maths program s3 yr 6 t1

Sharon Tooney

MATHS PROGRAM : STAGE THREE

YEAR SIX

WEEKLY ROUTINE

Monday Tuesday Wednesday Thursday Friday

Whole Number 2 Terms 1-4 Number & Algebra Terms 1-4: Addition and Subtraction 2 Terms 1-4 : Multiplication & Division 2 Terms 1 & 3: Patterns and Algebra 2 Terms 2 & 4: Fractions and Decimals 2

Statistics & Probability Terms 1 & 3: Data 2 Terms 2 & 4: Chance 2

Measurement & Geometry Term 1: Length 2 / Time 2/ 2D 2 / Position 2 Term 2: Mass 2 / 3D 2 / Angles 2 Term 3: Volume and Capacity 2 / Time 2 / 2D 2 / Position 2 Term 4: Area 2 / 3D2 / Angles 2

Sharon Tooney

K-6 MATHEMATICS SCOPE AND SEQUENCE

NUMBER AND ALGEBRA MEASUREMENT AND GEOMETRY STATISTICS & PROBABILITY

TERM

Whole Number

Addition & Subtraction

Multiplication & Division

Fractions & Decimals

Patterns & Algebra

Length Area Volume & Capacity

Mass Time 3D 2D Angles Position Data Chance

K 1 2 3 4

Yr 1 1 2 3 4

Yr 2 1 2 3 4

Yr 3 1 2 3 4

Yr 4 1 2 3 4

Yr 5 1 2 3 4

Yr 6 1 2 3 4

NB: Where a content strand has a level 1 & 2, the 1 refers to the lower grade within the stage, eg. Whole Number 1 in S1 is for Yr 1, Whole Number 2 is for Yr 2.

Sharon Tooney

MATHEMATICS PROGRAM PROFORMA

STAGE: Year 6 ES1 S1 S2 S3

STRAND: NUMBER AND ALGEBRA

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Whole Number 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › gives a valid reason for supporting one possible solution over another MA3-3WM › orders, reads and represents integers of any size and describes properties of whole numbers MA3-4NA

Background Information

Students could investigate further the properties of square and triangular numbers, such as all square numbers have an odd number of factors, while all non-square numbers have an even number of factors; when two consecutive triangular numbers are added together, the result is always a square number. Language Students should be able to communicate using the following language: number line, whole number, zero, positive number, negative number, integer, prime number, composite number, factor, square number, triangular number. Words such as 'square' have more than one grammatical use in mathematics, eg draw a square (noun), square three (verb), square numbers (adjective) and square metres (adjective).

Investigate everyday situations that use integers; locate and represent these numbers on a number line • recognise the location of negative whole numbers in relation to zero and place them on a number line • use the term 'integers' to describe positive and negative whole numbers and zero • interpret integers in everyday contexts, eg temperature • investigate negative whole numbers and the number patterns created when counting backwards on a calculator - recognise that negative whole numbers can result from subtraction - ask 'What if' questions, eg 'What happens if we subtract a larger number from a smaller number on a calculator?' Identify and describe properties of prime, composite, square and triangular numbers • determine whether a number is prime, composite or neither - explain whether a whole number is prime, composite or neither by finding the number of factors, eg '13 has two factors (1 and 13) and therefore is prime', '21 has more than two factors (1, 3, 7, 21) and therefore is composite', '1 is neither prime nor composite as it has only one factor, itself' - explain why a prime number, when modelled as an array, can have only one row • model square and triangular numbers and record each number group in numerical and diagrammatic form - explain how square and triangular numbers are created - explore square and triangular numbers using arrays, grid paper or digital technologies - recognise and explain the relationship between the way each pattern of numbers is created and the name of the number group

Learning Across The Curriculum

Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s engagement with Asia Sustainability General capabilities

Critical & creative thinking Ethical understanding Information & communication technology capability Intercultural understanding Literacy Numeracy Personal & social capability Other learning across the curriculum areas Civics & citizenship Difference & diversity Work & enterprise

Sharon Tooney

CONTENT WEEK TEACHING, LEARNING and ASSESSMENT

ADJUSTMENTS RESOURCES

Investigate everyday situations that use integers; locate and represent these numbers on a number line

Identify and describe properties of prime, composite, square and triangular numbers

1

Ordering numbers Teachers writes the following examples on the board for the students to work through with the teacher: Place these numbers in order from smallest to largest (ascending order): 10 002, 102, 1002, 12 Answer = 12, 102, 1002, 10 002 Place these numbers in order from largest to smallest (descending order): Three thousand and thirty, 30 500, three hundred and fifty, 33 Answer = 30 500, three thousand and thirty, three hundred and fifty, 33 Provide additional examples for students to complete independently. Check answers together as a class.

whiteboard and markers, paper and pencils

2

Writing numbers Teacher explains we can write numbers in several ways; Example: The number, 4365 can be written in:

numeric form: 4 365 words: four thousand, three hundred and sixty five expanded form: 4 000 (4 x 1 000) + 300 (3 x 100) + 60 (6 x 10) + 5 (5 x 1).

Provide additional examples for students to complete independently. Check answers together as a class.

Number expanders for students who require support

whiteboard and markers, paper and pencils, number expanders

3

Expanded notation Numbers can be expanded by writing the number according to its place value. Example: 234 567 The number two hundred and thirty four thousand, five hundred and sixty seven can be written in expanded notation as: = 200 000 + 30 000 + 4 000 + 500 + 60 + 7 which is the same as: (2 x 100 000) + (3 x 10 000) + (4 x 1 000) + (5 x 100) + (6 x 10) + (7 x 1) Provide additional examples for students to complete independently. Check answers together as a class.

Number expanders for students who require support

whiteboard and markers, paper and pencils

4

Negative Whole Numbers Negative Whole Numbers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

So, numbers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0} We can put that all together like this: Numbers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... } Student examples to try: provide students with blank number lines and have them identify and mark a selection of negative and positive whole numbers, as well as zero, on the number line.

