Multiplication as repeated addition
By the end of this chapter you will be able to
- See a multiplication as equal groups
- Write a multiplication sentence
- Use arrays and turn them round
- Say whether a total is odd or even
- Solve word problems with equal groups
You should already know
- Adding within 1000 (chapter 4)
- Odd and even numbers (Level 2)
Where this leads
- Multiplying with 2, 5 and 10 (chapter 7)
Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Solve problems using repeated addition and equal groups (MD5), Write multiplication statements with the × and = signs (MD3), Recognise that multiplication can be done in any order, using arrays (MD4), Say whether a number is odd or even (MD2).
Exercise P Do you remember?
Non-calculatorMethod. Add the numbers one at a time, from the left.
- Add 3 and 3. Work from the left, two numbers at a time.3 + 3 = 6
- Add 3. Keep adding one number at a time.6 + 3 = 9
- Write the answer. This is the total.9
Check. Add them in a different order to check: the total is still 9.
Watch out. Add the numbers two at a time. Each step is small.
Method. Add the numbers one at a time, from the left.
- Add 5 and 5. Work from the left, two numbers at a time.5 + 5 = 10
- Write the answer. This is the total.10
Check. Add them in a different order to check: the total is still 10.
Watch out. Add the numbers two at a time. Each step is small.
Method. Add the numbers one at a time, from the left.
- Add 2 and 2. Work from the left, two numbers at a time.2 + 2 = 4
- Add 2. Keep adding one number at a time.4 + 2 = 6
- Add 2. Keep adding one number at a time.6 + 2 = 8
- Write the answer. This is the total.8
Check. Add them in a different order to check: the total is still 8.
Watch out. Add the numbers two at a time. Each step is small.
Method. Add the numbers one at a time, from the left.
- Add 4 and 4. Work from the left, two numbers at a time.4 + 4 = 8
- Add 4. Keep adding one number at a time.8 + 4 = 12
- Write the answer. This is the total.12
Check. Add them in a different order to check: the total is still 12.
Watch out. Add the numbers two at a time. Each step is small.
Method. Add the numbers one at a time, from the left.
- Add 6 and 6. Work from the left, two numbers at a time.6 + 6 = 12
- Write the answer. This is the total.12
Check. Add them in a different order to check: the total is still 12.
Watch out. Add the numbers two at a time. Each step is small.
Equal groups and repeated addition
Equal groups are the same number of things in each group. Three groups of 4 means 4 + 4 + 4.
Add the same number once for each group. Count the groups first, then add.
Key ideas
- Equal groups: the same number in each group.
- Repeated addition: add the group size once for each group.
- Count the groups, then add them up.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 3 groups, so there are 3 lots of 4.4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 = 12
- Write the answer. This is the total altogether.12
Check. Count in 4s 3 times and you reach 12.
Watch out. Add 4 3 times. Do not add 3 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 4 groups, so there are 4 lots of 3.3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 = 12
- Write the answer. This is the total altogether.12
Check. Count in 3s 4 times and you reach 12.
Watch out. Add 3 4 times. Do not add 4 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 5 groups, so there are 5 lots of 2.2 + 2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. This is the total altogether.10
Check. Count in 2s 5 times and you reach 10.
Watch out. Add 2 5 times. Do not add 5 2 times.
Watch out
Watch out. 3 groups of 4 is 4 + 4 + 4, which is 12. It is not 3 + 4.
Exam tip
Grown-up tip. Use egg boxes or cups. Put the same number in each box, then count the boxes and the total together.
Exercise 6A Practice: equal groups and repeated addition
Non-calculatorMethod. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 3 groups, so there are 3 lots of 2.2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 = 6
- Write the answer. This is the total altogether.6
Check. Count in 2s 3 times and you reach 6.
Watch out. Add 2 3 times. Do not add 3 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 2 groups, so there are 2 lots of 3.3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 = 6
- Write the answer. This is the total altogether.6
Check. Count in 3s 2 times and you reach 6.
Watch out. Add 3 2 times. Do not add 2 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 4 groups, so there are 4 lots of 4.4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 = 16
- Write the answer. This is the total altogether.16
Check. Count in 4s 4 times and you reach 16.
