maths program proforma yr 6 t2

7/22/2019 Maths Program Proforma Yr 6 T2

1/57

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


2/57

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.


3/57

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 avariety 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, positivenumber, negative number, integer, prime number,

compositenumber, 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 inrelation 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 & Australias 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


4/57

Sharon Tooney

CONTENT WEEK TEACHING, LEARNING and ASSESSMENT ADJUSTMENTS RESOURCES REG

Investigate

everyday

situations that

use integers;

locate and

represent these

numbers on anumber line

Identify and

describe

properties of

prime,

composite,

square and

triangular

numbers

1

Whole Number Basics 1

Revise some basic whole number facts previously learnt. Have students solve the following

problems:1. In the number 84869, which digit is in the hundreds place?

2. In the number 9765, what is the value of the digit 7?

3. Which number represents two million, four hundred thousand, fifty six?

4. Write the following number in numerals: four million, six hundred fifty thousand, twohundred fifty six

5. Write the following numerals with words: 4,650,256

6. 448 rounded to the nearest ten is

7. Round 6285 to the nearest hundred

8. Add 864 + 35 + 144 + 9 ___________

9.

10. When subtracting 25 from 104, the answer is?

Have students in small groups create a rap/rhyme/jingle for a given multiplication table.

Have each group perform for the rest of the class. Discuss whether they think that the

performances would enhance or not enhance their ability to remember the given table.Students should justify their answer with reasons.

Support: provide concrete

materials, adjust content to

student level

Whiteboard and

markers, paper and

pencils

2

Whole Number Basics 2

Revise some basic whole number facts previously learnt. Have students solve the following

problems:

1.

2. What is the product of 36 and 488?

3.

4. What is the product of 36 and 488?

5. How many times 25 goes into 2275 (Hint: divide 2275 by 25)

6.

7. Mark sells ice cream for a living on Monday through Friday. This week, he sold ice cream

for 245, 180, 200, 95, and 150 dollars. Mark spent 450 dollars to make those ice cream

What is Mark's profit?

8. A small train can hold 85 passengers. How many trains are needed to carry 1700



student level

Whiteboard and

markers, paper and

pencils
http://www.google.com.au/url?q=http://www.dennisholmesdesigns.com/cartoons_clipart.html&sa=U&ei=-pwrU5OsBISRkgXFrIG4Aw&ved=0CFMQ9QEwEw&sig2=6pNcFqjXRR8ow_1jlM59LQ&usg=AFQjCNEn7btqCedZyyN9SdW6he0s1otKuw


5/57

Sharon Tooney

passengers

9. A car travelled 420 miles in 4 hours. Do you think the driver should have gotten a speed

ticket?

10. Which division gives the b iggest remainder? A division of 56 by 9 or a division of 157 by

3?

Play a couple of rounds of Zap or Buzz Off to get students counting in basic number

patterns.

3

Identify a Rule For Number Patterns

Play a couple of rounds of Zap or Buzz Off to get students counting in basic 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, 10Pattern 10: 52, 47, 42, 37, 32, 27, 22

Descriptions by students should include:

- How did I work out what the operation was?

- How did I work out what the rule was?



student level

Whiteboard and

markers, paper and

pencils

4

Create a Number Pattern Based on a Rule

Revise the rules identified for different patterns last lesson. Explain to students thatfor the

following situations their job is to create a number pattern based on the rule stated. They

should create three different patterns for each rule.

Note:Some starting numbers are not practical to use. Allow students to change their

starting numbers if they have chosen ones that are too difficult, but make sure that they

account for these changes in a justification.

Rule 1: Add 4Rule 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? ___________

Support:allow students to

complete the task in pairs so

that they have someone to

discuss patterns with.

Extension:A pattern was

made using the following

rule: subtract 3. If the lastnumber in the pattern was

14, what were the previous

3 numbers? What would the

next 2 numbers be? Explain.

Whiteboard and

markers, paper and

pencils


6/57

Sharon Tooney

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:

5

Writing Rules From Number Patterns

Revise the format that patterns have been presented in previous lessons. Explain to

students that they may also find number patterns within tables of data, for example.

Outline to students that today they will start writing rules or equations from tables of

values, using activities, such as:

1. Jenny earned $2 for each hour she worked. See the table below:Hours Jenny

worked:

1 2 3 4 5

Money Jenny

earned:

2 4 6 8 10

- 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:

Try these:

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:Sams age 1 2 3 4 5

Michaels age 2 3 4 5 6

- 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:

Try these:

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:Tylers lollies 1 2 3 4 5

Michs lollies 4 5 6 7 8- 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?



student level

Whiteboard and

markers, paper and

pencils

6

Counter Patterns

This activity focuses on the patterns of adding another line of counters using triangular

numbers. Help students to focus on what is being added each time and to represent this in

a table or as a number sentence (e.g. 1 + 2 + 3 for a 3 line number).

Possible questions:

Support:move the counters

so that the first ones all

align, then work from there:

Whiteboard and

markers, paper and

pencils, counters


7/57

Sharon Tooney

- What shape do the counters form? So what do you think the next shape might be?

- How many counters are there in the bottom line of the triangle? Can you find a pattern?

- Where are the counters placed (in the gaps and on the ends)? So if we were going to add

another line of counters on the bottom here, where do you think the counters should go?

How many is this? How is this similar to the last shape that you made?

- Lets look at the bottom line of counters in each of the triangles. How many are in this

one? Now how many in this one? How many more is this? Now lets look at the third one.

How many more is this than the second one? Now lets look at the fourth one. How many

more is this than the third one? How much are we adding?

Make the pattern below, then work out what the pattern is and answer the questions.

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:How many lines? 1 2 3 4 5 6 7 8 9

How many counters in the bottom line? 1 2 3 4

How many counters altogether?

1 3 6 10How did we work out how many countersaltogether?

- 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

Discuss:

- 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?

Extension:Square numbers

are similar to triangular

numbers. Look at the

following patterns and work

out what the seventh

square number would be.

7

Subsets: Multiples and Factors

Multiples and factors have to do with multiplying or dividing numbers. Looking at these

examples, can you work out how the terms are used:Factors:

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

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

1. What operation do you think we are using to find the factors of 12? Explain.

2. Explain what you think factors might be.

3. Using your explanation of factors, list all the factors of 20. How did you know what

numbers were factors and which werent?

