - Measure the outline of the shape (perimeter) - Compare perimeter and coloured squares - Determine this relationship for different squares and rectangles on grid paper (include
half blocks) - Compare perimeter and area of different squares and rectangles.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 3 examples every day for homework. Two involving calculations and one involving problem-solving. Revise measurement and conversions in the homework. ASSESSMENT ASSESSMENT TASK 6: Test on decimals and measurement including the practical work. ______________________________________________________________________________
- 88 -
WEEK 10 CORE CONCEPT Volume / capacity RESOURCES Text books Illustrative examples MST kit 3D items e.g. containers Geostrips INTEGRATION Technology, NS IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Practically investigate: Volume: (SI units-mm³, cm³, m³). (6.4.8) Select and use appropriate measuring instrument and SI unit. (6.4.7) Solves problems involving selecting, calculating with and converting between appropriate S.I. units listed above and integrating appropriate contexts for Technology and Natural Sciences. (6.4.6)
Activities o Use the following method to investigate the volume of rectangular prisms:
- Pack and fill a number of 3-D objects with cubes i.e. volume - Count the number of cubes - Fill small containers with cubes - Count the number of squares on each surface area/ side - Explain a rule to calculate volume.
o Example
- Packing and filling of 3-D objects (solids) to find volume in cubic units.
- How many cubes are there in this stack?
MATHEMATICAL VOCABULARY Volume, pack, fill, cubes, tower, block, container, 3-D objects cubes, surface area/side, squares, stack
- 89 -
- How did you work this out?
- Compare your method with a friend/another group. How did they work theirs out?
o It is a good idea to let learners estimate the number of cubes before getting them to count
the number of cubes in a 3-D object e.g. - Estimate number of cubes from a given diagram (Tower block) or - Estimate number of cubes to fill a container - Fill small containers with cubes - Count the number of cubes - Compare the estimated amount with the counted amount.
How many cubes are there in this stack?
How did you work this out?
Compare your method with a friend/another group. How did they work theirs out?
LO and ASs Investigates relationships between surface area, volume and the dimensions of
rectangular prisms. (6.4.11). This assessment standard can be clustered with 6.4.8.
Activities o Use the following method to investigate the relationship between surface area, volume and
the dimensions of rectangular prisms: - Pack a cube containing smaller cubes - Calculate the area of the top side - Calculate the total area of all the sides of the cube - Calculate the total cubes used in the object - Compare the surface area and volume.
o Example
- 90 -
- What is the area of the front face? - How did you work it out? - Did you have to count all, or did you find a shorter method? - What is the total surface area of this stack? - How did you work it out? - You could not have counted all, what was your method? - How many cubes make up this stack? - How did you work it out? - You could not have counted all, what was your method?
- Look at this picture:
- If you could only see this much, how would you work out: - The surface area of the front face - The total surface area of the stack - The number of cubes that make up the stack (volume) - Can you make up a formula to work out the volume of the stack?
o Revise capacity. The volume of a liquid is measured in millilitres (ml) and litres (l). Through Technology and Natural Science make learners aware of the different SI units for volume of a solid and volume of a liquid (capacity). EXTENDED ACTIVITY Through investigation discover if there is a relationship between the SI units for solids and liquids. CONSOLIDATION Classwork; A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 3 examples every day for homework. Two involving calculations and one involving problem-solving. Revise the basic 4 operations. ASSESSMENT Informal: Observation and mark classwork. ______________________________________________________________________________
- 91 -
TERM 4 WEEK 1 CORE CONCEPT Angles RESOURCES Textbooks Illustrative examples Maths kit INTEGRATION Natural Sciences and Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Recognises and describes angles in two-dimensional shapes, three-dimensional objects and the environment in terms of: right angles; angles smaller than right angles; angles greater than right angles.
Activities o Refer to the Grade 5 Teacher’s Guide for practical activities if learners do not know what
right angles are. o Recognise and describe right angles (90o) in and outside class e.g.
- There are plenty of examples of right angles in the environment, especially in the classroom.
Look at: the angle at the corners of the chalkboard, the door, the window, the cupboard, etc.
o Recognise and describe right angles (90o) in polygons (2D) e.g. rectangles and polyhedra
(3D). Use concrete objects and revise properties of the 3-D objects. o Recognise and describe angles less than 90o in and outside class.
Angles smaller than right angles
MATHEMATICAL VOCABULARY Angle, right angle tetrahedron, pyramid parallelogram rectangle
- 92 -
o Recognise and describe angles less than 90o in polygons (2D) e.g. parallelograms and polyhedra (3D). Use concrete objects.
o Recognise and describe angles greater than 90o in and outside class. Angles greater than right angles.
Can you see that the angles in this stop sign are all bigger than right angles?
Recognise and describe angles greater than 90o in polygons e.g. trapeziums (2D) or polyhedra (3D). Do concretely and practically.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise fractions. EXTENDED ACTIVITY Classifies angles into acute, right, obtuse, straight, reflex or revolution. ASSESSMENT ASSESSMENT TASK 7: ACTIVITY 7.1 e.g Investigation on angles _____________________________________________________________________________ WEEK 2 CORE CONCEPT Space and shape Practical exploration RESOURCES Textbooks Illustrative examples Maths kit INTEGRATION Technology
MATHEMATICAL VOCABULARY space shape symmetry asymmetrical rotation reflection translation triangle quadrilateral
- 93 -
IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Uses the vocabulary and properties of rotations, reflections and translations to describe the relationships between distinct two-dimensional shapes and three-dimensional objects within patterns (including transformations and symmetry). (6.3.4)
Activities o Revise lines of symmetry in 2-D shapes. (Grade 5 teacher’s Guide.)
o Distinguish between symmetry and asymmetrical. (Grade 5 teacher’s Guide.)
o Rotate, slide and flip different shapes to make patterns. Use pattern shapes to do this concretely at first. i.e. rotation, translation and reflection.