Number line with a moveable arrow to demonstrate negative and positive numbers concretely

whiteboard and markers, paper and pencils, number lines

5

Factors The factors of 12 are: 1 and 12, 2 and 6, 3 and 4

100s chart to support those students who still require

whiteboard and markers, paper and

Sharon Tooney

The factors of 10 are: 1 and 10, 2 and 5 The factors of 100 are: 1 and 100, 2 and 50, 4 and 25, 5 and 20, and 10 - What operation do you think we are using to find the factors of 12? Explain. - Explain what you think ‘factors’ might be. - Using your explanation of ‘factors’, list all the factors of 20. How did you know what numbers were factors and which weren’t? - What number are all of these factors for: 1 and 24, 2 and 12, 3 and 8, 4 and 6 Provide additional examples for students to complete independently. Check answers together as a class.

concrete examples pencils, 100s charts

6

Multiples The multiples of 5 include: 5, 10, 15, 20, 25, 30… The multiples of 7 include: 7, 14, 21, 28, 35… The multiples of 16 include: 16, 32, 48, 64… - What operation do you think we are using to find multiples? Explain. - Explain what you think ‘multiples’ might be. - Using your explanation of ‘multiples’, list 10 multiples of 4: - List 10 multiples of 8: - List 10 multiples of 7: Provide additional examples for students to complete independently. Check answers together as a class.

100s chart to support those students who still require concrete examples

whiteboard and markers, paper and pencils, 100s chart

7

Prime numbers Some prime numbers are 2, 3, 5, 7, 11, 19 - For each of these numbers, list all of their factors: - What pattern do you notice? 15 is not a prime number. List its factors and determine why it is not a prime number. - How many distinct factors do prime numbers have?

Number cards for students to manipulate patterns with

whiteboard and markers, paper and pencils, number cards

8

Composite numbers: Some composite numbers are 4, 6, 8, 9, 10, 12 - For each of these numbers, list all of their factors: - What pattern do you notice? 23 is not a composite number. List its factors and determine why it is not a composite number. - How many distinct factors do composite numbers have? Explain what composite and prime numbers are. Give some of your own examples Discuss the number 1 and the number 2. What kind of numbers are they?

Number cards for students to manipulate patterns with

whiteboard and markers, paper and pencils, number cards

9 Revision

10 Assessment

Sharon Tooney

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Addition and Subtraction 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › gives a valid reason for supporting one possible solution over another MA3-3WM › selects and applies appropriate strategies for addition and subtraction with counting numbers of any size MA3-5NA

Background Information Refer to background information in Addition and Subtraction 1. Language Students should be able to communicate using the following language: plus, sum, add, addition, increase, minus, the difference between, subtract, subtraction, decrease, equals, is equal to, operation, digit. When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, eg 'amount to pay = …', 'change = …'. Refer also to language in Addition and Subtraction 1.

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers • solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' - select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems - explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method - reflect on their chosen method of solution for a problem, considering whether it can be improved - give reasons why a calculator was useful when solving a problem • record the strategy used to solve addition and subtraction word problems - use selected words to describe each step of the solution process


Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s engagement with Asia Sustainability General capabilities

Critical & creative thinking Ethical understanding Information & communication technology capability Intercultural understanding Literacy Numeracy Personal & social capability Other learning across the curriculum areas Civics & citizenship Difference & diversity Work & enterprise

Sharon Tooney



Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers

1

Missing Addends 1 Write the following problems on the board for students to solve. Before beginning, discuss with the students all of the possible strategies they could use to solve addition problems. List these with examples of each as a reference point _________ + 826 + 486 = 1369 _________ + 721 + 197 = 948 94 + _________ + 142 = 608 608 + _________ + 6 = 682 440 + 487 + _________ = 1016 1 + _________ + 820 = 897 _________ + 447 + 60 = 858 _________ + 325 + 91 = 1346 41 + 527 + _________ = 1421 _________ + 288 + 95 = 513 _________ + 315 + 44 = 426 77 + 613 + _________ = 747 223 + 0 + _________ = 734 400 + _________ + 24 = 1318 905 + _________ + 83 = 1389 440 + 37 + _________ = 1082 When students have completed the problems and answers have been checked. Invite students to explain which strategy they used for solving the problems. Ask them: - Do you think that was the best strategy? Why/why not? - What alternate strategy could you have used?

Adjust the difficulty of the sums based on ability level

whiteboards and markers, paper and pencils

2

Missing Addends 2 Using the strategy list from the previous lesson, have students draw one out of a hat. Tell them that the strategy they have chosen, is the only strategy they can employ. Write the following examples on the board: 196 + _________ + 49 + 8 + 300 = 641 14 + 35 + 180 + 67 + _________ = 1196 _________ + 800 + 54 + 165 + 10 = 1115 ______ + 35 + 52 + 14 + 100 = 401 _________ + 62 + 86 + 103 + 6 = 2157 _________ + 48 + 85 + 104 + 2500 = 2741 Invite students to explain what their strategy was and whether they felt it was effective. They should be encouraged to explain their answer giving reasons why or why not and offering an alternative strategy they would have preferred to use if give the option.



3

Missing Minuend or Subtrahend Problems Discuss with the students the types of strategies that can be used to solve subtraction problems. Discuss the similarities and differences between these strategies and the previous strategies identified for solving addition problems. Have students complete the following examples and explain the strategy they employed, giving reasons why. 18324 − _______ = 16594 7305 − _______ = 5530 8350 − _______ = 1538 21470 − _______ = 8117 _______ − 13083 = 14459 _______ − 13621 = 2237 10512 − _______ = 2105 40004 − _______ = 3176 _______ − 28443 = 9420 _______ − 10006 = 1032



http://www.homeschoolmath.net/worksheets/table.php?type=-&long=0&col=2&row=6&min1=100&max1=50000&step1=1&list1=&min2=100&max2=40000&step2=1&list2=&min3=&max3=&step3=1&list3=&M=2&D=2&xdiv=1&switchv=1&exd=1&neg=1&font=Default&FontSize=14pt&pad=25&ptitle=%3Cstrong%3EOnline+Reading+%26+Math%3A+www.k5learning.com%3C%2Fstrong%3E&Submit=Submit�

Sharon Tooney

_______ − 28443 = 9420 _______ − 10006 = 1032 _______ − 14654 = 27574 _______ − 19700 = 7009

4

Word Problems Provide students with a variety of word problems to solve that involve both addition and subtraction of numbers of any size. Examples should include real life examples, such as, those involving money, weights, lengths etc. Students need to be encourages to show all working out employed to solve the problem and present their answer in both words and numbers.