Support: provide X tables so

students can understand the

concepts without having to

remembering the facts

Use counters to create array

models. The number or

rows and columns in an

array relates to the factors

for a number

Extension:What number

Whiteboard and

markers, paper and

pencils


8/57

Sharon Tooney

4. What number are all of these factors for: 1 and 24, 2 and 12, 3 and 8, 4 and 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

1. What operation do you think we are using to find multiples? Explain.

2. Explain what you think multiples might be.

3. Using your explanation of multiples, list 10 multiples of 4:

4. List 10 multiples of 8:

5. List 10 multiples of 7:

Ask students to explain what multiples and factors are. Give some of your own examples.

has the following as

multiples: 36, 50

What number has the

following as factors: 1, 2, 3,

4, 5, 6

8

Prime and Composite Numbers

Prime numbers and composite numbers are defined by their factors. Explain to students

that theirjob is to examine the patterns below and determine what prime and composite

numbers are.

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?

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?

Ask students to explain what composite and prime numbers are. Give some of your own

examples.

Support: provide X tables so

students can understand the

concepts without having to

remembering the facts

Use counters to create array

models. The number or

rows and columns in an

array relates to the factors

for a number

Extension:Discuss thenumber 1 and the number

2. What kind of numbers are

they?

Whiteboard and

markers, paper and

pencils

9 Revision

10 Assessment

ASSESSMENT OVERVIEW


9/57

Sharon Tooney


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: Addition and Subtraction 2 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


conventions MA3-1WM






selects and applies appropriate strategies for addition and

subtraction with counting numbers of any size MA3-5NA


Refer to background information in Addition and Subtraction

1.

Language


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 add ition and subtraction

word problems

- use selected words to describe each step of the solution

process





Sustainability






Literacy

Numeracy





Work & enterprise


10/57

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.

1. 70 + __________ + 20 = 1520 2. 421 + 147 + __________ = 661

3. __________ + 110 + 339 = 451 4. 25 + __________ + 747 = 1586

5. 771 + __________ + 43 = 1166 6. 441 + 1 + __________ = 470

7. 894 + __________ + 826 = 1725 8. __________ + 262 + 81 = 984

9. 941 + 339 + __________ = 1334 10. 623 + 83 + __________ = 1456

11. 607 + 431 + __________ = 1137 12. __________ + 498 + 253 = 763

13. __________ + 126 + 351 = 535 14. 711 + 505 + __________ = 1293

15. 989 + __________ + 930 = 1981 16. __________ + 137 + 19 = 359

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:

1. 15 + 31 + __________ + 49 + 2600 = 2819 2. __________ + 91 + 86 + 151 + 2000 =

2337

3. 6 + 10 + 68 + __________ + 2900 = 3146 4. __________ + 800 + 80 + 147 + 11 =

1043

5. __________ + 76 + 39 + 111 + 300 = 531 6. 168 + 49 + __________ + 1500 =

1768

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 whynot and

offering an alternative strategy they would have preferred to use if give the option.

Working in pairs have students create 5 addends each for their partner to solve. Check and

discuss answers with each other.



whiteboards and

markers, paper and

pencils

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 thestrategy they employed,

giving reasons why.

1. __________ - 24519 = 4570 2. __________ - 4705 = 4532

3. 44780 - __________ = 29963 4. __________ - 10967 = 196

5. 36106 - __________ = 9959 6. 17563 - __________ = 6592



whiteboards and

markers, paper and

pencils
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=Submithttp://www.google.com.au/url?q=http://greenbeankindergarten.wordpress.com/2012/09/&sa=U&ei=gp0rU6vVBojrkAWEoYCoAQ&ved=0CFcQ9QEwFQ&sig2=88PZW3iv-P2DGUsbnDjMHg&usg=AFQjCNGSGEN9e7KQnewR9ZATEFxYSi3nGQhttp://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


11/57

Sharon Tooney

7. __________ - 36116 = 9185 8. 27144 - __________ = 16011

9. __________ - 1416 = 8577 10. 11545 - __________ = 3030

11. 15634 - __________ = 5557 12. __________ - 2107 = 1600

Check and discuss answers and strategies employed.

4

Cover them Up!

This is a game for two players. Instructions:

The men and monkeys on the game board have all entered a beauty contest. However, the

men have forgotten to put their clothes on! The monkeys are very embarrassed, so it is

your children's job to cover the men up with counters:

- Turn all of the cards upside down

- Players take it in turn to pick up two cards.

- Add the amount on the cards together. If the answer is the same as a number on one of

the boxes then you can cover up the man / monkey standing on it by placing a counter over

it.

- The winner is the first to cover up ten men (not monkeys, because monkeys are not

supposed to wear clothes anyway!)

See attached number cards and game board.

Variations:

- All of the cards are placed face upwards and each player has 30 seconds to pick two cards

which make any number on the playing board.

- Cover all of the men with counters. Remove one counter at a time and find the correct

two cards which make up that number.

Support:provide calculators

for students struggling with

mental calculations

Game board, game

card, counters

5

Deal or No Deal

This activity is designed to encourage students to use mental subtraction strategies to

quickly and accurately determine the answer to subtraction algorithms.

Using an IWB, the teacher provides an algorithm in a red box and an answer in a blue box:

If the blue box contains the correct answer, students call out deal if it is incorrect then

they call out No deal.

If No deal is called, a student is selected to provide the correct answer. A calculator could

be provided for this task to ensure quick and accurate answers, so that the game can keep

flowing.

Variation:

Students could play the same game using addition algorithms.

Support/Extension: instead

of using an IWB uses sets of

differentiated cards and

place students in ability

groups to play, with

students rotating roles as

the host to display cards.