Watch out. Add 4 4 times. Do not add 4 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 5 groups, so there are 5 lots of 4.4 + 4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 + 4 = 20
- Write the answer. This is the total altogether.20
Check. Count in 4s 5 times and you reach 20.
Watch out. Add 4 5 times. Do not add 5 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 5 groups, so there are 5 lots of 2.2 + 2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. This is the total altogether.10
Check. Count in 2s 5 times and you reach 10.
Watch out. Add 2 5 times. Do not add 5 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 4 groups, so there are 4 lots of 2.2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 = 8
- Write the answer. This is the total altogether.8
Check. Count in 2s 4 times and you reach 8.
Watch out. Add 2 4 times. Do not add 4 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 3 groups, so there are 3 lots of 3.3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 = 9
- Write the answer. This is the total altogether.9
Check. Count in 3s 3 times and you reach 9.
Watch out. Add 3 3 times. Do not add 3 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 4 groups, so there are 4 lots of 2.2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 = 8
- Write the answer. This is the total altogether.8
Check. Count in 2s 4 times and you reach 8.
Watch out. Add 2 4 times. Do not add 4 2 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 6 groups, so there are 6 lots of 4.4 + 4 + 4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 + 4 + 4 = 24
- Write the answer. This is the total altogether.24
Check. Count in 4s 6 times and you reach 24.
Watch out. Add 4 6 times. Do not add 6 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 2 groups, so there are 2 lots of 3.3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 = 6
- Write the answer. This is the total altogether.6
Check. Count in 3s 2 times and you reach 6.
Watch out. Add 3 2 times. Do not add 2 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 4 groups, so there are 4 lots of 4.4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 = 16
- Write the answer. This is the total altogether.16
Check. Count in 4s 4 times and you reach 16.
Watch out. Add 4 4 times. Do not add 4 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 6 for each group. There are 3 groups, so there are 3 lots of 6.6 + 6 + 6
- Add them up. Add the groups one after another, or count in steps of the group size.6 + 6 + 6 = 18
- Write the answer. This is the total altogether.18
Check. Count in 6s 3 times and you reach 18.
Watch out. Add 6 3 times. Do not add 3 6 times.
Method. Repeated addition: add the same number once for each group.
- Write one 6 for each group. There are 6 groups, so there are 6 lots of 6.6 + 6 + 6 + 6 + 6 + 6
- Add them up. Add the groups one after another, or count in steps of the group size.6 + 6 + 6 + 6 + 6 + 6 = 36
- Write the answer. This is the total altogether.36
Check. Count in 6s 6 times and you reach 36.
Watch out. Add 6 6 times. Do not add 6 6 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 4 groups, so there are 4 lots of 3.3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 = 12
- Write the answer. This is the total altogether.12
Check. Count in 3s 4 times and you reach 12.
Watch out. Add 3 4 times. Do not add 4 3 times.
Method. Repeated addition: add the same number once for each group.
- Write one 5 for each group. There are 6 groups, so there are 6 lots of 5.5 + 5 + 5 + 5 + 5 + 5
- Add them up. Add the groups one after another, or count in steps of the group size.5 + 5 + 5 + 5 + 5 + 5 = 30
- Write the answer. This is the total altogether.30
Check. Count in 5s 6 times and you reach 30.
Watch out. Add 5 6 times. Do not add 6 5 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 6 groups, so there are 6 lots of 3.3 + 3 + 3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 + 3 + 3 = 18
- Write the answer. This is the total altogether.18
Check. Count in 3s 6 times and you reach 18.
Watch out. Add 3 6 times. Do not add 6 3 times.
Writing multiplication sentences
A multiplication sentence shows equal groups in a short way. The sign × means groups of.
The number in front is the number of groups. The number after × is the size of each group.
Key ideas
- × means groups of.
- The first number is the number of groups.