- Make a pattern with this shape by sliding it, then tracing it:
Now make a pattern by flipping this shape.
Now make a pattern by rotating this shape. What do you notice? Is there any difference? Why not? Draw in the line/s of symmetry of this triangle. (An equilateral triangle will make the same pattern when slid, rotated or flipped.
Which other shapes share this property?)
o Do the same with diagrams and interpret from diagrams how a pattern was made e.g.
- Describe what is happening to the shape to make this pattern.
(flip, slide, flip, rotate, flip, rotate, flip, slide, flip )
LO and ASs Recognizes and describes shapes, objects, patterns with geometric properties in:-Nature and culture. (6.3.6)
Activities
o Let learners look at pictures or the real objects to identify shapes and patterns in nature and culture. e.g.
- Mother Nature relies on geometrical patterns and properties more than we realise.
Look at the following patterns:
- 94 -
Can you identify any geometric patterns in these pictures?
- Often people have copied this into their writings and artwork:
Can you identify any geometric patterns in these pictures?
LO and ASs Draws enlargements and reductions of two-dimensional shapes (at least quadrilaterals and triangles) using grid paper to compare their size and shape. (6.3.5)
Activities o Practical exploration:
- Let learners explore concretely enlargements and reductions using base 10 blocks. - Draw enlargements and reductions of 2-D (at least quadrilaterals and triangles) shapes
using grid paper. - Compare their size and shape
o Example.
- Is B an enlargement of A? Give reasons for your answer.
This example can be integrated with the Natural Science and Technology learning areas.
A
B
- 95 -
- Draw a reduction of triangle C.
- Allow the learners to look at photographs of the earth taken from satellites, as well as
vertical and oblique aerial photographs. (Integrate this with Natural Sciences and Human and Social Sciences – Geography.)
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise the basic 4 operations. EXTENDED ACTIVITY Give more difficult shapes to reduce and enlarge. ASSESSMENT Informal assessment of classwork. ______________________________________________________________________________
WEEK 3 CORE CONCEPT Orientation Location of position RESOURCES Grade 6 textbooks Illustrative examples Maths kit INTEGRATION Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
MATHEMATICAL VOCABULARY Sketches, position, view, perspective, angle, plot
C
- 96 -
LO and ASs Describes and sketches views of a simple three-dimensional object from different positions. (6.3.7)
Activities o Look at an object from different angles/ view (left, front, right and top view). Describe orally and in writing, changes in the view. Sketch the views. o Examples
Look at this stack of blocks:
Draw how it will look from the Right. How will it look from the Back? How will it look from the Top?
- Match the drawing to the child who drew it.
Front
Right Left
Andrew
Vuvu
Lundi
Drawn by: ……………….... Drawn by: ………………....
Drawn by: ………………....
- 97 -
o Give learners enough practice in drawing concrete objects from different positions. A good idea is to build shapes using different coloured cubes on the different sides. This assists learners in seeing the different layers and aids perception. (Learners who did not attend a pre-primary class will probably require considerable practice in using concrete objects before being able to recognize the object’s perspective from a diagram.)
LO and ASs Locates position on a coded (labelled) grid including maps and describes how to move between positions on the grid and recognizes maps as grids.(6.3.8)
Activities
o The following must be covered: - Locate position using verbal and written instructions - Locate and plot on a position on a coded (labeled) grid - Move between positions on a coded grid - Describe how to move between positions on a coded grid - Locate points/ positions using maps to trace a path between positions on a map.
o Examples - Farmer Brown walks across a field to check his crops. He stops often to take a rest. He starts at D1 and rests at the following places: H3 E4 F6 J7 G8 D9 A10 F12
Mark off his resting points on the grid, and then join the points to track his route.
1 2 3 4 5 6 7 8 9 10 11 12
A
B
C
D
E
F
G
H
I
J
K
L
- 98 -
o A person starts from the square marked X and proceeds (excluding the square marked X) 3 blocks North 4 blocks West 7 blocks North 5 blocks East 5 blocks South 4 blocks East 3 blocks South 2 blocks West Mark off his end position with an X
- Learners can plot their own routes along waypoints. - They can decorate their grids to the point of becoming maps.
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise numeric patterns. EXTENDED ACTIVITY Locates positions on co-ordinate systems (ordered grids) and maps using: -horizontal and vertical change -compass directions
N
S
W E
- 99 -
ASSESSMENT Informal: observation. __________________________________________________________________________ WEEK 4 CORE CONCEPT Data Handling (Handle as an assessment task – project) Pose questions Collect data RESOURCES Textbooks Illustrative examples Data Handling in the GET Band INTEGRATION Social Sciences, Natural Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Poses simple questions and identifies appropriate data sources. (6.5.1)
Activities o Data Handling (Handle as an assessment task – project)
o Follow the following steps to collect data: - Identify a problem to be investigated - Compare different sets of data (ages boys and girls) - Teach learners to set questions to obtain required data - Set questions in the form of a questionnaire - Use different sources.
o Example.
NOTE: Teachers can use the issues, categories and contexts mentioned in 6.5.7.
It is a good idea to ask questions which will be useful in real life when posing/asking a question as a basis for data gathering. This should give a real purpose/reason for gathering the data, e.g. using the information to plan the end-of-term class party, or to motivate the building of a footbridge across a busy road. Try to avoid asking questions for the sake of gathering useless/unrealistic information or data.
- Ask questions that could help in catering for a class party: “What are the popular take-away foods in the class?”
A survey could also be held at the school to find out how many learners don’t eat breakfast in the morning or bring lunch to school. This survey could be structured in such a way that the sample group stays anonymous. The results could indicate the need for a feeding scheme and the data collected could accompany a letter of motivation to the education department, or charity organisations.
The most important thing to remember is whether the data is realistically collectable, and whether the information will be useful.
