PR1ME Mathematics – Year 3 Teacher's Guide (Sample)

100% coverage of New Zealand Mathematics and Statistics Curriculum for Phases 1-3

All-in-one teaching support with clear explanations, assessments and resources Easy-to-follow structured lesson guidance that simplifies planning and teaching Math Pro for additional digital teaching resources and online professional development

Strand(s): Number

• CB: pp. 181–182

• Math Pro: Recall

• Recognise and name notes and coins

Scheme of Work

Let’s Remember

• Count and tell the amount of money in a group of coins only or a group of notes only, using more than one denomination

• Add and subtract numbers up to 100

1: Dollars and Cents New Zealand Curriculum Year 3: Number — Financial mathematics

Unit

1.1 Knowledge ( ★ ) and Practices ( ◆ )

★ New Zealand curr ency is a decimal system of dollars made up of 100 cents.

◆ Repr esenting currency values of mixed dollars and cents without using decimal notation (e.g. $2 and 50 cents)

• CB: pp. 183–184

• PB: pp. 132–133

• Math Pro: Practice

• Play money

• Count and tell the amount of money in a group of notes and coins in dollars and cents

1.1 Counting dollars and cents

1.2 Knowledge ( ★ ) and Practices ( ◆ )

★ New Zealand curr ency is a decimal system of dollars made up of 100 cents.

◆ Making amounts of money using oneand two-dollar coins and 5-, 10-, 20-, 50-, and 100-dollar notes

• CB: pp. 185–186

• PB: pp. 134–135

• Math Pro: Practice

• Play money

• Make up an amount of money using a group of coins and notes

1.2 Making up an amount of money

2: Shopping

Unit

New Zealand Curriculum Year 3: Number — Financial mathematics

2.1 Knowledge ( ★ )

★ Finding the total cost and giving change with money involves addition and subtraction.

• CB: pp. 187–188

• PB: pp. 136–137

• Math Pro: Practice

• Play money

• Read the price of an object and pay for it

2.1 Adding amounts of money

• Add money in cents up to $1

• Add money in dollars up to $100

2.2 Knowledge ( ★ ) and Practices ( ◆ )

★ Finding the total cost and giving change with money involves addition and subtraction.

◆ Using addition and subtraction to give change

• CB: pp. 189–190

• PB: pp. 138–139

• Math Pro: Practice

• Play money

• Read the price of an object and pay for it

2.2 Subtracting amounts of money

• Subtract money in cents up to $1

• Subtract money in dollars up to $100

• Count change like a cashier in a purchasing situation

Unit 3: Problem Solving

New Zealand Curriculum Year 3: Number — Financial mathematics

3.1 Knowledge ( ★ ) and Practices ( ◆ )

★ Finding the total cost and giving change with money involves addition and subtraction.

◆ Using addition and subtraction to give change

• CB: pp. 191–194

• PB: pp. 140–141

• Math Pro: Practice

• Solve 1-step word problems involving money

3.1 W ord problems

• CB: pp. 195–197

• Math Pro: Assessment

• 1 copy of Maths Journal (BM8.1) per student

• Solve a non-routine problem involving money using the strategy of making a supposition

• Solve a non-routine problem involving money using the strategy of drawing a bar model

The suggested duration for each lesson is 1 hour.

Chapter 8 Money

Chapter Overview

Let’s Remember Unit 1: Dollars and Cents Unit 2: Shopping Unit 3: Problem Solving

Let's Remember Recall:

1. Recognising and naming notes and coins (CB1 Chapter 10)

2. Counting and telling the amount of money in a group of coins only or a group of notes only, using more than one denomination (CB2 Chapter 11)

3. Adding and subtracting numbers up to 100 (CB3 Chapter 3)

EXPLORE

Have students read the word problem on CB p. 182. Discuss with students the following questions:

•Do you think we should use reusable shopping bags? Why?

•How can reusable shopping bags help the environment?

•Can you think of other ways to help the environment?

Have students form groups to complete the tasks in columns 1 and 2 of the table. Let students know that they do not have to solve the word problem. Ask the groups to present their work.

Tell students that they will come back to this word problem later in the chapter.