9

Revision

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Multiplication and Division 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › gives a valid reason for supporting one possible solution over another MA3-3WM › selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation MA3-6NA

Background Information Students could extend their recall of number facts beyond the multiplication facts to 10 × 10 by also memorising multiples of numbers such as 11, 12, 15, 20 and 25, or by utilising mental strategies, eg '14 × 6 is 10 sixes plus 4 sixes'. The simplest multiplication word problems relate to rates, eg 'If four students earn $3 each, how much do they have all together?' Another type of problem is related to ratio and uses language such as 'twice as many as' and 'six times as many as'. An 'operation' is a mathematical process. The four basic operations are addition, subtraction, multiplication and division. Other operations include raising a number to a power and taking a root of a number. An 'operator' is a symbol that indicates the type of operation, eg +, –, × and ÷. Refer also to background information in Multiplication and Division 1. Language Students should be able to communicate using the following language: multiply, multiplied by, product, multiplication, multiplication facts, area, thousands, hundreds, tens, ones, double, multiple, factor, divide, divided by, quotient, division, halve, remainder, fraction, decimal, equals, strategy, digit, estimate, speed, per, operations, order of operations, grouping symbols, brackets, number sentence, is the same as. When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, eg 'cost of goldfish = …', 'cost of plants = …', 'total cost = …'. 'Grouping symbols' is a collective term used to describe brackets [], parentheses () and braces {}. The term 'brackets' is often used in place of 'parentheses'.

Select & apply efficient mental & written strategies, & appropriate digital technologies, to solve problems involving multiplication & division with whole numbers • select & use efficient mental & written strategies, & digital tech, to multiply whole numbers up to 4 digits by 1 & 2 digit numbers • select & use efficient mental & written strategies, & digital tech, to divide whole numbers up to 4 digits by a 1 digit divisor, including where there is a remainder - estimate solutions to problems & check to justify solutions • use mental strategies to multiply & divide numbers by 10, 100, 1000 & their multiples • solve word problems involving multiplication & division - use appropriate language to compare quantities - use a table/similar organiser to record methods to solve problems • recognise symbols used to record speed in kilometres per hour • solve simple problems involving speed Explore the use of brackets & the order of operations to write number sentences • use the term operations to describe collectively the processes of addition, subtraction, multiplication & division • investigate & establish order of operations using real-life contexts - write number sentences to represent real-life situations • recognise that the grouping symbols () and [] are used in number sentences to indicate operations that must be performed 1st • recognise if more than 1 pair of grouping symbols are used, the operation within the innermost grouping symbols is performed 1st • perform calculations involving grouping symbols without digital tech, eg 5+(2x3)=5+6


Cross-curriculum priorities Aboriginal &Torres Strait Islander histories & cultures Asia & Australia’s engagement with Asia Sustainability General capabilities Critical & creative thinking Ethical understanding Information & communication technology capability Intercultural understanding Literacy Numeracy Personal & social capability Other learning across the curriculum areas Civics & citizenship Difference & diversity Work & enterprise

Sharon Tooney

Often in mathematics when grouping symbols have one level of nesting, the inner pair is parentheses () and the outer pair is brackets [], eg 360÷[4x(20-11)].

=11 (2+3)x(16-9)=5x7 =35 3+[20÷(9-5)]=3+[20÷4] =3+5 =8 • apply the order of operations to perform calculations involving mixed operations & grouping symbols, without digital tech, eg 32+2-4=34-4 =30 addition & subtraction only, therefore work from left to right 32÷2x4=16x4 =64 multiplication & division only, therefore work from left to right 32÷(2x4)=32÷8 =4 perform operation in grouping symbols first (32+2)x4=34x4 =136 perform operation in grouping symbols first 32+2x4=32+8 =40 perform multiplication before addition - investigate whether different digital tech apply order of operations • recognise when grouping symbols are not necessary, eg 32 + (2 × 4) has the same answer as 32 + 2 × 4

Sharon Tooney



Select & apply efficient mental & written strategies, & appropriate digital technologies, to solve problems involving multiplication & division with whole numbers Explore the use of brackets & the order of operations to write number sentences

5

Strategies 1 Select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbers. For example:

Vary the way questions are presented:

etc Have students check results with a calculator.


whiteboards and markers, paper and pencils, calculators

6

Strategies 2 Select and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainder. Estimate solutions to problems and check to justify solutions For example: 2)1336 4)3800 4)3100 5)2910 (without remainders) 6)2447 6)9718 5)9562 5)6426 (with remainders)



7

Order of Operations 1 Use the term 'operations' to describe collectively the processes of addition, subtraction, multiplication and division. Introducing brackets Brackets can change the order in which we perform operations. Examine the examples below and use your calculator to see if you can find the pattern. Examples: 223 – (185 – 22) = 60 but 223 – 185 – 22 = 16 345 – (34 + 221) = 90 but 345 – 34 + 221 = 532 - What patterns have I found in the way the operations order is affected by brackets? Test out your pattern on the following equations. Check your answers with the teacher when you have finished. You may not use calculators for these. Use the space below for your working. 1. 546 – (78 + 45) 2. 546 – 78 + 45 3. 56.798 – 34.32 – 2.342 4. 56.789 – (34.32 – 2.342) Explain how you used brackets to find the answers Use the pattern that you found in the last activity to solve the following equations. You may use a calculator if you choose, but you will need to determine the order of operations before calculating.

Work through the examples below to get you started. Examples: First rule: 4 x 5 x (9 + 3) = 240 The rule was: Second rule: 4 + 5 + 3 x 6 = 27

Adjust the difficulty of the sums based on ability level Poster of rules as a visual prompt


Sharon Tooney

4 + 5 + 15 ÷ 3 = 14 The rule was: Third rule: 5 x 6 ÷ 2 x 3 = 45 The rule was: Fourth rule: 6 – 3 + 4 – 5 = 2 The rule was: 1. Which one of the following orders of operations is correct? Circle it. • Brackets, addition and subtraction, multiplication and division • Multiplication and division, brackets, addition and subtraction • Brackets, multiplication and division, addition and subtraction • Addition and subtraction, brackets, multiplication and division • Brackets, multiplication, division, addition, subtraction 2. Calculate the solutions for the following problems. You may use a calculator. 7 x 9 + (3 + 7) = 12 ÷ 2 x 5 = 4 + 3 – 2 x 3 = 12 + 14 ÷ 2 = (5 – 3) x 5 + 9 = 19 – 5 x (7 – 4) = 12 x (3 + 2) ÷ 10 = 7 – 4 + 7 – 3 – 1 = 6 x 7 x 2 ÷ 12 = 12 + 4 x 5 ÷ 2 – 11 = How many different equations can you write that make 12 and use at least three different operations?