MATHEMATICAL VOCABULARY Investigate, compare data, questionnaire, population, tallies tables, sample
- 100 -
LO and ASs Uses simple data collection sheets (requiring tallies) and simple questionnaires (with yes/no type responses) in order to collect data (alone and/or as a member of a group or team) to answer questions posed by the teacher, class and self (6.5.2)
Activities o It is best to allow the learners to develop their own questionnaires. These may not work
effectively at first, but learners should be allowed to develop these in such a way that the information can be gathered and easily organised.
o Example of a simple collection sheet.
Grade: _______________________________Age: ___________
Do you have: Yes No
Breakfast in the morning?
Lunch in the afternoon?
Supper at night?
LO and ASs Distinguishes between samples and populations. (6.5.3)
Activities o Distinguishes between samples and populations.
- If you wanted to run the above survey at your school of 850 learners, it would be too expensive to print a questionnaire for every child, and handing out and collecting the information would take too long. All the school children would be your target population. You need to make a random selection of the children from each grade or class (draw names out of a hat?) so that you get a representative sample of the school population. If the target population is 850 children, then a fair (representative) sample could be about 50 to 150 learners.
- I wish to find out what the popular takeaway foods in my class are. What is my target population? All the children in the school? All the children in my grade? All the children in my class? All the girls in my class? All the boys in my class?
- I wish to find out what the most popular cooldrink at the school is. Which of the following is a representative sample? All the boys in the soccer team? All the grade 7s? 5 learners selected randomly from a class? Every tenth child I meet in the playground during second break?
LO and ASs Organises and records data using tallies and tables. (6.5.4)
- 101 -
Activities o Try to let the learners design their own table to organise their data. If they do not use
tallies and tables to do this, consider their methods.
o Example. Table of the popular flavours at Khulani Primary CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. Revise rate and ratio. EXTENDED ACTIVITY Let learners develop different questionnaires and collect data. Collect data from the internet. ASSESSMENT Start of ASSESSMENT TASK 7: ACTIVITY 7.2. Project ______________________________________________________________________________ WEEK 5 CORE CONCEPT Data Handling Group data Draw graphs RESOURCES Textbooks Illustrative examples INTEGRATION Social Sciences, Economic and Management Sciences IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
Type of Cooldrink No. of children who like the flavour
No.
Cola | | | | | | | | | | | | 14
Orange | | | | | | 7
Crème Soda | 1
Granadilla | | 2
Pineapple | | 2
Lemon | | | | | | | | 9
- 102 -
LO and ASs Examines ungrouped numerical data to determine the most frequently occurring score (mode) and the midpoint (median) of the data set in order to describe central tendencies. (6.5.5)
Activities o Learners need to know which central tendency mode or median will best be able to answer
the question posed.
o The learners must be able to organise raw data themselves, thereby developing an understanding of the need to do (organise) this. Presenting learners with problem scenarios in the form of ungrouped or raw data also forces them to develop their own methods of grouping and organising. This should result in them making their own authentic sense of methods of organising data. Learners must be able to interact with the data they have collected. They must be allowed to develop the various levels of data organisation/grouping. Some learners may be at the level where they will recognise that they need an organised method of gathering the data as in 6.5.2 or even 6.5.4 (tally tables). The process of organising the set of data for the popular cooldrink flavours immediately informs us of the mode (most popular flavour). The mode is very useful in this context, as the data will inform us of the quantities of flavours to buy. The most popular drink is evident upon organising the data. Finding the median (the midpoint of the data) for this set of data will probably not serve much of a purpose. (What can you do with this information?)
LO and ASs Draws a variety of graphs by hand/technology to display and interpret data (grouped and ungrouped) including: pictographs with a many-to one correspondence and appropriate keys and bar and double bar graphs. (6.5.6)
Activities o By Grade 6 learners should be able to draw pictographs, so just revise and give an
example for homework e.g. Graph showing the number of vehicles passing our school between 07h30 and 08h00 during one week.
= 10 vehicles
Monday Tuesday Wednesday Thursday Friday
- 103 -
o Give learners practice in drawing bar graphs. e.g. Bar Graph showing the number of vehicles passing the school during one week between 07h30 and 08h00
This graph may be drawn on grid paper or on graph paper. Some learners may be familiar with Microsoft Excel.
This graph may be drawn on grid paper or on graph paper. Some learners may be familiar with Microsoft Excel.
o Teach learners how to draw double bar graphs.
Double Bar Graph showing traffic volume during one week in February and one week in June
0
10
20
30
40
50
60
70
80
90
100
Mon Tue Wed Thur Fri
No.
of V
ehic
les
Days of the week
Volume of vehicular traffic during one
Volume of Traffic
0
20
40
60
80
100
Mon Tues Wed Thur Fri
Days of the Week
No. o
f Veh
icle
s
FebJun
- 104 -
o Discuss which graph suits what type of data. o Use examples from ‘ Data Handling in the GET Band.’
CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING: A minimum of 4 examples per day for homework. Two involving calculations and two involving problem- solving. EXTENDED ACTIVITY
o Consider this table: (Mean is included in Grade 7) Table showing Group Two’s assessment rating for the Cooldrink Project
- What was the mean for this group? 5 + 9 + 6 + 3 + 7 + 2 = 32 32 ÷ 6 = 5,3 The average rating (or mean) is 5,3
Who has been rated above the mean? Who has been rated below the mean? In this case the mean is quite useful, giving learners a point of reference with regard to their achievements. ASSESSMENT Continue with ASSESSMENT TASK 7: ACTIVITY 7.2. Project _________________________________________________________________________ WEEK 6 CORE CONCEPT Data handling Interpretation of data RESOURCES Grade 6 textbooks Illustrative examples Data Handling in the GET Band
Name Final Rating (1 -10)
Carol 5
Lundi 9
Khaashief 6
Edna 3
Nomvuyo 7
Sarie 2
- 105 -
INTEGRATION Social Sciences Natural Sciences Economic and Management Sciences Technology IDEAS OF METHODOLOGY & ACTIVITIES WITH EXAMPLES
LO and ASs Critically reads and interprets data presented in a variety of ways (including own representations, representations in the media – words, graphs, pie graphs) to draw conclusions and make predictions sensitive to the role of: context (e.g. rural or urban, national or provincial); categories within the data (e.g. age, gender, race); other human rights issues. (6.5.7) NOTE: Teachers can use these issues, categories and contexts for activities as in 6.5.1 and 6.5.2.