1.1 Counting dollars and cents

Unit 1: Dollars and Cents

1.1 Counting dollars and cents

Let's Learn Let's Learn

Objective:

•Count and tell the amount of money in a group of notes and coins in dollars and cents

Materials:

•Play money

Resources:

•CB: pp. 183–184

•PB: pp. 132–133

Stages: Concrete Experience and Pictorial Representation

Have students work in groups. Distribute play money to each group.

Have each group put a ten-dollar note, 2 fifty-cent coins, a twenty-cent coin and 2 ten-cent coins on the table.

Say: We want to find the total amount of money. Point out to students that there are 2 fifty-cent coins. Have them recall that $1 is equal to 100c. So, 2 fifty-cent coins are equal to $1.

Ask: How many dollars are there? (11) How many cents are there? (40)

Say: We read this as eleven dollars and forty cents. Let us write this amount.

Stage: Abstract Representation

Write: $11 and 40 cents

Say: Let us count the amount of money again. Count the dollars, then count the cents. $10, $10 and 50 cents, $11, $11 and 20 cents, $11 and 30 cents, $11 and 40 cents. There is $11 and 40 cents.

Point out to students that different countries use different types of money, such as the British pound, Indian rupee and Thai baht.

Let's Do Let's

Task 1 requires students to count and write the amount of money in a group of notes and coins.

Let's Practise Let's

Task 1 requires students to count and match the amounts of money in groups of coins or groups of notes and coins.

1.2 Making up an amount of money

Let's Learn Let's Learn

Objective:

•Make up an amount of money using a group of coins and notes

Materials: •Play money

Resources:

•CB: pp. 185–186

•PB: pp. 134–135

Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students work in pairs. Distribute play money to each pair. Get students to role-play a scenario where one is ‘Kiri’ and the other is a shopkeeper.

Have students look at the picture on CB p. 185. Say: Kiri wants to buy a book for $28. She has some money in her wallet.

Have students who are role-playing as ‘Kiri’ select the correct notes and coins from the play money to show the amount of money Kiri has in her wallet.

Have students who are role-playing as shopkeepers say the price of the book, $28. Have students who are role-playing as ‘Kiri’ choose the respective play notes and play coins to pay for the book.

Ask students who are role-playing as shopkeepers to check that the amount of money is correct.

Say: We count forwards to make $28. We start with the twenty-dollar note, then the five-dollar note, and so on.

Have students count forwards the money with you: $20, $25, $27, $28.

Ask: Which notes and coins should Kiri use to pay for the book? (1 twenty-dollar note, 1 five-dollar note, 1 two-dollar coin and 1 one-dollar coin.)

1.2

Making up an amount of money

Let's Do Let's Do

Task 1 requires students to make up an amount of money using a group of coins and notes.

Let's Practise Let's Practise

Task 1 requires students to make up an amount of money using a group of coins and notes.

EXPLORE

Have students go back to the word problem on CB p. 182.

Ask: Can you solve the problem now? (Answer varies.) What else do you need to know? (Answer varies.)

Students are not expected to be able to solve the problem now. They will learn more skills in subsequent lessons and revisit this problem at the end of the chapter.

2.1 Adding amounts of money

a) Kalanei buys an apple and an orange.

Kalanei has to pay.

40c + 50c = 90c

Kalanei has to pay 90c.

b) Mrs Walker buys a roast chicken and a box of cupcakes. How much does she have to pay? $14 + $8 = $ Mrs Walker has to pay $

Unit 2: Shopping

2.1 Adding amounts of money

Let's Learn Let's Learn Objectives:

•Read the price of an object and pay for it

•Add money in cents up to $1

•Add money in dollars up to $100

Materials:

•Play money

Resources:

•CB: pp. 187–188

•PB: pp. 136–137

(a) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students look at the pictures in (a) on CB p. 187.

Say: Kalanei buys an apple and an orange.

Ask: What is the price of the apple? (40c) What is the price of the orange? (50c)

Ask: How can we find how much money Kalanei has to pay? (Add the prices of the apple and the orange.)