IWB, calculators,

whiteboard and

markers, paper and

pencils

10

Revision and Assessment
http://www.google.com.au/url?q=http://greenbeankindergarten.wordpress.com/2012/09/&sa=U&ei=gp0rU6vVBojrkAWEoYCoAQ&ved=0CFcQ9QEwFQ&sig2=88PZW3iv-P2DGUsbnDjMHg&usg=AFQjCNGSGEN9e7KQnewR9ZATEFxYSi3nGQ


12/57

Sharon Tooney

ASSESSMENT OVERVIEW


13/57

1056 2284 3171 1000 863 9732 2165 398

25 7419 618 33 138 8391 7426 1234


14/57

1000 56 2200

84 2500 671

850 13 8652

1080 673 1492


15/57

8301 90 3713

3713 1004 230

2334 3344 6012

3000 514 519


16/57

Sharon Tooney


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: Multiplication and Division 2 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


conventions MA3-1WM






selects and applies appropriate strategies for multiplication

and division, and applies the order of operations to

calculations involving more than one operation MA3-6NA


Students could extend their recall of number facts beyond

the multiplication facts to 10 10 by also memorisingmultiples 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


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 solveproblems

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 innumber 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

Learning Across The CurriculumCross-curriculum priorities



Sustainability






Literacy Numeracy





Work & enterprise


17/57

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+[204]

=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

322x4=16x4

=64 multiplication & division only, therefore work

from left to right

32(2x4)=328

=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 ofoperations

recognise when grouping symbols are not necessary, eg 32

+ (2 4) has the same answer as 32 + 2 4


18/57

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

Using Related Facts

Write the following facts on the board.

1 32 = 32

2 32 = 64

32 = 128

8 32 =

32 = 512

- What are the missing numbers?

Explain that you were doubling each time. Ask the students to discuss in pairs how they

could find the other numbers in the 32 times table without carrying out any further

multiplication. Draw out that they could add the multiples together to work out other facts,

such as finding 6 32 by adding the answers to 2 32 and 4 32 together.

Give the students another two-digit number e.g. 26 and ask them to work out all its

multiples up to 16 using the same strategy, then to fill in the gaps by combining facts.

Check that their answers are correct and ask:

- For which of these multiples could you use a more efficient strategy? (e.g. 10, 5, 9, 11.)

Now demonstrate how you could use the multiples of 32 to generate other multiples of

32 by identifying and multiplying factors. Discuss 18 32, listing the factors of 18. Explain

that 18 32 could be found by multiplying the answer to 9 32 by 2 or by multiplying the

answer to 6 32 by 3. Explain that here you are using the factors of 18to helpmultiplication by 18. Record on the board to show this:

18 32

= 2 9 32

= 3 6 32

Set the students the task of finding 18 26 using a table in their books. Discuss the answers

with the class and ask how they would use this factor method to find 80 26, 24 26. Get

students to work through these on the board.

Give the students another number e.g. 43 and ask them to generate the multiplication

table and then use the factor method to work out other multiples of this number e.g. 56

43, 25 43, 120 43, 54 43. Draw the class together to look for a variety of methods e.g.

for 25 43 students might use 5 5 43 or halved 5 10 43 or halved and halved again

100 43.Provide additional examples for students to complete.

Support:provide concrete

materials and/or calculators

and multiplication tables

charts as a reference

Whiteboard and

markers, paper and

pencils

6

Order of Operation

Discuss with students, their understanding of the order of operations as discussed last

term. Students use their understanding of the order of operations to solve the following

equations. They may use a calculator if they choose, but they will need to determine the

order of operations before calculating. Work through the examples below to getstarted:

First rule: 4 x 5 x (9 + 3) = 240 The rule was:

Second rule: 4 + 5 + 3 x 6 = 27

Support:Use only two-step

processes

Extension:How many

different equations can you

write that make 12 and use

at least three different

Whiteboard and

markers, paper and

pencils, calculators


19/57

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 =

Provide additional examples for students to complete.

operations?

7

Interpreting Equations With Operations

Explain to students that In previous activities they have learned about order convention in

equations. Explain that they are to use that to help themto evaluate the following

situations and decide on some rules about which operation to perform first.

Example set 1:

(9 + 1) x 2 = 20 AND 2 x (9 + 1) = 20 What do you think that the rule is?(9 - 3) x 5 = 30 AND 5 x (9 - 3) = 30 (Brackets)

Example set 2:

2 x 5 + 1 = 11 AND 1 + 2 x 5 = 11 What do you think that the rule is?

10 2 + 3 = 8 AND 3 + 10 2 = 8 (Operations)

Questions:

1. Write the following words in the order that you perform them in an equation:

Multiplication and Division Brackets Addition and Subtraction

2. Is multiplication performed before division? Explain:

3. Is addition performed before subtraction? Explain:

4. When are the brackets completed?

Provide additional examples for students to complete.

Support:Use only two-step

processes

Extension:What can go in

the boxes to make this

equation true? Write asmany possibilities as you

can find.

(9 -) x= 15

Whiteboard and

markers, paper and

pencils

8Applying Order of OperationsUse what you have learned in the previous activities about order of convention to solve the

following equations. Select the answer that is correct. You may use a calculator.

1. 7 + 3 x 5= 2. 12 2 x 6= 3. 9 3 + 4 x 5= 4. 16 8 2= 5. 8 x (3 + 4)=

a. 50 b. 22 a. 0 b. 60 a. 35 b. 23 a. 12 b. 4 a. 28 b. 56

6. (8 x 3) + 4= 7. 8 (4 x 2)= 8. 8 4 x 2= 9. 8 (4 2)= 10. 8 4 2=

a. 28 b. 56 a. 1 b. 4 a. 1 b. 4 a. 6 b. 4 a. 2 b. 0

Extension: Put brackets intothe following equation so

that the answer is 10.88:

1.2 + 4.3 + 2.1 x 1.7 = 12.08

Whiteboard andmarkers, paper and

pencils
http://www.google.com.au/url?q=http://grade4beachycove.blogspot.com/2010_09_01_archive.html&sa=U&ei=3p0rU4XdFIXnkgWckID4DQ&ved=0CDcQ9QEwBQ&sig2=A_TvDVWodMUJ6AlUo5StWg&usg=AFQjCNGNEYbKZLPlkmumLaFxwEZacSrJ-Q


20/57

Sharon Tooney

11. 2 + 8 4= 12. (2 + 8) 2= 13. 7 + 2 3 x 2= 14. 8 9 3 + 5= 15. 9 3 x 4

5 + 2=

a. 2.5 b. 4 a. 5 b. 6 a. 3 b. 12 a. 0 b. 10 a. 9 b. 5

16. 9 3 x 4 (5 + 2)= 17. (5 2 + 3) (7 4)= 18. 5 (2 + 4) (7 4)=

a. 9 b. 5 a. 0 b. 2 Write your answer:

Describe what order you did things in to get the answers.