Activities o Learners must get practice in the following:
- Read and interpret data presented in own graphs - Interpret data to answer questions - Draw conclusions - Make predictions.
o Consider the context (e.g. rural or urban, national or provincial) and the example from week 5 of the traffic volume survey.
- In terms of the results of the traffic volume survey, one can draw the learners’
attention to the possibility that while high traffic volume poses a problem to them in terms of road safety, learners in rural settings do not encounter problems with traffic in this sense. Their issue will rather be the lack of frequent vehicular traffic and the subsequent lack of transport. An ideal survey to run in a rural setting could be to find out the distances that learners have to travel to school, and what their mode of transport is. A purpose for this type of information gathering would be to motivate for funding for transport from the provincial education department or from local business. Look at the graph in Week 5. The traffic flow seems lighter in February than in June. Why do you think this is so? Look at newspaper reports supplemented with graphs on a regular basis and interrogate the data. Try to ascertain if the data has been used to anybody’s advantage.
o Consider the context (e.g. age, gender, race) e.g. - We need to buy cooldrink for the school’s interclass netball competition. What were
the most popular flavours among the girls? Refer to data from Week 4. This activity will necessitate the “sifting” of information from the previously gathered data.
o Consider the context other human rights issues e.g. The graph below shows how people from a township near Cape Town get their water.
- 106 -
- How do most people get water? - How do most people get water? - Why do you think so few people have taps inside their houses?
o Choose data that is topical and of interest to the learners. CONSOLIDATION Classwork: A number of examples need to be practised daily by learners before they can grasp the concept. Use approved maths software to consolidate the concept. HOMEWORK/REFLECTION ON LEARNING Draw and interpret graphs. EXTENDED ACTIVITY ASSESSMENT Complete ASSESSMENT TASK 7: ACTIVITY 7.2. Project ______________________________________________________________________________ WEEK 7 REVISION AND CONSOLIDATION ______________________________________________________________________________ WEEK 8 AND WEEK 9 ASSESSMENT TASK 8: EXAMINATION _____________________________________________________________________________ WEEK 10 ADMINISTRATION _____________________________________________________________________________
How people get water
Walk > 100mWalk < 100mTap inside propertyTap inside house
i
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
2Cal
cula
te
Gra
des
R-7
M
athe
mat
ics
Eng
lish,
bu
t inp
ut
any
lang
uage
Pro
blem
sol
ving
, ca
lcul
atin
g, lo
gica
l &
crit
ical
thin
king
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
te-
boar
ds
Win
dow
s 2S
impl
e SA
A
n ou
tsta
ndin
g su
ite o
f sof
twar
e to
ols
for
foun
datio
n ph
ase
and
olde
r lea
rner
s, a
s w
ell a
s a
teac
her t
oolk
it fo
r cre
atin
g a
rang
e of
pr
ogra
ms
to m
ake
teac
hing
& le
arni
ng e
xciti
ng
& im
part
esse
ntia
l con
cept
s &
thin
king
ski
lls.
This
is a
spr
eads
heet
pro
gram
with
the
sam
e po
wer
as
a sp
read
shee
t with
out t
he
com
plex
ities
of s
prea
dshe
et fo
rmul
ae.
2Dra
w
Gra
des
1-7
Tech
nolo
gy,
Mat
hem
atic
s E
nglis
h,
but i
nput
an
y la
ngua
ge
Pro
blem
sol
ving
, ca
lcul
atin
g, c
reat
ive
thin
king
, writ
ing,
gr
aphi
cs, l
ogic
al &
cr
itica
l thi
nkin
g,
teac
her i
nput
tool
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
te-
boar
ds
Win
dow
s 2S
impl
e SA
A
n ou
tsta
ndin
g su
ite o
f sof
twar
e to
ols
for
foun
datio
n ph
ase
and
olde
r lea
rner
s, a
s w
ell a
s a
teac
her t
oolk
it fo
r cre
atin
g a
rang
e of
pr
ogra
ms
to m
ake
teac
hing
& le
arni
ng e
xciti
ng
& im
part
esse
ntia
l con
cept
s &
thin
king
ski
lls.
This
is a
sim
ple
draw
ing
prog
ram
to c
reat
e sc
alab
le v
ecto
r sha
pes
whi
ch c
an b
e en
larg
ed,
redu
ced,
rota
ted
& g
roup
ed.
It ca
n be
use
d fo
r gr
aphi
cal p
lann
ing,
dia
gram
s, m
aps,
gra
phs,
cl
ip-a
rt, il
lust
ratio
ns &
logo
s.
2Inv
estig
ate
Gra
des
R-7
A
ll le
arni
ng
area
s E
nglis
h,
but i
nput
an
y la
ngua
ge
Cal
cula
ting,
cr
eativ
e th
inki
ng,
writ
ing,
gra
phic
s,
logi
cal &
crit
ical
th
inki
ng
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
te-
boar
ds
Win
dow
s 2S
impl
e SA
A
n ou
tsta
ndin
g su
ite o
f sof
twar
e to
ols
for
foun
datio
n ph
ase
and
olde
r lea
rner
s, a
s w
ell a
s a
teac
her t
oolk
it fo
r cre
atin
g a
rang
e of
pr
ogra
ms
to m
ake
teac
hing
& le
arni
ng e
xciti
ng
& im
part
esse
ntia
l con
cept
s &
thin
king
ski
lls.
This
pro
gram
intro
duce
s da
taba
ses.