Write: 40c + 50c = ______

Point out to students that they can add money the same way they add whole numbers. Ask a student to work out the addition on the board. Have him/her complete the addition sentence on the board.

Remind students to include the c symbol in the addition sentence.

Say: Kalanei has to pay 90c.

Ask two students to role-play a scenario where one is ‘Kalanei’ and the other is a cashier. Give ‘Kalanei’ some play money. ‘Kalanei’ pays the ‘cashier’ 90c and the ‘cashier’ counts to check that the amount of money given is correct.

(b) Stages: Concrete Experience, and Pictorial and Abstract Representations

Follow the procedure in (a) to add amounts of money in dollars.

Let's Do Let's and Let's Practise

Task 1 requires students to add money in cents up to $1 and in dollars up to $100.

2.2 Subtracting amounts of money

Let's Learn Let's Learn

Objectives:

•Read the price of an object and pay for it

•Subtract money in cents up to $1

•Subtract money in dollars up to $100

•Count change like a cashier in a purchasing situation

Materials:

•Play money

Resources:

•CB: pp. 189–190

•PB: pp. 138–139

Vocabulary:

•change

(a) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students look at the picture in (a) on CB p. 189.

Say: Anna has 50c and does not have enough money to buy the eraser.

Ask: What is the price of the eraser? (70c) How can we find how much more money Anna needs? (Subtract the amount of money Anna has from the price of the eraser.)

Write: 70c – 50c = ______

Point out to students that they can subtract money the same way they subtract whole numbers. Ask a student to work out the subtraction on the board. Have him/her complete the subtraction sentence on the board.

Remind students to include the c symbol in the subtraction sentence.

Say: Anna needs 20c more to buy the eraser. Invite a student to the front of the class and give the student some play money. Ask the student to take out a fifty-cent coin.

Say: [Name of student] has 50c. He/she wants to buy an eraser that costs 70c.

Have the student take out play money that makes 70c with 50c. The student should take out 20c.

(b) Stages: Concrete Experience, and Pictorial and Abstract Representations

Have students look at the picture in (b) on CB p. 189.

Say: Mr Evans buys a toaster and gives the cashier $50.

Ask: What is the price of the toaster? ($37) How much does Mr Evans give the cashier? ($50) Say: The price of the toaster is $37 but Mr Evans pays more than $37. He will get some money back. The money he gets back is called change.

2.2 Subtracting amounts of money

a) Anna has 50c. She does not have enough money to buy the eraser.

Subtract 50c from the price of the eraser to find out how much more money Anna needs.

70c – 50c = 20c

Anna needs 20c more to buy the eraser.

b) Mr Evans buys a toaster. He gives the cashier $50.

Subtract the price of the toaster from $50.

$50 – $37 = $13

Mr Evans gets $13 in change

We can also count forwards from the price of the toaster to the amount given to the cashier. 37 38 39 40 50 + 1 + 1 + 1 + 10

We count forwards 13 so the change is $13.

Ask: How can we find the amount Mr Evans gets in change? (Subtract the price of the toaster from $50.)

Write: $50 – $37 = ______

Ask a student to work out the subtraction on the board. Have him/her complete the subtraction sentence on the board.

Remind students to include the $ symbol in the subtraction sentence.

Say: Mr Evans gets $13 in change. Besides subtraction, we can also count forwards from the price of the toaster to the amount given to the cashier to find the change.

Invite a student to the front of the class and give the student a fifty-dollar play note.

Say: [Name of student] wants to buy a toaster that costs $37. He/she pays me $50.

Ask the student to pass you the fifty-dollar note.

Say: Let us find out how much is the change by counting forwards from $37 to $50. We can use a number line to help us find the change.

Draw a number line on the board with ‘37’ and ‘50’ marked on two ends of the number line. Show students a one-dollar coin and place it on the desk.

Say: We count forwards 1 from 37.

Draw a curved arrow from 37 to 38 on the number line and label it ‘+ 1’.

(continued on next page)

Repeat the above procedure to count forwards 1 from 38 to 39 and from 39 to 40 and also count forwards 10 from 40 to 50.

Say: The note and coins on the desk are the change.

