100% coverage of New Zealand Mathematics and Statistics Curriculum for Phases 1-3
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Clear, step-by-step lessons for consistent, explicit teaching
Structured problem solving and reasoning for deep understanding
Let's Remember Let's Remember
1. Complete the multiplication sentences.
6 × 3 = 8 × 5 =
2. Complete the related multiplication and division facts. a) 2 × = 14 b) 4 × 9 = 14 ÷ 2 = ÷ 9 = 4
7 7
Ella donated 5 cartons of water bottles in a charity. There were 12 bottles in each carton. How many water bottles did Ella donate?
How can we solve this problem? Discuss in your group and fill in columns 1 and 2.
1.What I already know that will help me solve the problem
Multiply by 12. Answer varies. 18
Multiply by 2, 3, 4, 5, 6, 7, 8, 9 and 10.
2.What I need to find out and learn
3.What I have learnt
Let's Learn Let's Learn You
1.1 Multiplication and division facts up to 10 × 10
We can use a multiplication chart to complete related multiplication and division facts.
2 × 5 =
5 = 2 5 × 2 =
To find the product of 2 and 5, we move along the row from the number 2 to the column with the number 5 .
We can also move along the row from the number 5 to the column with the number 2 .
b) × 9 = 72
72 ÷ 9 = × 8 = 72
72 ÷ 8 =
We move down the column with the number 9 to reach 72 and then move left to get the number in the 1st blue column.
We move down the column with the number 8 reach 72 and then move left to get the number in the 1st blue column. and 9 are factors of 72. 72 is a multiple of and 9.
1. Complete the related multiplication and division facts.
Let's Practise Let's Practise
1. Complete the related multiplication and division facts.
You will learn to...
• Multiply numbers within the multiplication table of 11
• Divide numbers using the multiplication table of 11
a) Multiply 2 by 11.
2 groups of 11 = 22
2 × 11 = 22
b) Multiply 9 by 11.
9 × 11 = 99
11 × 9 = 99
9 × 11 = 99 and 11 × 9 = 99 are related multiplication facts.
c) Multiply 11 and 11.
d) Multiply 12 and 11.
Add 1 group of 11
Multiplication Table of 11
1 × 11 = 11
2 × 11 = 22
3 × 11 = 33
4 × 11 = 44
5 × 11 = 55
6 × 11 = 66
Let's Do Let's Do
7 × 11 = 77
8 × 11 = 88
9 × 11 = 99
10 × 11 = 110 11 × 11 = 121 12 × 11 = 132
Add 2 groups of 11
When you multiply 11 by a 1-digit number, the tens and ones places in the product have the same digits as the 1-digit number.
1. Complete the multiplication sentences.
1. Complete the multiplication sentences.
Let's Learn Let's Learn
We use related multiplication facts when we divide.
Let's Do Do
1. Complete the related multiplication and division facts.
Let's Practise
1. Divide.
I have learnt to...
Multiply numbers within the multiplication table of 11
Divide numbers using the multiplication table of 11
>> Look at EXPLORE on page 71 again. Can you solve the problem now? What else do you need to know?
You will learn to...
• Multiply numbers within the multiplication table of 12
• Divide numbers using the multiplication table of 12
Let's Learn Learn
a) Arrange 12 square units into equal groups.
1 × 12 = 12
12 × 1 = 12
1 × 12 = 12 12 × 1 = 12 These are related multiplication facts.
2 and 6 are factors of 12.
So, the multiplication table of 12 is related to the multiplication tables of 2 and 6.
2 × 6 = 12
6 × 2 = 12
3 and 4 are factors of 12.
So, the multiplication table of 12 is related to the multiplication tables of 3 and 4.
3 × 4 = 12
4 × 3 = 12
The multiplication table of 12 is related to the multiplication tables of 2, 3, 4 and 6.
b) When we double the products in the multiplication table of 6, we get the products in the multiplication table of 12.
Multiplication
Table of 6 × 2
1 × 6 = 6
2 × 6 = 12
3 × 6 = 18
4 × 6 = 24
5 × 6 = 30
6 × 6 = 36
7 × 6 = 42
8 × 6 = 48
9 × 6 = 54
10 × 6 = 60
Multiplication
Table of 12
1 × 12 = 12
2 × 12 = 24
3 × 12 = 36
4 × 12 = 48
5 × 12 = 60
6 × 12 = 72
7 × 12 = 84
8 × 12 = 96
9 × 12 = 108
10 × 12 = 120
5 × 6 = 30
5 × 12 = 60 × 2 × 2
The product of 5 × 12 is double the product of 5 × 6.
Double 30 is 60.
c) When we triple the products in the multiplication table of 4, we get the products in the multiplication table of 12.