- The = sign comes before the total.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 4 groups of 3.3 + 3 + 3 + 3
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.4 × 3
- Write the answer after the = sign. The total is the answer.4 × 3 = 12
Check. Check: 3 + 3 + 3 + 3 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 3. The first number tells how many groups.5 groups of 3
- Write the repeated addition. Add the group size once for each group.3 + 3 + 3 + 3 + 3 = 15
- Write the answer in the box. This is the missing number.15
Check. Check: 3 + 3 + 3 + 3 + 3 gives 15.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 2 groups of 6.6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.2 × 6
- Write the answer after the = sign. The total is the answer.2 × 6 = 12
Check. Check: 6 + 6 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Watch out
Watch out. 4 × 3 is four groups of three, not three groups of four. Read the first number as the groups.
Exam tip
Grown-up tip. Ask: “How many groups? How many in each group? Write the sentence, then the total.”
Exercise 6B Practice: writing multiplication sentences
Non-calculatorMethod. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 2 groups of 6.6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.2 × 6
- Write the answer after the = sign. The total is the answer.2 × 6 = 12
Check. Check: 6 + 6 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 6 groups of 3.3 + 3 + 3 + 3 + 3 + 3
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.6 × 3
- Write the answer after the = sign. The total is the answer.6 × 3 = 18
Check. Check: 3 + 3 + 3 + 3 + 3 + 3 gives 18.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 6 groups of 6.6 + 6 + 6 + 6 + 6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.6 × 6
- Write the answer after the = sign. The total is the answer.6 × 6 = 36
Check. Check: 6 + 6 + 6 + 6 + 6 + 6 gives 36.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 4. The first number tells how many groups.5 groups of 4
- Write the repeated addition. Add the group size once for each group.4 + 4 + 4 + 4 + 4 = 20
- Write the answer in the box. This is the missing number.20
Check. Check: 4 + 4 + 4 + 4 + 4 gives 20.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 4 groups of 6.6 + 6 + 6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.4 × 6
- Write the answer after the = sign. The total is the answer.4 × 6 = 24
Check. Check: 6 + 6 + 6 + 6 gives 24.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 4 groups of 5.5 + 5 + 5 + 5
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.4 × 5
- Write the answer after the = sign. The total is the answer.4 × 5 = 20
Check. Check: 5 + 5 + 5 + 5 gives 20.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 6 groups of 3. The first number tells how many groups.6 groups of 3
- Write the repeated addition. Add the group size once for each group.3 + 3 + 3 + 3 + 3 + 3 = 18
- Write the answer in the box. This is the missing number.18
Check. Check: 3 + 3 + 3 + 3 + 3 + 3 gives 18.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 5 groups of 5.5 + 5 + 5 + 5 + 5
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.5 × 5
- Write the answer after the = sign. The total is the answer.5 × 5 = 25
Check. Check: 5 + 5 + 5 + 5 + 5 gives 25.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 5 groups of 2.2 + 2 + 2 + 2 + 2
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.5 × 2
- Write the answer after the = sign. The total is the answer.5 × 2 = 10
Check. Check: 2 + 2 + 2 + 2 + 2 gives 10.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 3 groups of 5. The first number tells how many groups.3 groups of 5
- Write the repeated addition. Add the group size once for each group.5 + 5 + 5 = 15
- Write the answer in the box. This is the missing number.15
Check. Check: 5 + 5 + 5 gives 15.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 4 groups of 3. The first number tells how many groups.4 groups of 3
- Write the repeated addition. Add the group size once for each group.3 + 3 + 3 + 3 = 12
- Write the answer in the box. This is the missing number.12
Check. Check: 3 + 3 + 3 + 3 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 5 groups of 4.4 + 4 + 4 + 4 + 4
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.5 × 4
- Write the answer after the = sign. The total is the answer.5 × 4 = 20
Check. Check: 4 + 4 + 4 + 4 + 4 gives 20.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 2 groups of 3. The first number tells how many groups.2 groups of 3
- Write the repeated addition. Add the group size once for each group.3 + 3 = 6
- Write the answer in the box. This is the missing number.6
Check. Check: 3 + 3 gives 6.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 3. The first number tells how many groups.5 groups of 3
- Write the repeated addition. Add the group size once for each group.3 + 3 + 3 + 3 + 3 = 15
- Write the answer in the box. This is the missing number.15
Check. Check: 3 + 3 + 3 + 3 + 3 gives 15.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 2. The first number tells how many groups.5 groups of 2
- Write the repeated addition. Add the group size once for each group.2 + 2 + 2 + 2 + 2 = 10
- Write the answer in the box. This is the missing number.10
Check. Check: 2 + 2 + 2 + 2 + 2 gives 10.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 4 groups of 3.3 + 3 + 3 + 3
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.4 × 3
- Write the answer after the = sign. The total is the answer.4 × 3 = 12
Check. Check: 3 + 3 + 3 + 3 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Arrays, and multiplying in any order
An array is a set of dots in rows and columns. Each row is a group.