Guide students to count the amount of change. Say: The amount of change is $13. We can also count the amount of change using the number line.

Guide students to use the labels on the curved arrows of the number line to count the amount of change.

Say: The amount of change is $13.

Let's Do Let's

Task 1 requires students to count change like a cashier in a purchasing situation.

Task 2 requires students to subtract money in dollars up to $100.

Let's Practise Let's Practise

Task 1 requires students to subtract money in cents up to $1 and in dollars up to $100, and count change like a cashier in a purchasing situation.

Unit 3: Problem Solving

3.1 Word problems

Let's Learn Let's Learn

Objective:

•Solve 1-step word problems involving money

Resources:

•CB: pp. 191–194

•PB: pp. 140–141

1. Have students read the word problem on CB p. 191.

1. Understand the problem. Pose the questions in the thought bubble in step 1.

2. Plan what to do.

Point out to students that they can draw a bar model to show the amounts of money Devi saved.

3. Work out the Answer.

Say: Devi saved $29 in June.

Draw a bar to represent the amount of savings in June and label it as shown on the page.

Say: Devi saved more in July than in June, so we draw a longer bar to represent the amount of savings in July.

Draw a longer bar to represent the amount of savings in July.

Ask: How much more did she save in July than in June? ($15)

Label the difference in savings in the bar model as shown on the page.

Explain that we place a question mark in the bar model to indicate what we have to find.

Label the longer bar with a ‘?’ to show that we have to find the amount of money Devi saved in July.

Ask: How can we find the amount of money Devi saved in July? (Add the amount of money saved in June and the difference in savings.)

Write: $29 + $15 = ______

Ask a student to work out the addition on the board.

Say: Devi saved $44 in July.

3.1 Word problems

4. Check if your answer is correct. Guide students to check their answer by subtracting the amount of money Devi saved in June from the amount of money she saved in July to see if it is equal to $15.

Say: Since $44 – $29 is equal to $15, the answer is correct.

5. + Plus Solve the problem in another way. Have students try to solve the problem in a different way. Have 1 or 2 students share their methods. If students are unable to solve the problem in a different way, explain the method shown on CB p. 192.

Ask: Which method do you prefer? Why? (Answers vary.)

2. Have students read the word problem on CB p. 192.

1. Understand the problem. Pose the questions in the thought bubble in step 1.

2. Plan what to do.

Point out to students that they can draw a bar model to help them solve the word problem.

3. Work out the Answer

Say: There are 4 plates so we draw 4 units.

Draw 4 units to represent 4 plates as shown on the page.

Ask: How much does a plate cost? ($2) Label the cost of a plate in the bar model as shown on the page. Explain that we place a question mark in the bar model to indicate what we have to find. Label the bar model to show that we have to find the amount of money Mrs Jones spends.

Ask: How can we find the amount of money Mrs Jones spends? (Multiply the number of plates and the cost of each plate.)

Write: 4 × $2 = ______ Elicit the answer from students. ($8) Say: Mrs Jones spends $8.

+ Plus Solve the problem in another way.

$2 + $2 + $2 + $2 = $8 She spends $8. Compare the methods in steps 3 and 5. Which method do you prefer? Why?

Solve the word problems. Use or draw bar models to help you. Show your work clearly.

Next, try solving each problem in a different way. Which method do you prefer? Why?

1. Andy buys some pies for $21. Each pie costs $3. How

2.

4. Check if your answer is correct. Guide students to repeatedly subtract the cost of each plate from $8 to verify that the cost of 4 plates is $8.

Say: Since we can buy exactly 4 plates with $8, the answer is correct.

5. + Plus Solve the problem in another way. Have students try to solve the problem in a different way.

Have 1 or 2 students share their methods. If students are unable to solve the problem in a different way, explain the method shown on CB p. 193.

Ask: Which method do you prefer? Why? (Answers vary.)

Let's Do Let's

Task 1 requires students to solve a 1-step word problem involving division of money.

Task 2 requires students to solve a 1-step word problem involving subtraction of money.

Solve the word problems. Show your work clearly.