9 Solving Problems

Provide the following guide to the students for solving problems and discuss each step.

Step-by-step guide to solving problems1. Read the question. Underline key words that help you solve the problem.

2. Decide what operation(s) to use.

3. Write down the calculation(s) you are going to do. Use brackets if you need to.

4. Work out the approximate answer.

5. Decide how you will work out the calculation: mental, pencil and paper or calculator.

6. Do the calculation and interpret the answer.

7. Include any units such as kg, cm, $, pencils, tables.

8. Check that the answer makes sense.

Remember: if you are stuck, try to:

Describe the problem in your own words to a partner.

Talk through what you have done so far.

Break the problem up into smaller steps. Try it with simpler or fewer numbers.

Draw something to help you such as a picture, a table or number line.

Make a guess, see if it works, and if not try to improve it.

Problem solving problem examples:

1. There is space in the multi -storey car park for 17 rows of

30 cars on each of 4 floors.

How many cars on each of the 4 floors?

2. 196 children and 15 adults went on a school trip.

Coaches seat 57 people.

How many coaches were needed?

3. 960 marbles are put into 16 bags.

There is the same number of marbles in each bag.How many marbles are there in 3 of these bags?

4. In a dance there are 3 boys and 2 girls in every line.

42 boys take part in the dance.

How many girls take part?

5. I think of a number, add 3.7 and multiply by 5.

The answer is 22.5.

What was my number?

Support:partner work with

a peer tutor, adjusted

questions, concretematerials to recreate

problem

Whiteboard and

markers, paper and

pencils, problemsolving steps on

chart or IWB

10 Revision and Assessment
http://www.google.com.au/url?q=http://grade4beachycove.blogspot.com/2010_09_01_archive.html&sa=U&ei=3p0rU4XdFIXnkgWckID4DQ&ved=0CDcQ9QEwBQ&sig2=A_TvDVWodMUJ6AlUo5StWg&usg=AFQjCNGNEYbKZLPlkmumLaFxwEZacSrJ-Qhttp://www.google.com.au/url?q=http://grade4beachycove.blogspot.com/2010_09_01_archive.html&sa=U&ei=3p0rU4XdFIXnkgWckID4DQ&ved=0CDcQ9QEwBQ&sig2=A_TvDVWodMUJ6AlUo5StWg&usg=AFQjCNGNEYbKZLPlkmumLaFxwEZacSrJ-Q


21/57

Sharon Tooney

ASSESSMENT OVERVIEW


22/57

Sharon Tooney


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: Fractions and Decimals 2 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


conventions MA3-1WM






compares, orders and calculates with fractions, decimals

and percentages MA3-7NA


In Stage 3 Fractions and Decimals, students study fractions

with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. A unitfraction is any proper fraction in which the numerator is 1,

eg , , , , ...........

The process of writing a fraction in its 'simplest form'

involves reducing the fraction to its lowest equivalent form.

In Stage 4, this is referred to as 'simplifying' a fraction.

When subtracting mixed numerals, working with the whole-

number parts separately from the fractional parts can lead to

difficulties, particularly where the subtraction of the

fractional parts results in a negative value, eg in the

calculation of 2 - 1 , - results in a negative value.

Language


language: whole, equal parts, half, quarter, eighth, third,

sixth, twelfth, fifth, tenth, hundredth, thousandth, fraction,

numerator, denominator, mixed numeral, whole number,

number line, proper fraction, improper fraction, is equal to,

equivalent, ascending order, descending order, simplest

form, decimal, decimal point, digit, round to, decimal places,

dollars, cents, best buy, percent, percentage, discount,

sale price.

The decimal 1.12 is read as 'one point one two' and not 'one

point twelve'.

The word 'cent' is derived from the Latin word centum,

meaning 'one hundred'. 'Percent' means 'out of one hundred'

or 'hundredths'.

A 'terminating' decimal has a finite number of decimal

places, eg 3.25 (2 decimal places), 18.421 (3 decimal places).

Compare fractions with related denominators and locate and represent

them on a number line(ACMNA125)

model, compare &represent fractions with denominator of 2, 3, 4, 5, 6, 8,

10, 12 and 100 of a whole object, a whole shape & a collection of objects compare the relative size of fractions drawn on the same diagram

compare &order simple fractions with related denominators using

strategies such as diagrams, the number line, or equivalent fractions

find equivalent fractions by re-dividing the whole, using diagrams &

number lines

record equivalent fractions using diagrams & numerals

develop mental strategies for generating equivalent fractions, such as

multiplying or dividing the numerator & the denominator by the same

number

explain or demonstrate why 2 fractions are or are not equivalent

write fractions in their 'simplest form' by dividing the numerator & the

denominator by a common factor

recognise that a fraction in its simplest form represents the same value

as the original fraction

apply knowledge of equivalent fractions to convert between units oftime

Solve problems involving addition and subtraction of fractions with the

same or related denominators(ACMNA126)

add &subtract fractions, including mixed numerals, where 1 denominator

is the same as, or a multiple of, the other

convert an answer that is an improper fraction to a mixed numeral

use knowledge of equivalence to simplify answers when adding &

subtracting fractions

recognise that improper fractions may sometimes make calculations

involving mixednumerals easier

solve word problems involving the addition & subtraction of fractions

where 1 denominator is the same as, or a multiple of, the other

multiply simple fractions by whole numbers using repeated addition,

leading to a rule

Find a simple fraction of a quantity where the result is a whole number,with/out the use of digital technologies(ACMNA127)

calculate unit fractions of collections, with/out the use of digital tech

describe the connection between finding a unit fraction of a collection

& the operation of division

calculate a simple fraction of a collection/quantity, with/ out the use of

digital technologies

explain how unit fractions can be used in the calculation of simple

fractions of collections/quantities

solve word problems involving a fraction of a collection/ quantity

Add and subtract decimals, with/out the use of digital technologies, and





Sustainability






Literacy

Numeracy





Work & enterprise


23/57

Sharon Tooney

use estimation and rounding to check the reasonableness of answers

(ACMNA128)