Turn an array round and the rows become columns. The total does not change, so 3 × 4 and 4 × 3 are both 12.
Key ideas
- An array shows rows and columns.
- Count the rows, then the dots in each row.
- The order of the numbers does not change the total.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.3 rows
- Count the dots in one row. Each row has the same number of dots.4 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.3 × 4 = 12
- Write the answer. This is the total number of dots.12
Check. Count the dots one by one: 12 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.5 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 5 = 20
- Write the answer. This is the total number of dots.20
Check. Count the dots one by one: 20 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.2 rows
- Count the dots in one row. Each row has the same number of dots.6 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.2 × 6 = 12
- Write the answer. This is the total number of dots.12
Check. Count the dots one by one: 12 in all.
Watch out. An array has rows and columns. The rows show the groups.
Watch out
Watch out. Count the dots in each row, not the number of rows. An array with 3 rows of 4 has 12 dots, not 3 or 4.
Exam tip
Grown-up tip. Use counters on a tray. Make rows, then turn the tray round and count again.
Exercise 6C Practice: arrays and turning them round
Non-calculatorMethod. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.6 rows
- Count the dots in one row. Each row has the same number of dots.6 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.6 × 6 = 36
- Write the answer. This is the total number of dots.36
Check. Count the dots one by one: 36 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.5 rows
- Count the dots in each row. Each row has the same number of dots.3 dots
- Multiply. Rows times dots in a row.5 × 3 = 15
- Write the answer. This is the total number of dots.15
Check. Count the dots one by one to check: 15.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 3 rows. Each row now has the same dots as before, but turned.3 rows
- Multiply 3 by 5. Rows times dots in each row.3 × 5 = 15
- Write the answer. The total is the same as before.15
Check. 5 × 3 and 3 × 5 both give 15.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.3 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 3 = 12
- Write the answer. This is the total number of dots.12
Check. Count the dots one by one: 12 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.2 rows
- Count the dots in one row. Each row has the same number of dots.2 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.2 × 2 = 4
- Write the answer. This is the total number of dots.4
Check. Count the dots one by one: 4 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.3 rows
- Count the dots in each row. Each row has the same number of dots.2 dots
- Multiply. Rows times dots in a row.3 × 2 = 6
- Write the answer. This is the total number of dots.6
Check. Count the dots one by one to check: 6.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 2 rows. Each row now has the same dots as before, but turned.2 rows
- Multiply 2 by 3. Rows times dots in each row.2 × 3 = 6
- Write the answer. The total is the same as before.6
Check. 3 × 2 and 2 × 3 both give 6.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.5 rows
- Count the dots in one row. Each row has the same number of dots.3 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.5 × 3 = 15
- Write the answer. This is the total number of dots.15
Check. Count the dots one by one: 15 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.6 rows
- Count the dots in each row. Each row has the same number of dots.4 dots
- Multiply. Rows times dots in a row.6 × 4 = 24
- Write the answer. This is the total number of dots.24
Check. Count the dots one by one to check: 24.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 4 rows. Each row now has the same dots as before, but turned.4 rows
- Multiply 4 by 6. Rows times dots in each row.4 × 6 = 24
- Write the answer. The total is the same as before.24
Check. 6 × 4 and 4 × 6 both give 24.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.4 rows
- Count the dots in each row. Each row has the same number of dots.3 dots
- Multiply. Rows times dots in a row.4 × 3 = 12
- Write the answer. This is the total number of dots.12