8

Order of Operations 2 Investigate and establish the order of operations using real-life contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 × 10 + 2 × 4 but, to obtain the total cost, multiplication must be performed before addition. Write number sentences to represent real-life situations. Example: Money from Chores Manuel wanted to save to buy a new bicycle. He offered to do extra chores around the house. His mother said she would pay him $8 for each door he painted and $4 for each window frame he painted. If Manuel earned $40 from painting, how many window frames and doors could he have painted?

1. Write an expression showing how much Manuel will make from his painting chores. 2. Use the table below to find as many ways as possible Manuel could have earned $40

painting window frames and doors. Windows Doors Working Out Area Money Earned



9 Revision

10 Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Patterns and Algebra 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › gives a valid reason for supporting one possible solution over another MA3-3WM › analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane MA3-8NA

Background Information Refer to background information in Patterns and Algebra 1. In Stage 2, students found the value of the next term in a pattern by performing an operation on the previous term. In Stage 3, they need to connect the value of a particular term in the pattern with its position in the pattern. This is best achieved through a table of values. Students need to see a connection between the two numbers in each column and should describe the pattern in terms of the operation that is performed on the position in the pattern to obtain the value of the term. Describing a pattern by the operation(s) performed on the 'position in the pattern' is more powerful than describing it as an operation performed on the previous term in the pattern, as it allows any term (eg the 100th term) to be calculated without needing to find the value of the term before it. The concept of relating the number in the top row of a table of values to the number in the bottom row forms the basis for work in Linear and Non-Linear Relationships in Stage 4 and Stage 5. The notion of locating position and plotting coordinates is established in the Position sub strand in Stage 2 Measurement and Geometry. It is further developed in this sub strand to include negative numbers and the use of the four-quadrant number plane. The Cartesian plane (commonly referred to as the 'number plane') is named after the French philosopher and mathematician René Descartes (1596–1650), who was one of the first to develop analytical geometry on the number plane. On the number plane, the 'coordinates of a point' refers to the ordered pair describing the horizontal position x first, followed by the vertical position y. The Cartesian plane is applied in real-world contexts, eg when determining the incline (slope) of a road between two points. The Cartesian plane is used in algebra in Stages 4 to 6 to

Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence • continue and create number patterns, with/out the use of digital technologies, using whole numbers, fractions and

decimals, eg , , ,..... or 1.25, 2.5, 5, …

- describe how number patterns have been created and how they can be continued • create simple geometric patterns using concrete materials, eg ∆, ∆∆, ∆∆∆, ∆∆∆∆,........... • complete a table of values for a geometric pattern and describe the pattern in words, eg

, , , ,... − describe the number pattern in a variety of ways & record descriptions using words − determine the rule to describe the pattern by relating the bottom number to the top number in a table − use the rule to calculate the corresponding value for a larger number • complete a table of values for number patterns involving 1 operation (including patterns that decrease) & describe the pattern in words, eg

− describe the pattern in a variety of ways & record descriptions in words, − determine a rule to describe the pattern from the table − use the rule to calculate the value of the term for a large position number - explain why it is useful to describe the rule for a pattern by describing the connection between the position in the pattern & the value of the term - interpret explanations written by peers & teachers that accurately describe geometric & number patterns • make generalisations about numbers & number



Sharon Tooney

describe patterns and relationships between numbers. Language Students should be able to communicate using the following language: pattern, increase, decrease, term, value, table of values, rule, position in pattern, value of term, number plane (Cartesian plane), horizontal axis (x-axis), vertical axis (y-axis), axes, quadrant, intersect, point of intersection, right angles, origin, coordinates, point, plot.

relationships, eg If you add a number & then subtract the same number, the result is the number you started with Introduce the Cartesian coordinate system using all four quadrants • recognise that the number plane (Cartesian plane) is a visual way of describing location on a grid • recognise that the number plane consists of a horizontal axis (x-axis) & a vertical axis (y-axis), creating 4 quadrants

- recognise that the horizontal axis & the vertical axis meet at right angles • identify the point of intersection of the 2 axes as the origin, having coordinates (0, 0) • plot & label points, given coordinates, in all 4 quadrants of the number plane - plot a sequence of coordinates to create a picture • identify & record the coordinates of given points in all 4 quadrants of the number plane - recognise that the order of coordinates is important when locating points on the number plane, eg (2, 3) is different from (3, 2)

Sharon Tooney



Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence

Introduce the Cartesian coordinate system using all four quadrants

4

Identify a rule for number patterns For the number patterns below work out what operation is being used to generate the next term (e.g. add 4 each time, multiply by two each time). Write a sentence beneath each pattern to describe the pattern. Pattern 1: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Pattern 2: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Pattern 3: 18, 16, 14, 12, 10, 8, 6, 4, 2, 0 Pattern 4: 2, 4, 8, 16, 32, 64 Pattern 5: 24, 12, 6, 3 Pattern 6: 6, 11, 16, 21, 26, 31, 36, 41 Pattern 7: 32, 29, 26, 23, 20, 17, 14, 11, 8 Pattern 8: 2, 6, 18, 54, 162 Pattern 9: 270, 90, 30, 10 Pattern 10: 52, 47, 42, 37, 32, 27, 22 Possible Questions: - How did I work out what the operation was? - How did I work out what the rule was?

Adjust difficulty of pattern based on ability 100s chart to colour pattern to provide visual support


5

Create a number pattern based on a rule For the following situations your job is to create a number pattern based on the rule stated. You should create three different patterns for each rule. - Rule 1: Add 4 - Rule 2: Subtract 2 - Rule 3: Multiply by 2 - Rule 4: Divide by two Work out what the rule is in the situations below and create your own pattern using this rule. - Rule 5: 3, 11, 19, 27, 35, 43, 51, 59 What is the rule? ___________ My pattern: - Rule 6: 6, 24, 96, 384, 1536 What is the rule? ___________ My pattern: - Rule 7: 6400, 1600, 400, 100, 25 What is the rule? ___________ My pattern: - Rule 8: 59, 53, 47, 41, 35, 29, 23 What is the rule? ___________ My pattern: A pattern was made using the following rule: subtract 3. If the last number in the pattern was 14: - - What were the previous 3 numbers? - What would the next 2 numbers be?