add &subtract decimals with the same number of decimal places,

with/out the use of digital tech

add &subtract decimals with a different number of decimal places,

with/out the use of digital tech

relate decimals to fractions to aid mental strategies

round a number of up to 3 decimal places to the nearest whole number

use estimation &rounding to check the reasonableness of answers when

adding & subtracting decimals

describe situations where the estimation of ca lculations with decimals

may be useful solve word problems involving the addition & subtraction of decimals,

with/out the use of digital tech, including those involving money

use selected words to describe each step of the solution process

interpret a calculator display in the context of the problem

Multiply decimals by whole numbers & perform divisions by non-zero

whole numbers where the results are terminating decimals, with/out the

use of digital technologies(ACMNA129)

use mental strategies to multiply simple decimals by single-digit numbers

multiply decimals of up to 3 decimal places by whole numbers of up to 2

digits, with/out the use of digital tech

divide decimals by a 1-digit whole number where the result is a

terminating decimal

solve word problems involving the multiplication & division of decimals,

including those involving money

Multiply and divide decimals by powers of 10(ACMNA130)

recognise the number patterns formed when decimals are multiplied &

divided by 10, 100 & 1000

multiply & divide decimals by 10, 100 &1000

use a calculator to explore the effect of multiplying & dividing decimals

by multiples of 10

Make connections between equivalent fractions, decimals and percentages

(ACMNA131)

recognise that the symbol % means 'percent'

represent common percentages as fractions & decimals

recognise fractions, decimals & percentages as different

representations of the same value

recall commonly used equivalent percentages, decimals & fractions

represent simple fractions as decimals & as percentages

interpret & explain the use of fractions, decimals & percentages in

everyday contexts

represent decimals as fractions & percentages

equate 10% to , 25% to & 50% to

calculate commonpercentages (10%, 25%, 50%) of quantities, with/out

the use of digital tech

choose the most appropriate equivalent form of a percentage to aid

calculation

use mental strategies to estimatediscounts of 10%, 25% &50%

calculate the sale price of an item after a discount of 10%, 25% & 50%,

with/out the use of digital tech, recording the strategy & result


24/57

Sharon Tooney


Compare

fractions with

related

denominators

and locate and

represent them

on a number line

Solve problems

involving

addition and

subtraction of

fractions with

the same or

related

denominators

Find a simple

fraction of a

quantity wherethe result is a

whole number,

with/out the use

of digital

technologies

Add and

subtract

decimals,

with/out the use

of digital

technologies,and use

estimation and

rounding to

check the

reasonableness

of answers

Multiply

4

Recognising Equivalent Fractions

Using a fraction wall:

recap equivalent fractions, record = =

Ask child students to continue the sequence, repeating with thirds, sixths and twelfths.

- Can you write four more fractions equivalent to half? Repeat with , ,

Revise the meanings of numerator and denominator.

Reduce a fraction to its simplest form by cancelling common factors in the numerator and

denominator. Using the Fraction Cards attached, order fractions by converting them to

fractions with a common denominator and position them on a number line. Lead on to

questions such as:

- How do you know that is more than ?Establish the need to change to a common denominator. Discuss other examples such as

comparing and , and etc. Repeat with other examples if appropriate.

Discuss other examplesand encourage students to explain their reasoning.

Show a fraction family such as:

= =

- How can we work backwards to reduce to a family of fractions with smaller numbers?

Introduce harder examples e.g. where different factors are required and cancelling can

be introduced.

- Can you continue the fraction family?

- What is happening to the numerator / denominator?

Repeat with other fraction families.

Support:individual fraction

walls, individual support as

required

Fraction wall chart,

whiteboard and

markers, paper and

pencils, Fraction

cards

5

Improper Fractions and Mixed Numerals

Write on the board. Pose the question:

- Can you think of a different way to write this fraction?

If necessary, suggest writing a mixed number. Practise converting from mixed numbersto

improper fractions and back.

Support:individual fraction

walls, individual support as

required

Whiteboard and

markers, paper and

pencils

6

Recognising Equivalence Between the Decimal and Fraction Forms

Write the following fractions on the board:

Support:Provide

differentiated examples for

Whiteboard and

markers, paper and
http://cjr218.global2.vic.edu.au/files/2013/11/fractionwall-1ee7k9h.jpg


25/57

Sharon Tooney

decimals by

whole numbers

& perform

divisions by non-

zero whole

numbers where

the results are

terminating

decimals,

with/out the useof digital

technologies

Multiply and

divide decimals

by powers of 10

Make

connections

between

equivalent

fractions,decimals and

percentages

- Can you put these fractions in order?

Discuss how it can be done, leading to converting to hundredths.

- Would it have been easier it the numbers had already been written in hundredths or as

decimal fractions?

Discuss how they can be converted to decimal form (i.e. 0.3, 0.25, 0.08, 0.8) and use the

discussion to assess childrens previous knowledge of decimal notation in hundredths.

Repeat with other examples.

Draw a number line on the board. Give out the Fraction and Decimal cards attached.

- Can you place your cards in the correct place on the number line?

Encourage students to justify why they choose a particular place on the number line. Drawstudents attention to the fact that some students will want to put two or more cards in the

same place. For example , and 0.75.

Write on the board:

0.5 =

0.25 =

=

=

0.01 =

=

Discuss what goes in the boxesand have students complete.

pupils to practise ordering

fractions, decimals, then a

mixture of both on a

number line.

pencils, Fraction

and Decimal cards

7

Decimal Notation

Ask questions like:

- When do we meet decimals in real life?

- What in this room would measure 0.5m, 0.08m, 15.7cm etc.?

- What in this room holds 0.27 litres?

Explore metric units and the relationship between them.Students should be encouraged to

convert larger metric units to smaller and convert halves, quarters, tenths and hundredths

to larger units.

e.g.

kg =grams

3.5m =cm

1.25 km =metres2 litres =ml

500 ml =litres

6000 cm =m

100 mm =cm

Write on the board and discuss:

- If the running track is 500m how many laps are needed to run 2.5km?

Establish that conversion to the same unit of measurement is necessary to solve the

problem ;

Support/Extension:Some

students might be limited to

one decimal place whilst

others can be introduced to

thousandths and associated

word problems.