Lea
rner
s w
atch
the
data
they
inpu
t mov
e to
form
imag
es
such
as
grap
hs, V
enn
diag
ram
s, in
real
tim
e.
CA
MI
Dia
gnos
tics
All
Lang
uage
, M
athe
mat
ics
Eng
lish
/ Af
rikaa
ns
Iden
tifyi
ng
prob
lem
s &
cau
ses
Indi
vidu
als
one
on o
ne
Win
dow
s C
AM
I R
emed
ial p
rogr
am -
diag
nost
ic to
ol to
ass
ess
lear
ners
with
read
ing,
spe
lling,
writ
ing
& m
aths
di
fficu
lties
. Pos
sibl
e ca
uses
iden
tifie
d as
wel
l as
poss
ible
rem
edia
tion.
Rem
edia
tion
exer
cise
s su
gges
ted
with
in C
AM
I Per
cept
ual &
CA
MI
Mat
hs.
ii
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
CA
MI L
RA
A
t sta
rt of
all
Lang
uage
, M
athe
mat
ics
Eng
lish
Af
rikaa
ns
Bas
elin
e as
sess
-m
ent t
ool
Inte
rval
s on
e on
one
W
indo
ws
CA
MI
Des
igne
d to
be
done
at t
he b
egin
ning
of G
rade
1.
Ass
esse
s as
pect
s of
dev
elop
men
t, e.
g. e
arly
ch
ildho
od h
isto
ry, m
edic
al h
isto
ry, l
angu
age
deve
lopm
ent,
Tour
ette
syn
drom
e et
c.
Ass
essm
ent o
f lea
rner
imm
edia
tely
ava
ilabl
e.
CA
MI M
aths
G
rade
s 1-
12
Mat
hem
atic
s E
nglis
h
isiX
hosa
Af
rikaa
ns
Dril
l & p
ract
ice,
pr
oble
m s
olvi
ng,
criti
cal t
hink
ing
Indi
vidu
als
Win
dow
s C
AM
I G
ood
for c
onso
lidat
ion
& re
info
rcem
ent w
hen
corre
ctly
use
d. M
athe
mat
ical
con
cept
ualis
atio
n sh
ould
take
pla
ce w
ithin
the
clas
sroo
m, s
o th
at
lear
ners
can
use
CA
MI f
or d
rill a
nd p
ract
ice
in
the
com
pute
r lab
. Le
arne
r rec
ords
are
kep
t C
AM
I P
erce
p-tu
als
Gra
des
1-7
Lang
uage
, M
athe
mat
ics
Eng
lish
is
iXho
sa
Afrik
aans
Dev
elop
ing
perc
eptio
n In
divi
dual
s W
indo
ws
CA
MI
Goo
d, c
olou
rful t
ool f
or p
erce
ptua
l dev
elop
men
t in
the
mai
nstre
am a
s w
ell a
s fo
r lea
rner
s w
ith
spec
ial n
eeds
. C
apta
in
Coo
rdin
ate
& th
e Lo
st
Din
osau
r E
gg
Gra
des
2-6
Soc
ial
Scie
nces
: G
eogr
aphy
, M
athe
mat
ics,
& or
ient
eerin
g in
Life
O
rient
atio
n G
rade
s 7
& 8
Eng
lish
Info
rmat
ion,
pr
oble
m s
olvi
ng,
drill
& p
ract
ice,
si
mul
atio
n
Indi
vidu
als,
sm
all
grou
ps,
who
le c
lass
in
tera
ctiv
e w
hite
boar
d
Win
dow
s M
ac
She
rsto
n P
ublis
h-in
g G
roup
Goo
d re
sour
ce fo
r int
rodu
cing
& d
evel
opin
g ge
ogra
phy,
ICT
& n
umbe
r ski
lls.
Act
iviti
es
incl
ude
calc
ulat
ing
rout
es, u
nder
stan
ding
tim
etab
les,
com
pass
poi
nts,
coo
rdin
ates
, map
sy
mbo
ls, s
cale
, usi
ng a
dat
abas
e &
inte
rpre
ting
an a
eria
l vie
w. S
oftw
are
can
disr
upt r
egul
ar
disp
lay
setti
ng o
n m
achi
ne.
Com
pute
rs
4 K
ids
Gra
des
R-7
A
ll le
arni
ng
area
s E
nglis
h &
Af
rikaa
ns
ICT
skills
, In
form
atio
n, d
rill &
pr
actic
e, c
ritic
al &
cr
eativ
e th
inki
ng
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
tebo
ard
Win
dow
s Li
nux
Com
pute
rs 4
Kid
s Th
e fo
cus
is o
n IC
T sk
ills, b
ut c
onte
nt is
in
clud
ed fr
om m
ost l
earn
ing
area
s so
that
the
use
of IC
T sk
ills a
re p
rese
nted
& p
ract
ised
in
cont
ext.
Goo
d ad
ditio
nal e
duca
tiona
l gam
es &
pu
zzle
s fo
rm p
art o
f the
pac
kage
.
Cry
stal
Rai
n Fo
rest
V2
Gra
des
5-7
Tech
nolo
gy
& Mat
hem
atic
s
Eng
lish
Sim
ulat
ion,
logi
c,
prob
lem
sol
ving
&
criti
cal t
hink
ing.
Indi
vidu
als,
sm
all
grou
ps &
in
tera
ctiv
e
Win
dow
s M
ac
She
rsto
n P
ublis
h-in
g G
roup
This
intro
duce
s, d
evel
ops
& te
ache
s Lo
go w
ith
all t
he a
ppea
l of t
he o
rigin
al a
dven
ture
& m
ore.