1. A cake costs $9. Mr Davis buys 2 such cakes. How much money does he spend?

2. Paul spends $42. He spends $16 more than Joe. How much money does Joe spend?

3. Mrs Lee buys 5 notebooks for $20. The cost of each notebook is the same.

How much does each notebook cost?

4. Vicky bought a hair clip for 60c. She got 10c in change. How much money did she give the cashier?

5. Aaron spends $12 on some mangoes. Each mango costs $2. How many mangoes does he buy?

CREATE YOUR OWN

$16 + $24 = $40

Read the addition sentence above. Write a word problem for the addition sentence. How did you come up with the word problem? What did you learn?

Answer varies. Sample: Emily buys a cap and a bag. The cap costs $16 and the bag costs $24. How much does she spend altogether?

Let's Practise Let's

Task 1 requires students to solve a 1-step word problem involving multiplication of money.

Task 2 requires students to solve a 1-step word problem involving subtraction of money.

Tasks 3 and 5 require students to solve 1-step word problems involving division of money.

Task 4 requires students to solve a 1-step word problem involving addition of money.

CREATE YOUR OWN

Have students work in groups to create the word problem. Have a few groups present their work.

Students can create word problems with different addition situations. For example, $16 and $24 can be the costs of two items and the problem asks for the total cost of the items. Alternatively, $16 can be the cost of an item, $24 is the change after purchasing the item and the problem asks for the amount of money given to the cashier.

3.2 Mind stretcher

Let's Learn Let's Learn

Objectives:

•Solve a non-routine problem involving money using the strategy of making a supposition

•Solve a non-routine problem involving money using the strategy of drawing a bar model

Materials:

•1 copy of Maths Jour nal (BM8.1) per student

Resource:

•CB: pp. 195–197

Have students read the problem on CB p. 195.

1. Understand the problem. Pose the questions in the thought bubble in step 1.

2. Plan what to do.

Explain that we do not know how many $5 and $10 notes Rachel has but we can make a supposition or assumption about the value of the notes.

3. Work out the Answer. Say: Suppose all of Rachel’s notes are $10 notes.

Ask: How many notes does she have? (6) How do we find the amount of money if she has six $10 notes? (Multiply 6 and $10.)

Write: 6 × $10 = ______

Elicit the answer from students. ($60)

Say: If all her notes are $10 notes, Rachel will have $60.

Ask: Is that the amount of money she is supposed to have? (No) How much money does Rachel have? ($50)

Say: Let us find how much more money she would have if she has six $10 notes.

Write: $60 – $50 = ______

Elicit the answer from students. ($10)

Say: If Rachel has six $10 notes, she will have $10 more.

Explain that we can decrease the amount of money Rachel has by replacing $10 notes with $5 notes since a $5 note is worth less than a $10 note.

Write: $10 – $5 = $5

Say: If one $10 note is replaced with one $5 note, Rachel will have $5 less.

Lead students to see that to have $50 altogether, we find the number of $10 notes that would have to be replaced by $5 notes so that Rachel has $10 less.

3.2 Mind stretcher

Rachel has 6 notes. The notes are $5 and $10 notes only. She has $50 altogether. How many $5 notes and how many $10 notes does Rachel have?

Understand the problem. 1 Plan what to do. 2

Work out the Answer 3

How many notes does Rachel have? How much money does she have altogether? What do I have to find?

I can make a supposition

Suppose all of Rachel’s notes are $10 notes.

6 × $10 = $60

If all her notes are $10 notes, Rachel will have $60.

$60 – $50 = $10

If Rachel has six $10 notes, she will have $10 more.

$10 – $5 = $5

For every $10 note that is replaced with one $5 note, she will have $5 less.

$10 ÷ $5 = 2

For Rachel to have $50, two $10 notes should be replaced with two $5 notes.

6 – 2 = 4

So, Rachel has two $5 notes and four $10 notes.

Check if your answer is correct. 4

2 + 4 = 6

2 × $5 = $10

4 × $10 = $40 $10 + $40 = $50 My answer is correct.

Write: $10 ÷ $5 = ______

Elicit the answer from students. (2)

Say: If we replace two $10 notes by two $5 notes, Rachel will have $10 less.