Whiteboard and

markers, paper and

pencils, conversion

charts
http://www.google.com.au/url?q=http://www.picstopin.com/400/fractions-cartoons-cartoon-picture-/http:%257C%257Cwww*cartoonstock*com%257Clowres%257Chsc3648l*jpg/&sa=U&ei=NJ4rU_iZNca9kAWH1oCoBA&ved=0CNkBEPUBMFY&sig2=40K9w7GxQNes-ZaXpg50Rw&usg=AFQjCNFASxxnpZUKYd_l7BJbiW7jvxKvhA


26/57

Sharon Tooney

- There are 2.54cm to 1 inch. 1 yard is 36 inches. About how many centimetres are there in

a yard?

Provide additional examples for students to work through independently.

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.picstopin.com/400/fractions-cartoons-cartoon-picture-/http:%257C%257Cwww*cartoonstock*com%257Clowres%257Chsc3648l*jpg/&sa=U&ei=NJ4rU_iZNca9kAWH1oCoBA&ved=0CNkBEPUBMFY&sig2=40K9w7GxQNes-ZaXpg50Rw&usg=AFQjCNFASxxnpZUKYd_l7BJbiW7jvxKvhA


27/57

Fraction Cards


28/57

Fraction and Decimal Cards


29/57

0.5 0.25 0.07 0.1

0.2 0.01 0.75 0.03

0.3 0.007 0.6 0.4


30/57

Sharon Tooney


STAGE: Year 6

ES1 S1 S2 S3

STRAND:

MEASUREMENT AND GEOMETRY

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Mass 2 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


conventions MA3-1WM




selects and uses the appropriate unit and device to

measure the masses of objects, and converts between units

of mass MA3-12MG


One litre of water has a mass of one kilogram and a volume

of 1000 cubic centimetres. While the relationship betweenvolume and capacity is constant for all substances, the same

volumes of substances other than water may have different

masses, eg 1 litre of oil is lighter than 1 litre of water, which

in turn is lighter than 1 litre of honey. This can be

demonstrated using digital scales.

Refer also to background information in Mass 1.

Language


language: mass, measure, scales, tonne, kilogram, gram.

Refer also to language in Mass 1.

Connect decimal representations to the metric system

(ACMMG135)

recognise the equivalence of whole-number and decimalrepresentations of measurements of mass, eg 3 kg 250 g is

the same as 3.25 kg

interpret decimal notation for masses, eg 2.08 kg is the

same as 2 kilograms and 80 grams

measure mass using scales and record using decimal

notation of up to three decimal places, eg 0.875 kg

Convert between common metric units of mass

(ACMMG136)

convert between kilograms and grams and between

kilograms and tonnes

explain and use the relationship between the size of a

unit and the number of units needed to assist indetermining whether multiplication or division is

required when converting between units, eg 'More

grams than kilograms will be needed to measure the

same mass, and so to convert from kilograms to grams, I

need to multiply' (Communicating, Reasoning)

solve problems involving different units of mass, eg find the

total mass of three items weighing 50 g, 750 g and 2.5 kg

relate the mass of one litre of water to one kilogram





Sustainability






Literacy

Numeracy





Work & enterprise


31/57

Sharon Tooney


Connect decimal

representations

to the metric

system

Convert between

common metric

units of mass

1

School Bags Full

Students in groups of four or five find the average mass of their full school bags. This

measurement is used to calculate the mass of all bags in the class. Students predict the

mass of all bags in the school.

Extension:how many

teachers bags or baskets

make a tonne?

School bags, scales,

calculators, pencils

and paper

2

How Many Kids to the Elephant?

Students find the mass of the average student in the class. Students estimate and then

calculate, how many students would have the same mass as an elephant (average 4

tonne).Note:students should not be required to publ ically reveal their weight. Provision should be

made for them to weigh themselves and record on a piece of paper and hand this to the

teacher to use for final calculation.

Support:individual support

as required, questioning

techniques

Bathroom scales,

calculators, pencils

and paper

3

Largest?

Students work in pairs or small groups to investigate:

Were dinosaurs the largest living creatures ever? Students research the question and order

the animals that they have studied, from heaviest to lightest. Calculate the d ifference in

mass between the heaviest and lightest animals in the list.

Support:peer tutor

grouping strategies

Access to research

material, pencils and

paper

4

Cars

Students use car handbooks or brochures to find the mass of a small car. Collect

information from the local bus company to find the mass of full and empty buses.

Estimate and then calculate how many small cars have the equivalent mass of a full bus.


as required

Car brochures, local

bus company,

calculators, paper

and pencils

5

Cool!

Use ice cube trays, find how many ice cubes would be needed to make a tonne of ice.


as required

Ice cube trays, litre

measures,

calculators, paper

and pencils

6

Towering Tins

Students calculate the height of a tower of items where the tower has a total mass of 1

tonne.

Examples of items may include: drink cans (full or empty), books, br icks, an average Stage

3 student.


as required

Kitchen or bathroom

scales, calculators,

paper and pencils

7

Follow That Jellybean

Students investigate the length of a line of jellybeans, if 0.5t of jellybeans were placed end

to end. How long would the line be?


as required

Kitchen scales,

jellybeans, rulers or

tape measures,calculators, paper

and pencils

8

Tonnes of Tables

Students work in pairs or small groups to find the mass of all of the desks in the school.

Variation:

Students nominate objects or materials to measure.

Support:peer tutor

grouping strategies

Bathroom scales,

calculators, paper

and pencils

9

A Wet Week

Students calculate the mass of rainwater that would fall on a football field in a wet week.

Extension:students

compare the mass of water

Rain gauge, weather

reports, calculators,
http://www.google.com.au/url?q=http://www.dreamstime.com/stock-photography-weightlifter-image711582&sa=U&ei=qZ4rU_mtJ4f1kQWVwoCQCQ&ved=0CEMQ9QEwCg&sig2=1aLzpZUNRQJKmyo4GtwS2w&usg=AFQjCNEbYvNI8QmBBkUxRKG36fXP0IsIoQ


32/57

Sharon Tooney

Either, measure rainfall, or select reports of rainfall from the newspaper or television

weather reports. Calculate by finding the volume of water on the football field and then

converting to units of mass.

on a football field to a

netball court.

tape measures or

trundle wheels,

pencils and paper

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.dreamstime.com/stock-photography-weightlifter-image711582&sa=U&ei=qZ4rU_mtJ4f1kQWVwoCQCQ&ved=0CEMQ9QEwCg&sig2=1aLzpZUNRQJKmyo4GtwS2w&usg=AFQjCNEbYvNI8QmBBkUxRKG36fXP0IsIoQ


33/57

Sharon Tooney


STAGE: Year 6

ES1 S1 S2 S3

STRAND:


TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Angles 2 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


conventions MA3-1WM

measures and constructs angles, and applies angle

relationships to find unknown angles MA3-16MG


Students should be encouraged to give reasons when finding

unknown angles.