Th
e va
lue
lies
in th
e th
inki
ng s
kills
invo
lved
.
iii
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
whi
tebo
ard
Eva
lune
t XT
Gra
des
4-7
All
lear
ning
ar
eas
Eng
lish
&
Afrik
aans
, in
put a
ny
lang
uage
Rev
isio
n &
as
sess
men
t too
l to
crea
te re
leva
nt
test
s &
stor
e le
arne
r ach
ieve
-m
ent
Indi
vidu
als,
pa
irs o
r sm
all
grou
ps
Win
dow
s E
valu
Net
E
valu
net X
T is
a re
visi
on a
nd a
sses
smen
t too
l fo
r lim
ited
use
in th
e as
sess
men
t pro
cess
(i.e
. fo
r set
ting
test
s on
fact
ual c
onte
nt o
r con
verg
ent
thin
king
) in
prim
ary
scho
ols.
Tea
cher
s ca
n se
t di
ffere
nt k
inds
of t
ests
& d
iffer
ent k
inds
of
ques
tions
, in
all l
earn
ing
area
s. E
lect
roni
c te
sts
are
mar
ked,
reco
rded
, & th
e re
sults
sto
red.
It
incl
udes
a q
uest
ion
bank
from
whi
ch b
egin
ner
teac
hers
can
sel
ect t
est q
uest
ions
, but
this
co
nten
t sho
uld
be c
heck
ed fo
r rel
evan
ce b
efor
e be
ing
used
. Fu
rble
s G
rade
s R
-4
Num
erac
y E
nglis
h In
form
atio
n tra
nsfe
r, D
rill a
nd
prac
tice,
pro
blem
so
lvin
g
Indi
vidu
als
Who
le
clas
s in
tera
ctiv
e w
hite
boar
d
Win
dow
sA
pple
M
ac
She
rsto
n P
ublis
h-in
g G
roup
P
ublis
h-in
g G
roup
The
prod
uct o
ffers
chi
ldre
n a
uniq
ue &
im
agin
ativ
e in
sigh
t int
o lin
ks b
etw
een
data
&
grap
hs. B
ar C
harts
, Pie
Cha
rts, C
arro
ll D
iagr
ams,
Ven
n D
iagr
ams
and
Tally
Cha
rts a
re
indi
vidu
ally
pre
sent
ed in
13
colo
urfu
l &
enga
ging
act
iviti
es, e
ncou
ragi
ng c
hild
ren
to
cons
truct
ivel
y de
velo
p th
eir u
nder
stan
ding
&
inte
rpre
tatio
n of
the
diffe
rent
gra
ph ty
pes.
The
fle
xibl
e st
ruct
ure
allo
ws
teac
hers
to e
xplo
re th
e da
ta h
andl
ing
aspe
cts
of n
umer
acy
in
imag
inat
ive
way
s.
Gom
ez
Ret
urns
G
rade
s 4-
7 Te
chno
logy
,
Mat
hem
atic
s &
Nat
ural
Sc
ienc
es
Eng
lish
Cas
e st
udie
s,
Pro
blem
sol
ving
&
criti
cal t
hink
ing.
Indi
vidu
als
& s
mal
l gr
oups
Win
dow
s S
hers
ton
Pub
lish-
ing
Gro
up
Use
of s
imul
ated
dat
alog
ging
equ
ipm
ent &
ex
plor
atio
n m
odel
s to
ans
wer
que
stio
ns in
an
adve
ntur
e co
ntex
t. T
he s
oftw
are
is d
esig
ned
to
deve
lop
an a
war
enes
s of
sen
sors
& d
ata
logg
ing
& th
e in
terp
reta
tion
of d
ata.
Tea
cher
op
tions
are
ava
ilabl
e.
Infa
nt V
ideo
To
olki
t G
rade
s R
-7
Lang
uage
, M
athe
mat
ics,
Li
fe
Orie
ntat
ion
Eng
lish,
bu
t inp
ut
any
lang
uage
Pro
blem
sol
ving
, ca
lcul
atin
g, c
reat
ive
thin
king
, writ
ing,
gr
aphi
cs, l
ogic
al &
cr
itica
l thi
nkin
g,
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
Win
dow
s 2S
impl
e SA
A
n ou
tsta
ndin
g su
ite o
f sof
twar
e to
ols
for
foun
datio
n ph
ase
and
olde
r lea
rner
s, a
s w
ell a
s a
teac
her t
oolk
it fo
r cre
atin
g a
rang
e of
pr
ogra
ms
to m
ake
teac
hing
& le
arni
ng e
xciti
ng
& im
part
esse
ntia
l con
cept
s &
thin
king
ski
lls.
iv
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
teac
her i
nput
tool
in
tera
ctiv
e w
hite
boar
d E
ach
prog
ram
is a
vaila
ble
sepa
rate
ly, a
nd
toge
ther
they
can
enh
ance
all
lear
ning
are
as.
This
is a
sui
te o
f 6 p
rogr
ams
intro
duci
ng b
asic
sk
ills s
uch
as c
ount
ing,
pai
ntin
g, p
ublis
hing
&
dire
ctio
n, e
nabl
ing
lear
ners
to w
ork
inde
pend
ently
. M
aste
r M
aths
G
rade
s 4-
12
Mat
hem
atic
s E
nglis
h &
Af
rikaa
ns
Info
rmat
ion
trans
fer,
drill
&
prac
tice,
pro
blem
so
lvin
g, c
ritic
al
thin
king
Indi
vidu
als,
w
hole
cla
ss
inte
ract
ive
whi
tebo
ard
Win
dow
s M
aste
r M
aths
In
tera
ctiv
e m
ultim
edia
sof
twar
e w
hich
cov
ers
the
NC
S M
athe
mat
ics
curr
icul
um.
Ther
e ar
e co
ncep
tual
exp
lana
tions
& e
xerc
ises
with
im
med
iate
feed
back
. It t
rack
s le
arne
rs' p
rogr
ess
& te
ache
rs c
an a
lloca
te a
ppro
pria
te a
ctiv
ities
to
indi
vidu
al le
arne
rs.