Check. Count the dots one by one to check: 12.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 3 rows. Each row now has the same dots as before, but turned.3 rows
- Multiply 3 by 4. Rows times dots in each row.3 × 4 = 12
- Write the answer. The total is the same as before.12
Check. 4 × 3 and 3 × 4 both give 12.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.3 rows
- Count the dots in one row. Each row has the same number of dots.3 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.3 × 3 = 9
- Write the answer. This is the total number of dots.9
Check. Count the dots one by one: 9 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.3 rows
- Count the dots in each row. Each row has the same number of dots.3 dots
- Multiply. Rows times dots in a row.3 × 3 = 9
- Write the answer. This is the total number of dots.9
Check. Count the dots one by one to check: 9.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 3 rows. Each row now has the same dots as before, but turned.3 rows
- Multiply 3 by 3. Rows times dots in each row.3 × 3 = 9
- Write the answer. The total is the same as before.9
Check. 3 × 3 and 3 × 3 both give 9.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.2 rows
- Count the dots in one row. Each row has the same number of dots.4 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.2 × 4 = 8
- Write the answer. This is the total number of dots.8
Check. Count the dots one by one: 8 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.6 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 6 = 24
- Write the answer. This is the total number of dots.24
Check. Count the dots one by one: 24 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.6 rows
- Count the dots in each row. Each row has the same number of dots.3 dots
- Multiply. Rows times dots in a row.6 × 3 = 18
- Write the answer. This is the total number of dots.18
Check. Count the dots one by one to check: 18.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 3 rows. Each row now has the same dots as before, but turned.3 rows
- Multiply 3 by 6. Rows times dots in each row.3 × 6 = 18
- Write the answer. The total is the same as before.18
Check. 6 × 3 and 3 × 6 both give 18.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.5 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 5 = 20
- Write the answer. This is the total number of dots.20
Check. Count the dots one by one: 20 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.6 rows
- Count the dots in each row. Each row has the same number of dots.6 dots
- Multiply. Rows times dots in a row.6 × 6 = 36
- Write the answer. This is the total number of dots.36
Check. Count the dots one by one to check: 36.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 6 rows. Each row now has the same dots as before, but turned.6 rows
- Multiply 6 by 6. Rows times dots in each row.6 × 6 = 36
- Write the answer. The total is the same as before.36
Check. 6 × 6 and 6 × 6 both give 36.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.4 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 4 = 16
- Write the answer. This is the total number of dots.16
Check. Count the dots one by one: 16 in all.
Watch out. An array has rows and columns. The rows show the groups.
Odd and even totals
Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.
Find the total of the equal groups, then look at its last digit.
Key ideas
- Even numbers end in 0, 2, 4, 6 or 8.
- Odd numbers end in 1, 3, 5, 7 or 9.
- An even number can be shared into two equal groups.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 = 12
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.12 ends in 2
- Write the answer. 12 is even.even
Check. Share 12 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.5 + 5 + 5 = 15
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.15 ends in 5
- Write the answer. 15 is odd.odd
Check. Share 15 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 + 3 + 3 = 18
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.18 ends in 8
- Write the answer. 18 is even.even
Check. Share 18 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Watch out
Watch out. 3 groups of 5 is 15, which is odd, not even. Check the last digit of the total.
Exam tip
Grown-up tip. Ask: “Can you share the total into two equal piles with none left over?”