Language


language: angle, right angle, straight angle, angles on a

straight line, angle of revolution, angles at a point, vertically

opposite angles.

A pair of adjacent angles has a common vertex and a

common arm.

Investigate, with and without the use of digital

technologies, angles on a straight line, angles at a point,

and vertically opposite angles; use the results to findunknown angles(ACMMG141)

identify and name angle types formed by the intersection

of straight lines, including right angles, 'angles on a straight

line', 'angles at a point' that form an angle of revolution, and

'vertically opposite angles'

recognise right angles, angles on a straight line, and

angles of revolution embedded in diagrams (Reasoning)

identify the vertex and arms of angles formed by

intersecting lines (Communicating)

recognise vertically opposite angles in different

orientations and embedded in diagrams (Reasoning)

investigate, withand without the use of digitaltechnologies, adjacent angles that form a right angle and

establish that they add to 90

investigate, withand without the use of digital

technologies, adjacent angles on a straight line and establish

that they form a straight angle and add to 180

investigate, with and without the use of digital

technologies, angles at a point and establish that they form

an angle of revolution and add to 360

use the results established for adjacent angles that form

right angles, straight angles and angles of revolution to find

the size of unknown angles in diagrams

explain how the size of an unknown angle in a diagram

was calculated (Communicating, Reasoning)

investigate, withand without the use of digital

technologies, vertically opposite angles and establish that

they are equal in size

use the equality of vertically opposite angles to find the size

of unknown angles in diagrams



Aboriginal &Torres Strait Islander histories & cultures Asia & Australias engagement with Asia

Sustainability






Literacy

Numeracy





Work & enterprise


34/57

Sharon Tooney


Investigate, with

and without the

use of digital

technologies,

angles on a

straight line,

angles at a point,

and vertically

opposite angles;

use the results to

find unknown

angles

1

Revise Angles

What is an Angle?

Angles are a measure of turn. Follow these simple rules for angles:

Angles are measured in degrees. The sign for degrees is .

One whole turn is 360. a is an example of a whole turn.

One quarter turn is 90or a right angle. b is an example of a quarter turn.

One half turn is 180 or a straight line. c is an example of a half turn.

Types of angles

a) An angle less than 90 is acute.

b) An angle between 90 and 180 is obtuse.

c) An angle greater than 180 is reflex.

Vertically opposite anglesThe two angles marked in this diagram are called vertically opposite angles and are equal

to each other.

Using a protractor:

Angles are measured using a protractor. You can guess the rough size of an angle by

looking to see if it's acute or obtuse, but you'll need a protractor for a precise

measurement.

Here's how to use a protractor to measure an angle:

- Line up the protractor so the 'cross hair' i s exactly on the angle.

- Line up one of the lines with the 0 line on the protractor.- See which numbers the angle comes between. If it is between 30 and 40, the angle must

be thirty something degrees.

- Count the small degrees up from 30. In this example, the angle is 35.

http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html

Support:Individual support

as required, particularly with

manipulation of protractors

Computers, angles

reference posters or

equivalent on IWB,

whiteboard and

markers, paper and

pencils, protractors,

Angles Revision BLM
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.htmlhttp://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.htmlhttp://www.google.com.au/url?q=http://www.teachingideas.co.uk/maths/contents_angles.htm&sa=U&ei=Bp8rU4nNB8aKlAXKx4HwCA&ved=0CIsBEPUBMC8&sig2=wgUV-IeIifb6OzXYx8TFWg&usg=AFQjCNEhzsulu9zzzy71mi076uSmXzokWghttp://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html


35/57

Sharon Tooney

Perpendicular and parallel lines:

- Parallellines are always the same distance apart, like ain the example.

- Perpendicularlines cross at right angles to each other, like b in the example.

Complete attached worksheet Angles Revision.

2Determining Angles By DegreesProvide students with a list of measurements in degrees and have them determine if the

angle described is acute, obtuse, right or straight. Examples may include:

1) 90 Right 2) 88 Acute3) 180 Straight4) 155 Obtuse5) 6 Acute

6) 172 Obtuse7) 45 Acute8) 171 Obtuse 9) 160 Obtuse10) 95 Obtuse

11) 33 Acute 12) 90 Righ13) 120 Obtu 14) 36 Acute 15) 5 Acute

16) 180 Strai 17) 48 Acu 18) 55 Acute 19) 146 Obtuse20) 114 Obt

Students should be encouraged to draw each angle with a protractor.

Support:Individual supportas required, particularly with

manipulation of protractors

Whiteboard andmarkers, paper and

pencils, protractors,

rulers

3

Determining the Size of Angles

Provide students with a variety of angles in which they must use the given measurements

to determine the total degrees of the angle or the amount of degrees needed to give the

total degrees of a given angle. Examples may include:

- Determine the value of 'A'.

Examples should include; right angles, acute angles, obtuse angles, straight angles, reflex

angles, angles of revolution and vertically opposite angles.


as required, calculators to

complete addition and

subtraction of angle values

Whiteboard and

markers, paper and

pencils

4

Angles In Construction

Provide students with laminated copies of the attached iconic buildings from around the

world (2 sets of each should be enough for a large class). Each building has a series of

naturally occurring angles found in the buildings construction highlighted for the students.

Each of these angles needs to be measured with a protractor and the results recorded in

the students workbooks.

Students should work in pairs and swap their picture with another pair when complete.