Adjust difficulty of pattern based on ability 100s chart to colour pattern to provide visual support


6

Writing rules from number patterns Writing rules or equations from tables of value: 1. Jenny earned $2 for each hour she worked. See the table below:

Adjust difficulty of pattern based on ability 100s chart to colour pattern


Sharon Tooney

- What pattern is being followed to turn the grey number into the white number? - How do we turn a 1 into a 2, how do we turn a 3 into a 6 etc.? - Finish the number sentence: hours ___________ = money - Explain the pattern: - How much money would Jenny earn after 6 hours? - How much money would Jenny earn after 10 hours? 2. Michael was one year older than Sam. See the table below:

- What pattern is being followed to turn the grey number into the white number? - How do we turn a 1 into a 2, how do we turn a 3 into a 6 etc.? - Finish the number sentence: Sam ____________ = Michael - Explain the pattern: - How old will Michael be when Sam is 6? - How old will Michael be when Sam is 10? 3. Michelle always had 3 more lollies than Tyler. See the table below:

- The rule would be: Tyler ___________ = Michelle - How many lollies would Michelle have if Tyler had 6? - How many lollies would Michelle have if Tyler had 10?

to provide visual support

7

Counter Patterns Make the pictures below, then work out what the pattern is and answer the questions. Pattern 1:

- Describe the patterns using words and numbers: - If you were going to draw a fifth line of counters for the shape, what would you draw? - How many counters would be in the shape altogether? How do you know? Complete the following table:

Adjust difficulty of pattern based on ability

whiteboards and markers, paper and pencils, counters

Sharon Tooney

- What patterns are there in the table? - If the shape had 12 lines, how would you work out how many counters were in the shape altogether? - Write a number sentence to explain your pattern: The number of counters altogether in each of the patterns above is called a ‘triangular number’. What do you think this might mean? Why would they be called triangular numbers?

9 Revision

10 Assessment

ASSESSMENT OVERVIEW

Sharon Tooney



STRAND: MEASUREMENT AND GEOMETRY

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Length 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › gives a valid reason for supporting one possible solution over another MA3-3WM › selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length MA3-9MG

Background Information Refer to background information in Length 1. Language Students should be able to communicate using the following language: length, distance, kilometre, metre, centimetre, millimetre, perimeter, dimensions, width.

Connect decimal representations to the metric system • recognise the equivalence of whole-number and decimal representations of measurements of length, eg 165 cm is the same as 1.65 m • interpret decimal notation for lengths and distances, eg 13.5 cm is 13 centimetres and 5 millimetres • record lengths and distances using decimal notation to three decimal places, eg 2.753 km Convert between common metric units of length • convert between metres and kilometres • convert between millimetres, centimetres and metres to compare lengths and distances - explain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg 'More metres than kilometres will be needed to measure the same distance, and so to convert from kilometres to metres, I need to multiply' Solve problems involving the comparison of lengths using appropriate units • investigate and compare perimeters of rectangles with the same area - determine the number of different rectangles that can be formed using whole-number dimensions for a given area • solve a variety of problems involving length and perimeter, including problems involving different units of length, eg 'Find the total length of three items measuring 5 mm, 20 cm and 1.2 m'



Sharon Tooney



Connect decimal representations to the metric system

Convert between common metric units of length

Solve problems involving the comparison of lengths using appropriate units

1

Measuring Perimeter Students select the appropriate measuring device and unit of measurement to measure the perimeter of their desktops, the perimeter of the classroom floor and the perimeter of the school. Students compare their measurements and discuss. Variation: Students find the perimeter of a face of a small object eg an eraser. Students write their own list of objects for which perimeters could be measured. Possible questions include: - how could we categorise the list? In small groups, students categorise items into groups under the headings suggested.

Support as required 1m ruler, measuring tape, trundle wheels, paper and pencil

2

Calculating Perimeter Students are given a sheet of paper on which a square, a rectangle, an equilateral triangle and an isosceles triangle have been drawn. Students calculate the perimeter of each shape. Students record and compare their findings. Possible questions include: - how will you calculate the perimeter of each shape? - did you discover an easy way to calculate the perimeter of squares, rectangles and triangles?

Support as required shape outlines, 30cm rulers, paper and pencils

3

Three Decimal Places Students choose a distance of less than one kilometre and write their distances in metres on a card. On the back of the card students record the distance in kilometres eg 276 m = 0.276 km. The teacher asks: - ‘Who has the shortest distance?’ This student stands at the front of the room. - ‘Who has the longest distance?’ This student stands at the back of the room. The remainder of the class sort themselves between these two students in order. Students compare the two ways of recording the distances. Variation: Students write other distances and repeat the activity.

Questioning techniques Support as required

blank cards, pencils

4

Adding Lengths Students measure dimensions of three items, each involving a different unit of length eg thickness of an eraser, length of a pencil and length of a desk. They add these three measurements eg 5 mm, 20 cm and 1.2 m together to find the total length. Students choose three other items and measure and add their lengths. Variation: Students record measurements in decimal notation. They record and order their lengths.

Support as required 30cm and 1m rulers, tape measures, paper and pencils

5

Metre, Centimetre and Millimetre Race Students are told they are going to race across the playground in small groups. Students are given three different coloured dice, one for metres, one for centimetres and one for millimetres. They are asked to choose the equipment they would need to measure the playground eg a metre ruler and a centimetre/millimetre ruler. The groups start at one side of the playground. Each student takes a turn at rolling the three dice. They measure the distance shown on the three dice (eg 3 m, 5 cm and 4 mm), add to the group’s line on the ground, and record the total distance each time eg 3.54 m or 354 cm. The winner is the first group to reach the other side of the playground. Students compare and discuss the results. Results could be checked on the calculator. Possible questions include:

Peer tutoring strategy for group formation

Sharon Tooney

-what strategies did you use to record your distances? -were there any differences in distances between the groups? Why? - would you do it differently next time? Variation: Students measure a smaller/larger distance and vary the equipment used.

6

Design a Cross Country Track Students work in pairs or small groups to design a 3 kilometre cross country course for their school. Students draw the course to scale and label their plan with the scale used and the length of each part of the course.

Peer tutoring strategy for pairings

grid paper, 30cm rulers, trundle wheels, pencils and paper

7

Walk for 1 Kilometre Students use a street map and its scale to mark routes 1km from the school. Each route of 1km must follow streets on the map.

Support as required street maps, 30cm rulers, paper, pencils, paper strips

8

Marathon Students use a local street map to plan a marathon route of 42km.

Extension: compare the geographical & weather conditions on the designed route with the Sydney 2000 Olympic route & predict a winning time to complete the marathon

local maps, paper, grid paper, pencils

9 Mystery Flight Students use the scale on an atlas map of NSW. Students plan a mystery flight of 1000km, for example, which commences from the nearest airport and includes up to four take-offs and landings.