Ask: How do we find the number of $10 notes Rachel has? (6 – 2 = 4)

Say: Rachel has two $5 notes and four $10 notes.

4. Check if your answer is correct.

First, guide students to check their answer by verifying the number of notes.

Write: 2 + 4 = 6

Say: There are 6 notes.

Next, guide students to find the total value of two $5 notes and four $10 notes.

Write: 2 × $5 = $10

Say: The value of the $5 notes is $10.

Write: 4 × $10 = $40

Say: The value of the $10 notes is $40.

Write: $10 + $40 = ______

Elicit the answer from students. ($50)

Say: Since the number of notes is 6 and the total value is $50, the answer is correct.

+ Plus Solve the problem in another way.

Guess and check the number of $5 notes and $10 notes that Rachel has.

Guess 1: Rachel has three $5 notes and three $10 notes.

3 × $5 = $15

3 × $10 = $30

$15 + $30 = $45

$45 is less than $50.

Guess 1 is not correct. There should be more $10 notes.

Guess 2: Rachel has two $5 notes and four $10 notes.

2 × $5 = $10

4 × $10 = $40

$10 + $40 = $50

Guess 2 is correct.

So, Rachel has two $5 notes and four $10 notes.

Compare the methods in steps 3 and 5. Which method do you prefer? Why?

1. Understand 2. Plan 3. Answer 4. Check 5. Plus

8: Money

5. + Plus Solve the problem in another way. Have students try to solve the problem in a different way. Have 1 or 2 students share their methods. If students are unable to solve the problem in a different way, explain the method shown on CB p. 196.

Ask: Which method do you prefer? Why? (Answers vary.)

A hotdog costs $2 and a burger costs $3. Violet buys the same number of hotdogs and burgers. She gives the cashier $50 and receives $15 in change.

How many hotdogs and burgers does she buy altogether?

Let's Do Do Strategy: Draw a bar model.

$2 + $3 = $5

The total cost of a hotdog and a burger is $5.

$50 – $15 = $35

Violet spends $35 on the hotdogs and burgers.

$35

$5

$35 ÷ $5 = 7 She buys 7 groups of a hotdog and a burger.

7 + 7 = 14

Violet buys 14 hotdogs and burgers altogether.

Let's Do Let's Do

Have students first find the total cost of a hotdog and a burger. Get them to observe that Violet gives the cashier $50 and receives $15 in change. So, she spends $35 on the hotdogs and burgers. Point out to students that she buys the same number of hotdogs and burgers. Guide students to draw a bar model to represent this situation by considering a hotdog and a burger as one group. Have them divide $35 by $5 to find the number of groups of a hotdog and a burger Violet buys. Have students add to conclude that Violet buys 14 hotdogs and burgers altogether.

EXPLORE

Have students go back to the word problem on CB p. 182. Get them to write down in column 3 of the table what they have learnt that will help them solve the problem, and then solve the problem.

Have a student present his/her work to the class.

Maths Journal Maths Journal

Have students work on the tasks in Maths Journal (BM8.1) independently to check and reinforce their understanding. Use the rubric provided on page 320 of the blackline masters to score students’ work.

Practice Book Chapter 8: Answers

Exercise 1.1

1. a) 14 b) 20; 10 c) 2; 40 d) 13; 50 e) 56; 70 f) 23; 20 g) 221; 80

2. 40; 80

3. 26; 10

Exercise 1.2

1. a) Circle 1 five-dollar note and 2 one-dollar coins.

b) Circle 5 five-dollar notes and 1 two-dollar coin.

c) Circle 2 ten-dollar notes, 2 five-dollar notes and 1 one-dollar coin.

d) Circle 1 fifty-dollar note, 4 ten-dollar notes and 4 one-dollar coins.

e) Circle 1 fifty-dollar note, 2 twenty-dollar notes, 3 two-dollar coins and 2 one-dollar coins.

Exercise 2.1

Maths Journal Maths Journal

1. Explain how to count an amount of money in dollars and cents.

2. Draw notes and coins to show the exact amount you need to buy your favourite snack.

3. Emily uses a $50 note to pay for a bag that costs $24. Show different ways to find the amount of change she will get.