Students could be encouraged to estimate the size of the angle prior to measure.


as required, particularly with

manipulation of protractors,

per tutor strategies in

grouping

Iconic Building BLM,

protractors, pencils

and paper
http://www.google.com.au/url?q=http://www.teachingideas.co.uk/maths/contents_angles.htm&sa=U&ei=Bp8rU4nNB8aKlAXKx4HwCA&ved=0CIsBEPUBMC8&sig2=wgUV-IeIifb6OzXYx8TFWg&usg=AFQjCNEhzsulu9zzzy71mi076uSmXzokWg


36/57

Sharon Tooney

When a set number of pictures have been completed by each pair, discuss results as a

class. Discussion should include the accuracy of the students measurements, the

effectiveness of their estimation skills and the names of the types of angles measured.

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.teachingideas.co.uk/maths/contents_angles.htm&sa=U&ei=Bp8rU4nNB8aKlAXKx4HwCA&ved=0CIsBEPUBMC8&sig2=wgUV-IeIifb6OzXYx8TFWg&usg=AFQjCNEhzsulu9zzzy71mi076uSmXzokWg


37/57

ANGLES REVISION

Estimate the size of each angle in the triangle and write down what kind of angle itis (right, acute, obtuse). When you have done that, measure each angle carefullyusing your protractor. Write down what kind of triangle it is too.

My estimation Measurement Names of angles

A: __________ A: __________ A: ____________________

B: __________ B: __________ B: ____________________

C: __________ C: __________ C: ____________________


38/57

a

b

c


39/57

a

b


40/57

ab

c


41/57

a

b

c

d


42/57

a

b

c

d


43/57

a

b

c

d


44/57

a

b


45/57

a

b


46/57

a

b

c

d


47/57

Sharon Tooney


STAGE: Year 6

ES1 S1 S2 S3

STRAND:


TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: 3D 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

identifies three-dimensional objects, including prisms and

pyramids, on the basis of their properties, and visualises,

sketches and constructs them given drawings of different

views MA3-14MG

Background information

In Stage 3, students are continuing to develop their skills of

visual imagery, including the ability to perceive and hold an

appropriate mental image of an object or arrangement, and

to predict the orientation or shape of an object that has been

moved or altered.

Refer also to background information in Three-Dimensional

Space 1.

Language


language: object, shape, three dimensional object (3D

object), prism, cube, pyramid, base, uniform cross-section,

face, edge, vertex (vertices), top view, front view, side view,

net.

Construct simple prisms and pyramids(ACMMG140)

create prisms and pyramids using a variety of materials, eg

plasticine, paper or cardboard nets, connecting cubes

construct as many rectangular prisms as possible using a

given number of connecting cubes (Problem Solving)

create skeletal models of prisms and pyramids, eg using

toothpicks and modelling clay or straws and tape

connect the edges of prisms and pyramids with the

construction of their skeletal models (Problem Solving)

construct three-dimensional models of prisms and

pyramids and sketch the front, side and top views

describe to another student how to construct or draw a

three-dimensional object (Communicating)

construct three-dimensional models of prisms and

pyramids, given drawings of different views



Aboriginal &Torres Strait Islander histories & cultures Asia & Australias engagement with Asia

Sustainability






Literacy

Numeracy





Work & enterprise


48/57

Sharon Tooney


Construct simple

prisms and

pyramids2

Properties of 3D Shapes

Show the class a closed cardboard box, an empty container such as a cerealbox.

- If this box was opened out into asingle piece of cardboard, what would it look like?

Give the students centimetre squared paper and ask them to sketch the single piece of

cardboard to give the shape but not to scale, only a small diagram is needed.

Remind them this single piece of cardboard is called the net of the shape it can be folded

into the shape exactly. Agree the net is something like the shape below:

Explainthat the box is called a rectangular prism and you want the students to work on

cubes now. Discuss the differences between cubes and rectangular prisms, reminding them

that all the faces of a cube are identical squares.

- What is the net of a closed cube with dimensions 3cm by 3cm by 3cm?

Give students time to sketch a net on the squared paper. Collect one correct net from the

students and discuss why this works.

Sketch the shape below on the board:

- Could this be the net of a cube?Agree that it cannot be and if necessary demonstrate using a strip of six squares.Ask

students to continue to find nets for the 3cm cube on the cm squared paper. Collect

answers, discuss which are correct and why. Establish there is more than one answer and

compare different nets for the cube.

Remind children of the names and features of prisms and pyramids. Explain that the cube

and rectangular prism are both prisms, and the name given to any pyramid refers to the

shape of the base, e.g. square-based pyramid. Hold up a square-based pyramid.

- How many faces has it got?

- What shapes are they?

Ask students what pyramids would be formed by the following nets:


as required, particularly

sketching nets

Cardboard box,

whiteboard and

markers, paper and

pencils, centimetre

square paper,

rulers

3

Visualising 3D Shapes From Drawings

Display the diagram below on IWB and/or provide to students as a BLM. Explain that the

diagrams shows four views of the same object which is made up of cubes. Discuss the

shape.

Support:ensure concrete

models of each shape are

available for students to

manipulate

IWB, whiteboard

and markers,

interlocking cubes,

dot paper, paper
http://edit%2879404%29/


49/57

Sharon Tooney

- How many cubes were used to make the shape?

- Can you make the shape?

Establish that six cubes were used and get the students to make the shape using

interlocking cubes, working in pairs or small groups. Ask students to hold their shape up inthe same position as shown by the bottom left view. Get the students to rotate their shapes

through quarter turns to show each of the four views, working anti-clockwise.

In pairs, ask students to use five of their six cubes to make a shape of their own. Using a

shape made from six cubes show the students how to draw a view of the shape on dot

paper.Emphasise starting with the front edge and working away from this to build up the

cubes that make the shape.

Give students a sheet of dot paper and with ruler and pencil get them to draw a view of

their own shapes. Pairs swap their drawings and make the shapes represented by the other

pairs. Discuss the 3D drawings and any difficulties the students had.

Display the diagram below for the students:

- How many cubes were used to make this shape?

- Are there any cubes we cannot see?

Encourage students to speculate about the number of cubes and decide that the greatest

number of cubes could be more than 14.

- What is the least number of cubes we could use to make this shape?

Give students time to make the shape. Conclude that 10 cubes is the least number. Display

the diagram of two views of the shape, below for the students:

- How many cubes now? (Establish there are 12 cubes needed, get children

maths program proforma yr 6 t2

Documents