It ca
n be
use
d fo
r in
tegr
atin
g w
ith c
lass
teac
hing
as
wel
l as
for
lear
ners
to w
ork
on th
eir o
wn
in a
com
pute
r lab
. M
ath
Bas
e 1-
5 G
rade
s 1-
7 M
athe
mat
ics
Eng
lish
Dril
l & p
ract
ice,
pr
oble
m s
olvi
ng,
criti
cal t
hink
ing
Indi
vidu
als,
w
hole
cla
ss
inte
ract
ive
whi
tebo
ard
Win
dow
s M
ath
Bas
e U
K
Dea
ling
with
key
con
cept
s in
the
foun
datio
n,
inte
rmed
iate
and
sen
ior p
hase
s of
the
curr
icul
um, t
hese
pro
gram
s ar
e re
com
men
ded
for m
enta
l Mat
hs p
ract
ice
on a
regu
lar b
asis
. M
ath
Circ
us
3, 4
, 5
Gra
des
R -
9 M
athe
mat
ics
Lang
uage
E
nglis
h St
ruct
ured
thin
king
sk
ills, d
rill &
pr
actic
e, p
robl
em
solv
ing
indi
vidu
als
sm
all
grou
ps &
in
tera
ctiv
e w
hite
boar
d
Win
dow
s M
ac
Gre
ygum
A
ll th
e ac
tiviti
es a
re N
CS
alig
ned
& a
ddre
ss
criti
cal,
logi
cal &
pro
blem
sol
ving
ski
lls.
Ther
e ar
e 12
attr
activ
e an
d en
joya
ble
puzz
les
in a
ci
rcus
con
text
, eac
h w
ith 1
0 le
vels
of d
iffic
ulty
, en
gagi
ng w
ith m
athe
mat
ical
con
cept
s,
proc
esse
s an
d th
inki
ng.
Mul
t-e-
Mat
hs
Tool
box
Gra
des
R-7
M
athe
mat
ics
Eng
lish
Info
rmat
ion
trans
fer,
prob
lem
so
lvin
g
Indi
vidu
als,
in
tera
ctiv
e w
hite
boar
d
Win
dow
s C
am-
brid
ge
Uni
vers
i-ty
Pre
ss
A p
ower
ful,
flexi
ble,
inte
ract
ive
whi
tebo
ard
reso
urce
. The
Mul
t-e-M
aths
Too
lbox
con
sist
s of
a
wor
kspa
ce a
nd to
ols
that
you
com
bine
and
us
e to
cre
ate
lear
ning
exp
erie
nces
cus
tom
ized
fo
r you
r cla
ss.
v
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
My
Wor
ld
Afri
ca
FP &
IP
Gr 1
-4
Lang
uage
&
Mat
hem
atic
s E
nglis
h,
but a
ny
lang
uage
ca
n be
us
ed to
cr
eate
ac
tiviti
es
Dril
l & p
ract
ise,
pr
oble
m s
olvi
ng,
crea
tive
thin
king
, dr
ag &
dro
p
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
tebo
ard
Win
dow
s M
ac
Gra
nada
A
col
ourfu
l sof
twar
e pa
ckag
e w
ith 3
0 sc
reen
s to
ch
oose
from
. It
incl
udes
topi
cs s
uch
as M
aths
fu
nctio
ns, p
icto
grap
hs, y
our b
ody,
wea
ther
, etc
.
The
teac
her c
an c
reat
e ad
ditio
nal s
cree
ns &
fu
rther
mat
eria
l is
avai
labl
e on
the
Web
. S
peci
al g
raph
ics
rela
ting
to A
frica
hav
e be
en
adde
d to
the
inte
rnat
iona
l edi
tion.
N
umbe
r-sh
ark
Gra
des
R-9
M
athe
mat
ics,
m
ainl
y LO
1
Eng
lish
Con
cept
s of
nu
mbe
r ope
ratio
ns,
calc
ulat
ion,
pr
oble
m s
olvi
ng,
drill
& p
ract
ice
Indi
vidu
als
& inte
ract
ive
whi
tebo
ard
Win
dow
s W
hite
S
pace
G
reat
var
iety
of a
ctiv
ities
(41
gam
es) e
ach
on
man
y le
vels
, for
all
asse
ssm
ent s
tand
ards
in L
O
1. E
xcel
lent
for l
earn
ers
need
ing
rem
edia
tion,
fo
r und
erst
andi
ng &
pra
ctis
ing
the
four
mai
n op
erat
ions
in n
umbe
r wor
k. T
each
er m
anua
l gi
ves
brea
kdow
n of
all
topi
cs a
vaila
ble.
Num
erac
y Ac
tivity
B
uild
er
Gra
des
R-5
N
umer
acy
/ M
aths
E
nglis
h P
robl
em s
olvi
ng
Indi
vidu
als,
sm
all
grou
ps
Win
dow
s G
rana
da
Lear
ning
U
sing
wiz
ard-
styl
e te
mpl
ates
, tea
cher
s ca
n en
ter t
heir
own
cont
ent e
asily
in a
ny o
f the
nin
e ac
tivity
fram
ewor
ks. E
ach
fram
ewor
k su
ppor
ts
all a
reas
of t
he N
CS
and
is c
ompl
etel
y fle
xibl
e,
so th
at y
ou c
an a
dapt
reso
urce
s to
fit y
our
lear
ners
' nee
ds.
Num
erac
y B
anks
G
rade
s 3-
4, 4
-5,
5-6,
6-7
Mat
hem
atic
s E
nglis
h D
rill &
pra
ctis
e &
pr
oble
m s
olvi
ng
Indi
vidu
als,
sm
all
grou
ps
Win
dow
s M
ac
She
rsto
n P
ublis
h-in
g G
roup
This
pro
gram
is a
ligne
d w
ith N
CS
LO
1,
Num
bers
, ope
ratio
ns &
rela
tions
hips
. The
te
ache
r can
sel
ect a
ctiv
ities
& tr
ack
prog
ress
of
lear
ners
who
ans
wer
que
stio
ns in
a q
uiz
form
at.
