Step-by-step Maths Level 3: Arrays, and multiplying in any order
Part of the Step-by-step Maths Level 3 multiplication as repeated addition chapter. Chapter overview · whole chapter on one page
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.