Exercise 6D Practice: odd and even totals
Non-calculatorMethod. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.2 + 2 + 2 = 6
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.6 ends in 6
- Write the answer. 6 is even.even
Check. Share 6 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 + 3 + 3 = 18
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.18 ends in 8
- Write the answer. 18 is even.even
Check. Share 18 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.5 + 5 + 5 = 15
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.15 ends in 5
- Write the answer. 15 is odd.odd
Check. Share 15 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.4 + 4 + 4 = 12
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.12 ends in 2
- Write the answer. 12 is even.even
Check. Share 12 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.6 + 6 = 12
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.12 ends in 2
- Write the answer. 12 is even.even
Check. Share 12 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 + 3 = 15
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.15 ends in 5
- Write the answer. 15 is odd.odd
Check. Share 15 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.6 + 6 + 6 = 18
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.18 ends in 8
- Write the answer. 18 is even.even
Check. Share 18 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.2 + 2 + 2 + 2 = 8
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.8 ends in 8
- Write the answer. 8 is even.even
Check. Share 8 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.6 + 6 + 6 + 6 + 6 = 30
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.30 ends in 0
- Write the answer. 30 is even.even
Check. Share 30 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 = 6
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.6 ends in 6
- Write the answer. 6 is even.even
Check. Share 6 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.6 + 6 + 6 + 6 = 24
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.24 ends in 4
- Write the answer. 24 is even.even
Check. Share 24 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.5 + 5 = 10
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.10 ends in 0
- Write the answer. 10 is even.even
Check. Share 10 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 = 9
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.9 ends in 9
- Write the answer. 9 is odd.odd
Check. Share 9 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 = 12
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.12 ends in 2
- Write the answer. 12 is even.even
Check. Share 12 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.5 + 5 + 5 + 5 + 5 = 25
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.25 ends in 5
- Write the answer. 25 is odd.odd
Check. Share 25 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.4 + 4 + 4 + 4 + 4 + 4 = 24
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.24 ends in 4
- Write the answer. 24 is even.even
Check. Share 24 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Chapter summary
| Skill | Method |
|---|---|
| Equal groups | Add the group size once for each group |
| Multiplication sentence | Groups of is ×: 4 groups of 3 is 4 × 3 = 12 |
| Arrays | Count the rows and the dots in each row, then multiply; turning round gives the same total |
| Odd and even | Even ends in 0, 2, 4, 6 or 8; odd ends in 1, 3, 5, 7 or 9 |
Can you…?
- I can see a multiplication as equal groups and as repeated addition
- I can write a multiplication sentence with × and =
- I can use an array and see that the order does not change the total
- I can say whether a total is odd or even
- I can solve a word problem with equal groups
Key terms
- equal groups
- groups with the same number in each
- array
- a set of objects in rows and columns
- multiply
- add equal groups; the sign is ×
- odd number
- a number that ends in 1, 3, 5, 7 or 9
- even number
- a number that ends in 0, 2, 4, 6 or 8
Exercise 6Z Check-up
Non-calculatorMethod. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.6 + 6 + 6 = 18
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.18 ends in 8
- Write the answer. 18 is even.even
Check. Share 18 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 6 groups of 6.6 + 6 + 6 + 6 + 6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.6 × 6
- Write the answer after the = sign. The total is the answer.6 × 6 = 36
Check. Check: 6 + 6 + 6 + 6 + 6 + 6 gives 36.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 2 groups, so there are 2 lots of 3.3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 = 6
- Write the answer. This is the total altogether.6
Check. Count in 3s 2 times and you reach 6.
Watch out. Add 3 2 times. Do not add 2 3 times.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 2 groups of 3.3 + 3
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.2 × 3
- Write the answer after the = sign. The total is the answer.2 × 3 = 6
Check. Check: 3 + 3 gives 6.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 6 groups, so there are 6 lots of 2.2 + 2 + 2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 + 2 + 2 = 12
- Write the answer. This is the total altogether.12
Check. Count in 2s 6 times and you reach 12.
Watch out. Add 2 6 times. Do not add 6 2 times.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 5. The first number tells how many groups.5 groups of 5
- Write the repeated addition. Add the group size once for each group.5 + 5 + 5 + 5 + 5 = 25
- Write the answer in the box. This is the missing number.25
Check. Check: 5 + 5 + 5 + 5 + 5 gives 25.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 5 groups, so there are 5 lots of 4.4 + 4 + 4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 + 4 + 4 = 20
- Write the answer. This is the total altogether.20
Check. Count in 4s 5 times and you reach 20.
Watch out. Add 4 5 times. Do not add 5 4 times.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 3 groups, so there are 3 lots of 3.3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 = 9
- Write the answer. This is the total altogether.9
Check. Count in 3s 3 times and you reach 9.
Watch out. Add 3 3 times. Do not add 3 3 times.