Maps and scales map need to be enlarged

atlas map of NSW or Australia, 30cm rulers, paper and pencils

10 Plan a Trip Students use a website to complete an itinerary for a trip. On the site www.Travelmate.com.au students can click on Smart trip and enter trip details, e.g. from Sydney to Bathurst for a detailed itinerary. From the driving directions, students will need to convert units to calculate time and distance. Students could complete a timeline of their trip using 24 hour time. Students can use www.qantas.com.au to plan a holiday with a flight.

Support as required computers, paper and pencils

ASSESSMENT OVERVIEW

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Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Time 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › uses 24-hour time and am and pm notation in real-life situations, and constructs timelines MA3-13MG

Background Information Refer to background information in Time 1. Language Students should be able to communicate using the following language: timetable, timeline, scale, 12-hour time, 24-hour time, hour, minute, second, am (notation), pm (notation).

Interpret and use timetables • read, interpret and use timetables from real-life situations, including those involving 24-hour time • use bus, train, ferry and airline timetables, including those accessed on the internet, to prepare simple travel itineraries - interpret timetable information to solve unfamiliar problems using a variety of strategies Draw and interpret timelines using a given scale • determine a suitable scale and draw an accurate timeline using the scale, eg represent events using a many-to-one scale of 1 cm = 10 years • interpret a given timeline using the given scale Learning Across The Curriculum


Sharon Tooney



Interpret and use timetables

Draw and interpret timelines using a given scale

1

Look at a TV programme guide.

Television programme guide

BBC 1 ITV 1

5:35 pm Neighbours 5:15 pm Soapstar Superchef

6:00 pm BBC News 6:00 pm London Tonight

6:15 pm Regional news 6:30 pm ITV Evening News

6:30 pm Mission Africa 7:00 pm Emmerdale

7:25 pm Holiday 7:30 pm Coronation Street

8:00 pm Match of the Day 8:00 pm Cash in your house

Ask questions such as: - How long does the programme ‘Mission Africa’ last? - If I turn over to BBC 1 at the end of ‘Emmerdale’, what programme is on? - How long is it until your favourite programme starts? What did you need to know to work that

out? - How long does Channel 4 spend broadcasting news programmes in one day? Is it the same on

weekdays and at the weekend? Have students, both predict how long they think will be spent on news programmes, then work to add up the times. Who was closer to the actual time?

Support as required TV guides, paper and pencils

2

Look at a timetable such as the London to Dublin train and ferry timetable Train and ferry timetable

London to Dublin

London Euston train depart: 06:46 09:00 11:28 19:38

Holyhead train arrive: 11:30 13:03 15:30 23:29

Change trains at: Crewe direct Crewe direct

Holyhead ferry depart: 12:00 14:10 17:15 02:40

Dublin Ferryport arrive: 13:49 17:25 19:04 05:55

Ask questions such as: - How long does the first train from London Euston take to travel to Holyhead? - If you left London Euston at 9:00 am, when should you arrive in Dublin? - If you arrive at Holyhead at 15:30, how long do you have to wait for the ferry to depart? - you had to be in Dublin by 2:00 pm, which train would you catch from London Euston? - Which of these journeys from London to Dublin is the quickest?

Support as required timetables, paper and pencils

3

Leyton Bus Company 1. Write these times in the 12 hour clock. The first has been done for you as an example.

Extension: Below is an incomplete timetable. Can you complete it using the

timetables, paper and pencils

Sharon Tooney

2. Write these times in the 24 hour clock. The first has been done for you as an example.

3. Look at the bus timetable below carefully and then answer the questions. Timetable W15 Bus – Leyton Station to Walthamstow Central

(a) What time does the first bus leave Leyton Station in the morning? (b) When does the first bus arrive at Baker’s Arms? (c) How long has it taken to get there? (d) When does it arrive at Walthamstow Central? (e) Is there a bus from Leyton Station at 10 to 10 in the morning? (f) If I want to get to Leyton Town Hall at 8.20am, what bus must I catch from Leyton Station? (g) How long does it take the 9.30 from Tesco’s to get to the Baker’s Arms? (h) How long does it take for the bus that leaves at 3.30pm from Leyton Station to get to Leyton Town Hall? (i) How many W15 buses call at the High Road? (j) Can I catch a bus from Leyton Town Hall at 6.30pm?

information below to help you?

- It takes 10 minutes to get to Leyton Leisure Lagoon from Leyton Station usually. - New Road is only 5 minutes before Chingford Mount. - The 2pm bus* from Leyton takes 5 minutes longer at each stop! - The 8pm bus** from Leyton takes 10 minutes longer at each stop.

4

ICT Links Use the internet to find other examples of timetables and time differences around the world. Explore the Tell Time ITP at http://www.standards.dfes.gov.uk/ primaryframeworks/library/Mathematics/ICTResources/itps/ Ask your students to make comparisons between analogue and digital clocks, and between 12-hour and 24-hour times.

support as required computers paper and pencils

9

Revision

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http://www.standards.dfes.gov.uk/primaryframeworks/library/Mathematics/ICTResources/itps/�

Sharon Tooney

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: 2D 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties MA3-15MG

Background information When drawing diagonals, students need to be careful that the endpoints of their diagonals pass through the vertices of the shape. Language Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, centre, radius, diameter, circumference, sector, semicircle, quadrant, triangle, equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, diagonal, vertex (vertices), line (axis) of symmetry, translate, reflect, rotate, clockwise, anti-clockwise. A diagonal of a two-dimensional shape is an interval joining two non-adjacent vertices of the shape. The diagonals of a convex two-dimensional shape lie inside the figure.

Investigate the diagonals of two-dimensional shapes • identify and name 'diagonals' of convex two-dimensional shapes - recognise the endpoints of the diagonals of a shape as the vertices of the shape • determine and draw all the diagonals of convex two-dimensional shapes • compare and describe diagonals of different convex two-dimensional shapes - use measurement to determine which of the special quadrilaterals have diagonals that are equal in length - determine whether any of the diagonals of a particular shape are also lines (axes) of symmetry of the shape Identify and name parts of circles • create a circle by finding points that are all the same distance from a fixed point (the centre) • identify and name parts of a circle, including the centre, radius, diameter, circumference, sector, semicircle and quadrant Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies • identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90° once and then reflected once' • construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software • predict the next translation, reflection or rotation in a pattern, eg 'The arrow is being rotated 90° anti-clockwise each time' - choose the correct pattern from a number of options when given information about a combination of transformations



Sharon Tooney



Investigate the diagonals of two-dimensional shapes Identify and name parts of circles Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies

2

Diagonals of a Polygon Definition: The diagonal of a polygon is a line segment linking two non-adjacent vertices. Provide the students with pictures of regular polygons and have them explore the number of verticals which can be drawn on each one. Example Solutions:

A diagonal of a polygon is a line segment joining two vertices. From any given vertex, there is no diagonal to the vertex on either side of it, since that would lay on top of a side. Also, there is obviously no diagonal from a vertex back to itself. This means there are three less diagonals than there are vertices. (diagonals to itself and one either side are not counted).