Multiplication
Table of 4 × 3
1 × 4 = 4
2 × 4 = 8
3 × 4 = 12
4 × 4 = 16
5 × 4 = 20
6 × 4 = 24
7 × 4 = 28
8 × 4 = 32
9 × 4 = 36
10 × 4 = 40
Multiplication
Table of 12
1 × 12 = 12
2 × 12 = 24
3 × 12 = 36
4 × 12 = 48
5 × 12 = 60
6 × 12 = 72
7 × 12 = 84
8 × 12 = 96
9 × 12 = 108
10 × 12 = 120
5 × 4 = 20
5 × 12 = 60 × 3 × 3
The product of 5 × 12 is triple the product of 5 × 4.
d) Multiply 11 and 12.
e) Multiply 12 and 12.
Let's Do Let's Do
1. Complete the multiplication sentences.
1. Complete the multiplication sentences.
We use related multiplication facts when we divide.
Let's Do Let's Do Let's Practise
1. Complete the related multiplication and division facts.
Let's Practise
1. Divide.
You will learn to...
• solve 1-step word problems involving multiplication and division
• solve non-routine problems involving multiplication tables Let's Learn Let's Learn
A shop has 3 packets of pens. Each packet has 12 pens. How many pens does the shop have in all?
2
1 Plan what to do. Whakaaro
Understand the problem. Mārama
How many packets of pens are there? How many pens are there in each packet? What do I need to find?
I should multiply to find the total number of pens in the shop.
Work out the Answer. Whakaatu
4 36 ÷ 12 = 3 My answer is correct.
3 3 × 12 = 36 The shop has 36 pens in all. 12 ? Check if your answer is correct. Tirohia
Draw pictures to represent the packets of pens.
Compare the methods in steps 3 and 5. Which method do you prefer? Why? + Plus Solve the problem in another way. Tāpiri
3 × 12 = 36
The shop has 36 pens in all.
1. Understand 2. Plan 3. Answer 4. Check 5. Plus
Let's Do Let's Do
Solve the word problems. Use the 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. Understand 2. Plan 3. Answer 4. Check 5. Plus
1. A florist has 72 roses. She needs 12 roses to make a bouquet. How many bouquets can she make?
2. Jack has 11 toy cars. Noah has five times as many toy cars as Jack. How many toy cars does Noah have? 11 ? Jack Noah 6 55
Solve the word problems. Show your work clearly.
1. Wiremu bought 6 boxes of marbles. There were 11 marbles in each box. How many marbles did he buy altogether?
2. Ariki saved $4 in a week. His sister saved 12 times as much money as him. How much money did Ariki’s sister save?
3. Oliver jogged a total distance of 44 kilometres over 11 days. He jogged the same distance each day. How many kilometres did he jog each day?
4. 144 children were divided into teams of 12. How many teams were there?
Grace cousin 3 years
Read the given words.
Use the words and the bar model to write a multiplication word problem. How did you come up with the word problem?
Answer varies. Sample: Grace is 3 years old. Her cousin is 12 times as old as her. How old is Grace’s cousin?
12 × 3 = 36
Grace’s cousin is 36 years old.
Next, solve the word problem. Show your work clearly. What did you learn?
Viliami is 3 years old this year. His mother is 11 times as old as him. In how many years' time will his mother be 3 times his age? Understand the problem.
Mārama
2
1 Plan what to do. Whakaaro
How old is Viliami this year? How many times is his mother as old as him? Will the difference in their age change? What do I have to find?
First, I find his mother's age this year. Then, I find the difference in their age. I can draw a bar model
4
5
Check if your answer is correct.
Tirohia
Tāpiri
15 × 3 = 45
45 − 33 = 12
My answer is correct.
Guess and check to solve the problem.
3 × 11 = 33
Viliami’s mother is 33 years old this year.
33 – 3 = 30
Compare the methods in steps 3 and 5. Which method do you prefer? Why? + Plus Solve the problem in another way.
Difference between their age is 30 years.
Guess Viliami’s age.
Viliami’s age Mother’s age Mother’s age is 3 times?
Viliami will be 15 years old when his mother is 3 times his age.
15 − 3 = 12
In 12 years’ time, Viliami’s mother will be 3 times his age.
Answer
Let's Do Let's Do
Look at the number pattern below.
1,000, 988, 976, 964, , , 928, 916, 904
What are the two missing numbers?
Strategy: Look for a pattern.
1,000, 988, 976, 964, , , 928, 916, 904
– 12 – 12 – 12 – 12 – 12
The next number decreases by 12 from the previous number each time.
964 – 12 = 952
952 – 12 = 940
The two missing numbers are 952 and 940.
I have learnt to...
solve 1-step word problems involving multiplication and division solve non-routine problems involving multiplication tables
>> Look at EXPLORE on page 71 again. Fill in column 3. Can you solve the problem now?