Method. Groups of is multiply. Write the sentence, then find the total.
- Read it as 3 groups of 5. The first number tells how many groups.3 groups of 5
- Write the repeated addition. Add the group size once for each group.5 + 5 + 5 = 15
- Write the answer in the box. This is the missing number.15
Check. Check: 5 + 5 + 5 gives 15.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.6 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 6 = 24
- Write the answer. This is the total number of dots.24
Check. Count the dots one by one: 24 in all.
Watch out. An array has rows and columns. The rows show the groups.
Total 19 marks. Allow about 19 minutes.
Exercise 6X Practice test questions
Non-calculatorMethod. Groups of is multiply. Write the sentence, then find the total.
- Read it as 5 groups of 5. The first number tells how many groups.5 groups of 5
- Write the repeated addition. Add the group size once for each group.5 + 5 + 5 + 5 + 5 = 25
- Write the answer in the box. This is the missing number.25
Check. Check: 5 + 5 + 5 + 5 + 5 gives 25.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.4 rows
- Count the dots in one row. Each row has the same number of dots.4 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.4 × 4 = 16
- Write the answer. This is the total number of dots.16
Check. Count the dots one by one: 16 in all.
Watch out. An array has rows and columns. The rows show the groups.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 = 12
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.12 ends in 2
- Write the answer. 12 is even.even
Check. Share 12 into two equal groups: yes, with none left.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Repeated addition: add the same number once for each group.
- Write one 5 for each group. There are 3 groups, so there are 3 lots of 5.5 + 5 + 5
- Add them up. Add the groups one after another, or count in steps of the group size.5 + 5 + 5 = 15
- Write the answer. This is the total altogether.15
Check. Count in 5s 3 times and you reach 15.
Watch out. Add 5 3 times. Do not add 3 5 times.
Method. Repeated addition: add the same number once for each group.
- Write one 2 for each group. There are 4 groups, so there are 4 lots of 2.2 + 2 + 2 + 2
- Add them up. Add the groups one after another, or count in steps of the group size.2 + 2 + 2 + 2 = 8
- Write the answer. This is the total altogether.8
Check. Count in 2s 4 times and you reach 8.
Watch out. Add 2 4 times. Do not add 4 2 times.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 6 groups of 5.5 + 5 + 5 + 5 + 5 + 5
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.6 × 5
- Write the answer after the = sign. The total is the answer.6 × 5 = 30
Check. Check: 5 + 5 + 5 + 5 + 5 + 5 gives 30.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Find the total, then look at its last digit.
- Work out the total. Use repeated addition or multiplication.3 + 3 + 3 + 3 + 3 = 15
- Look at the last digit. Even numbers end in 0, 2, 4, 6 or 8. Odd numbers end in 1, 3, 5, 7 or 9.15 ends in 5
- Write the answer. 15 is odd.odd
Check. Share 15 into two equal groups: no, one is left over.
Watch out. An even number can be shared into two equal groups with none left over.
Method. Groups of is multiply. Write the sentence, then find the total.
- Write the repeated addition. There are 2 groups of 6.6 + 6
- Use the multiplication sign. Groups of is the same as multiply, written with the × sign.2 × 6
- Write the answer after the = sign. The total is the answer.2 × 6 = 12
Check. Check: 6 + 6 gives 12.
Watch out. The number in front is the number of groups. The number after is the size of each group.
Method. Repeated addition: add the same number once for each group.
- Write one 5 for each group. There are 2 groups, so there are 2 lots of 5.5 + 5
- Add them up. Add the groups one after another, or count in steps of the group size.5 + 5 = 10
- Write the answer. This is the total altogether.10
Check. Count in 5s 2 times and you reach 10.
Watch out. Add 5 2 times. Do not add 2 5 times.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. Each row is one group.3 rows
- Count the dots in one row. Each row has the same number of dots.2 dots in each row
- Multiply the rows by the dots in each row. Add one row again and again to find the total.3 × 2 = 6
- Write the answer. This is the total number of dots.6
Check. Count the dots one by one: 6 in all.
Watch out. An array has rows and columns. The rows show the groups.