Support with fine motor activities

shape outlines, dot paper, 30cm rulers, paper and pencils

3

Diagonal Problem Solving Have students investigate the following problems:

1. Draw three different polygons. Each polygon should have 5 diagonals. Which strategy did you use? 2. Draw a polygon with 2 diagonals so that the triangles formed are: • 4 congruent right triangles • 2 pairs of congruent isosceles triangles What shape have you drawn?

Have students describe how they solved each problem.


30cm rulers, paper and pencils

4

Intersecting Lines Know that two lines that cross each other are called intersecting lines, and the point at which they cross is an intersection. For example:

Identify all the intersections of lines drawn from 2 points to, say, 3, 4, 5… other points. Predict the number of intersections from 2 points to 10 points.



5

Circles: Lines A line that goes from one point to another on the circle's circumference is called a Chord. If that line passes through the centre it is called a Diameter. A line that "just touches" the circle as it passes by is called a Tangent. And a part of the circumference is called an Arc.



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Sharon Tooney

Circles: Slices There are two main "slices" of a circle The "pizza" slice is called a Sector. And the slice made by a chord is called a Segment.

Explore creating circles from a fixed centre point. Use the diagram below as a prompt for this activity:

Have students evaluate the effectiveness of this method and the ‘perfectness’ of the end product.

6

ROTATIONAL SYMMETRY Rotational symmetry occurs when the position of a shape matches its original position after the shape has been rotated less than 360°. The order of rotational symmetry refers to the number of times the position of a shape matches its original position during a complete rotation about its centre. For example, a square has rotational symmetry.

When a square is rotated about its centre, its position matches its original position after a 1/4, 1/2, and 3/4 rotation: therefore, a square has rotational symmetry. It has rotational symmetry of order 4 because its position matches the original position four times during a complete rotation. Investigate: the relationship between the number of sides of the polygon and its order of rotational symmetry. Report findings to the class and make generalisations based on results.

Support with fine motor activities Concrete shapes to rotate and trace


7

Making Patterns That Show Translation, Reflection and Rotation Complete the following activities in small groups: Activity 1 In this activity students make patterns that show translations. 1. Show the students a piece of wallpaper, wall frieze or wrapping paper that shows a translation

pattern. 2. Ask the students: what picture is repeated on the paper to make a pattern?

Are the pictures the same each time? (Yes)

Peer tutoring strategy for groupings

wallpaper, wrapping paper, stamps, ink pads, paper, pencils, reflective pictures, mirrors, pictures

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Sharon Tooney

How are the pictures the same? (shape, size, orientation, colour) 3. Using A4 paper and stamps students are to make their own translation pattern on the page.

Ensure that the students keep the stamp orientated the same way as they make repeated stamps on the page.

Activity 2 In this activity students make patterns that show reflections.

1. Show the students pictures that show reflections, for example scenery reflections in lakes, butterfly wings.

2. Explain to the students that a reflection picture looks like it could be folded in half so the two sides match. Using a mirror on the fold to show students that the reflection is the same as the other side.

3. Colouring pictures of butterflies so the wings show a reflection pattern is a common and popular activity. Another idea is to make a reflection patterns on the wings of paper planes.

Activity 3 In this activity students make patterns that show rotations.

1. Show the students pictures that show rotations, for example, star fish arms, flower petals, windmill blades, propeller blades, bike spokes.

2. Explain to the students that in these types of examples part of the object has been turned around a centre point. Ask them to identify the part that has been rotated. For example, if you take one spoke on the bike wheel, leave one end at the centre and turn the other end it will rotate on to the position of the next spoke.

3. Show the students pictures where the object itself has been rotated, for example:

4. Using the stamps and inkpads students can show a rotation pattern where the whole

object is rotated. 5. Students can make patterns where part of the object is rotated. For example, drawing a

flower by cutting out multiple petal shapes and gluing them around the centre or an aircraft with nose and wing propellers that show blade rotation.

9 Revision

10 Assessment

ASSESSMENT OVERVIEW

Sharon Tooney




TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Position KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › locates and describes position on maps using a grid-reference system MA3-17MG

Background Information In Stage 2, students were introduced to the compass directions north, east, south and west, and north-east, south-east, south-west and north-west. In Stage 3, students are expected to use these compass directions when describing routes between locations on maps. By convention when using grid-reference systems, the horizontal component of direction is named first, followed by the vertical component. This connects with plotting points on the Cartesian plane in Stage 3 Patterns and Algebra, where the horizontal coordinate is recorded first, followed by the vertical coordinate. Language Students should be able to communicate using the following language: position, location, map, plan, street directory, route, grid, grid reference, legend, key, scale, directions, compass, north, east, south, west, north-east, south-east, south-west, north-west.

Use a grid-reference system to describe locations • find locations on maps, including maps with legends, given their grid references • describe particular locations on grid-referenced maps, including maps with a legend, eg 'The post office is at E4' Describe routes using landmarks and directional language • find a location on a map that is in a given direction from a town or landmark, eg locate a town that is north-east of Broken Hill • describe the direction of one location relative to another, eg 'Darwin is north-west of Sydney' • follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map • use a given map to plan and show a route from one location to another, eg draw a possible route to the local park or use an Aboriginal land map to plan a route - use a street directory or online map to find the route to a given location • describe a route taken on a map using landmarks and directional language, including compass directions, eg 'Start at the post office, go west to the supermarket and then go south-west to the park'



Sharon Tooney



Use a grid-reference system to describe locations

Describe routes using landmarks and directional language

5

The Key To Understanding Maps Maps can be drawn to represent a variety of information. This information might include things such as roads, tourist attractions and campgrounds, or they might represent the latest weather patterns. The objects on a map are represented using symbols. A symbol is a picture on the map that represents something in the real world. Understanding these symbols requires the use of a key (legend). Maps use a key, or legend, to explain the meaning of each of the symbols used in the map. These keys usually show a small picture of each of the symbols used on the map, along with a

written description of the meaning of each, for example: of these symbols.

Have students create a map of the school and surrounding area. The map must contain symbols and a key to identify the symbols used.