Stu
dent
repo
rts c
an b
e pr
inte
d or
sav
ed.
Prim
ary
Gam
es,
volu
mes
1,
2, 3
, 4
Gra
des
R-7
M
athe
mat
ics
Eng
lish
Dril
l & p
ract
ise,
pr
oble
m s
olvi
ng,
conc
eptu
al re
-in
forc
e-m
ent
Indi
vidu
als,
sm
all
grou
ps
Win
dow
s In
tera
c-tiv
e R
e-so
urce
s
Mai
nstre
am le
arne
rs a
s w
ell a
s th
ose
need
ing
rem
edia
tion
will
bene
fit fr
om th
ese
clea
rly
pres
ente
d ac
tiviti
es w
hich
are
des
igne
d fo
r in
divi
dual
use
or i
nter
activ
e w
hite
boar
d us
e fo
r th
e w
hole
cla
ss.
Ther
e ar
e m
any
leve
ls o
f di
fficu
lty &
ach
ieve
men
t for
eac
h ac
tivity
.
vi
WC
ED A
PPR
OVE
D M
ATH
EMA
TIC
S SO
FTW
AR
E FO
R T
HE
INTE
RM
EDIA
TE P
HA
SE
TITL
E G
rade
s Le
arni
ng
Are
a/s
or
Prog
ram
mes
La
ngua
ge
Purp
ose
For u
se b
y O
pera
ting
Syst
em
Publ
ishe
r C
omm
ent
Pro
fess
or
Rob
ert's
P
robl
em
Sol
ving
Kit
Gra
des
4-9
Mat
hem
atic
s,
Tech
nolo
gy
Eng
lish
Pro
blem
sol
ving
, lo
gic,
crit
ical
th
inki
ng, d
rill &
pr
actic
e
Indi
vidu
als,
sm
all
grou
ps,
inte
ract
ive
whi
tebo
ard
Win
dow
s S
hers
ton
Pub
lish-
ing
Gro
up
Cle
arly
pre
sent
ed g
rade
d ex
erci
ses
in m
otio
n pl
anni
ng (C
ontro
lIT),
Tang
ram
puz
zles
(S
olve
IT),
and
basi
c as
pect
s of
pro
gram
min
g (P
rogr
amIT
) whi
ch in
som
e w
ays
rese
mbl
es
Logo
. The
var
iety
add
s in
tere
st to
the
activ
ities
.
Sch
oolig
ans
Gra
des
R –
7
Lang
uage
, M
athe
mat
ics
Eng
lish
and
Afrik
aans
Dril
l and
pra
ctic
e,
skills
tran
sfer
, pr
oble
m s
olvi
ng
Indi
vidu
als,
sm
all
grou
ps,
inte
ract
ive
whi
tebo
ard
Win
dow
s E
duta
in
Sch
oolig
ans
is a
com
preh
ensi
ve s
pelli
ng, m
aths
an
d vo
cabu
lary
pro
gram
that
use
s pr
oven
te
achi
ng te
chni
ques
in e
duca
tiona
lly s
ound
, le
arni
ng a
ctiv
ities
. It
acco
mm
odat
es le
arne
rs
from
Gra
des
R-7
. S
pace
S
tatio
n A
lert
Gra
des
4-6
Mat
hem
atic
s E
nglis
h D
rill &
pra
ctic
e,
criti
cal t
hink
ing
&
prob
lem
sol
ving
Indi
vidu
als,
w
hole
cla
ss
& s
mal
l gr
oups
, in
tera
ctiv
e w
hite
boar
d
Win
dow
s M
ac
She
rsto
n P
ublis
h-in
g G
roup
Hig
hly
mot
ivat
ing
activ
ities
whi
ch d
evel
op
prob
lem
sol
ving
ski
lls a
s w
ell a
s an
un
ders
tand
ing
of s
hape
& s
pace
(LO
3).
The
focu
s is
on
the
skills
& th
eir c
onso
lidat
ion
thro
ugh
the
activ
ities
. Tw
o le
vels
of d
iffic
ulty
en
sure
diff
eren
tiatio
n &
pro
gres
sion
of s
kills
. S
pex+
G
rade
s 3-
7 Te
chno
logy
, EM
S,
Mat
hem
atic
s,
rem
edia
l
Eng
lish
Cre
ativ
e th
inki
ng,
grap
hics
, log
ical
&
criti
cal t
hink
ing
Indi
vidu
als,
sm
all
grou
ps,
who
le
clas
s,
inte
ract
ive
whi
tebo
ard
Win
dow
s R
M
Spe
x en
able
s le
arne
rs to
pla
n, b
udge
t for
, &
crea
te a
wid
e ra
nge
of e
nviro
nmen
ts u
sing
the
appr
opria
te u
nits
(suc
h as
furn
iture
, ac
cess
orie
s, a
rchi
tect
ural
and
pla
nt fe
atur
es,
etc)
. 2 &
3-d
imen
sion
al v
iew
s ar
e av
aila
ble,
as
wel
l as
spre
adsh
eets
for b
udge
ting.
Prin
tabl
e w
orks
heet
s ar
e av
aila
ble
for c
lass
wor
k aw
ay
from
the
com
pute
r. Th
e W
izar
d's
App
rent
ice
Gra
des
2-5
Mat
hem
atic
s E
nglis
h P
robl
em s
olvi
ng,
calc
ulat
ion,
logi
c,
criti
cal t
hink
ing,
si
mul
atio
n
Indi
vidu
als
Win
dow
s S
hers
ton
Pub
lish-
ing
Gro
up
The
grap
hics
and
eas
y-to
-follo
w in
stru
ctio
ns
mak
e th
is s
oftw
are
very
use
r-frie
ndly
for
lear
ners
. It
does
not
cov
er L
O 3
, but
cov
ers
som
e of
the
asse
ssm
ent s
tand
ards
in L
O 1
, LO
2,
LO
4 &
LO
5.