Support to draw symbols, using concrete examples as prompts

paper, pencils, rulers, coloured pencils

6

Mapping The Classroom Creating the Legend In their small groups, have students brainstorm ideas for symbols of objects in the classrooms, such as student desks, teacher desk, windows, or bulletin boards. Have students create a legend based on these symbols on a small piece of paper. Remind students that this will be the legend of the map. Creating the Map Have students measure the objects in the room, as well as the distance between the various objects. Assist them in their small groups as they use these measurements to create a map to scale. Remind them to use the symbols from their legend in their map. When the map is complete, help students find a place to attach their legend. Wrap Up If some groups finish this map skills lesson plan before others, encourage them to decorate their map as desired. When all of the groups have completed their maps, encourage them to present their creations to the class. As a class, discuss the difficulties they had in creating their maps and what they could do differently next time.



7

Grid Coordinates: Reading Coordinates are a set of values that show an exact position. On maps and graphs it is common to have a pair of numbers to show where a point is: the first number shows the distance along and the second number shows the distance up or down. Example: the point (12,5) is 12 units along, and 5 units up.

Support to locate items using rulers or cardboard strips to line items up

worksheet, pencils

Sharon Tooney

Using the attached worksheet revise reading grid coordinates to identify a location on a map.

8 Grid Coordinates: Writing Revise what grid coordinates how and have students identify how to read coordinates. Using the attached worksheet, have students locate addresses on a map and write the grid coordinates which identify that location.

Support to locate items using rulers or cardboard strips to line items up

worksheet, pencils

9

Revision

10

Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

Draw and Name

Find what is located at the following grid references. Draw the symbol and write what it represents.

1. E3 _____________________________________ 2. F6 _________________________________

3. E4 _____________________________________ 4. F1 _________________________________

5. B4 _____________________________________ 6. H7 _________________________________

7. E1 _____________________________________ 8. F3 _________________________________

9. H4 _____________________________________ 10. B3 _________________________________

11. H6 _____________________________________ 12. A6 _________________________________

13. B6 _____________________________________ 14. F7 _________________________________

15. B1 _____________________________________ 16. F4 _________________________________

17. H8 _____________________________________ 18. H5 _________________________________

Sharon Tooney

Write the grid coordinates of the buildings

1. 173 Brocketts Way __________ 2. 175 Brocketts Way __________

3. 7 Woodbine Street __________ 4. 174 Brocketts Way __________

5. 9 Woodbine Street __________ 6. 340 Boehme Street __________

7. 11 Woodbine Street __________ 8. 115 Buckner Avenue __________

9. 114 Buckner Avenue __________ 10.5 Woodbine Street __________

11. 170 Brocketts Way __________ 12. 163 Atlas Street __________

13. 112 Buckner Avenue __________ 14. 172 Brocketts Way __________

15. 113 Buckner Avenue __________ 16. 163 Atlas Street __________

17. 1 Woodbine Street __________ 18. 110 Buckner Avenue __________

19. 111 Buckner Avenue __________ 20. 5 Woodbine Street __________

Sharon Tooney



STRAND: STATISTICS AND PROBABILITY

TERM: 1 2 3 3

WEEK: 1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Data 2 KEY CONSIDERATIONS OVERVIEW OUTCOMES A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › gives a valid reason for supporting one possible solution over another MA3-3WM › uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables MA3-18SP

Background Information Data selected for interpretation can include census data, environmental audits of resources such as water and energy, and sports statistics. Refer also to background information in Data 1. Language Students should be able to communicate using the following language: data, collect, category, display, table, column graph, scale, axes, two-way table, side-by-side column graph, misleading, bias. Refer also to language in Data 1.

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables • interpret data presented in 2-way tables • create a 2-way table to organise data involving 2 categorical variables, eg

• interpret side-by-side column graphs for 2 categorical variables • interpret & compare different displays of the same data set to determine the most appropriate display for the data set - compare the effectiveness of different student-created data displays - discuss the dis/advantages of different representations of the same data - explain which display is the most appropriate for interpretation of a particular data set - compare representations of the same data set in a side-by-side column graph & in a 2-way table Interpret secondary data presented in digital media and elsewhere • interpret data representations found in digital media & in factual texts - interpret tables & graphs from the media & online sources - identify & describe conclusions that can be drawn from a particular representation of data • critically evaluate data representations found in digital media & related claims - discuss the messages that those who created a particular data representation might have wanted to convey - identify sources of possible bias in representations of data in the media by discussing various influences on data collection and representation - identify misleading representations of data in the media



Sharon Tooney



2

Tell me a Story Students use the placement of points on a line graph, that represent the changes in the depth of water, to write a story. They are provided with the completed line graph with axes marked eg time and depth of water in centimetres. Students give their graph a suitable title. Students brainstorm a checklist of events for each point on the line graph that they will include in their story and then write their story. Students share their story with the class. The class uses the checklist and the placement of points on the line graph to assess each story.

Support to interpret graph graphs, paper and pencils

3

Media Graphs Students collect a variety of graphs used in the media and in factual texts. They consider each graph separately. Possible questions include: - what type of graph is used? What is its purpose? - what information can you interpret from the graph? - who would use the information? - who produced the graph and why? - is the graph misleading? Why? Students represent the information in a different way.

Support to represent information after using questioning techniques to determine choice of format

magazines, newspapers, texts, computers, paper and pencils, rulers

4

Divided Bar Graphs Students are provided with examples of divided bar graphs and discuss their common features. They collect data and make a concrete model of a divided bar graph by attaching unifix cubes in bands of colour eg yellow for blond hair. Students then draw their divided bar graph using an appropriate scale. Students discuss the relative sizes of the sections. Possible questions include: - what did you name your bar graph and the categories represented by each section? - what fraction of the total does each section represent? - how can you check that you are correct? Students represent the data on a spreadsheet.

Support as required bar graphs, unifix blocks, paper and pencils, computers

5

Mean Students are provided with information presented in the media that uses the term ‘average’ eg travel brochures, weather forecasts. They find the meaning of the terms ‘mean’ and ‘average’ and discuss their usage. The students discuss both words and their meanings. The students collect mean temperatures of a city and represent the data in a graph.

Support as required papers, magazines, travel brochures, weather forecasts, paper, pencils, rulers

9 Revision

10 Assessment

ASSESSMENT OVERVIEW

Sharon Tooney

maths program s3 yr 6 t1

Documents

negative number

number patterns

prime number

composite number

number line

positive number

sequence number

smaller number