Tables, division and missing groups
Build the 2, 3, 4, 5 and 10 tables and use them in both multiplication and division.
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Build facts from equal groups
Three trays with four cups each hold 3 × 4 = 12 cups. Arrange the cups in three rows of four. Looking down the columns gives four columns of three: 4 × 3 = 12 too.
Build a multiplication table by adding one more equal group each time. In the 3 table, the totals are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 for one through ten groups.
Open the table you want to check. Each row adds one more equal group.
2 times table
| Groups | Total |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
| 6 | 12 |
| 7 | 14 |
| 8 | 16 |
| 9 | 18 |
| 10 | 20 |
3 times table
| Groups | Total |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |
| 6 | 18 |
| 7 | 21 |
| 8 | 24 |
| 9 | 27 |
| 10 | 30 |
4 times table
| Groups | Total |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |
| 8 | 32 |
| 9 | 36 |
| 10 | 40 |
5 times table
| Groups | Total |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |
| 6 | 30 |
| 7 | 35 |
| 8 | 40 |
| 9 | 45 |
| 10 | 50 |
10 times table
| Groups | Total |
|---|---|
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
| 5 | 50 |
| 6 | 60 |
| 7 | 70 |
| 8 | 80 |
| 9 | 90 |
| 10 | 100 |
Use a row to check a fact after you have tried it. Four groups of a number are twice two groups. Ten groups are twice five groups. These links help you rebuild a forgotten fact.
Division asks for a missing part of the groups
Share 20 counters equally between five plates. Each plate gets four: 20÷5 = 4.
Make groups of four from the same 20 counters. There are five groups: 20÷4 = 5.
The sign ÷ means divide. Both divisions use the multiplication fact 5 × 4 = 20. The number after ÷ can tell you how many groups to share between or how many belong in each group; read the story to find out.
Put division and equality in the right places
The equals sign joins two equal amounts. Both 18÷3 = 6 and 6 = 18÷3 are true. In both sentences, divide eighteen by three. The amount being divided is still eighteen.
Check your understanding 1 A division answer on the left
Complete 6 square 18 square 3. Use one ÷ sign and one = sign to make the number sentence true.
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The first sign is =; the second is ÷. The amount on each side is six. Moving = does not let you swap the numbers being divided.
Zero counters shared between five plates give zero on each plate: 0÷5 = 0. Five is still the number of plates. Dividing by zero is not allowed.
Use a known fact mentally
If 5 × 3 = 15, one more group of three gives 6 × 3 = 18. Then 18÷3 = 6. You can check a division by multiplying its answer by the number you divided by.
Check your understanding 2 How many equal groups?
There are 28 pencils. Put four in each packet. How many packets can you fill?
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Seven packets: 28÷4 = 7. Multiplying 7 × 4 = 28 checks that every pencil is used.
Check your understanding 3 The meaning of the answer changes
Thirty stickers are shared equally between three children. Another thirty stickers are packed with ten in each packet. Find the number each question asks for and give its unit.
Show answer
Each child gets 30÷3 = 10 stickers. There are 30÷10 = 3 packets. Ten stickers per child and three packets describe different quantities, even though both calculations use 3 × 10 = 30.
Check a claim
Lin says, “24÷3 = 7, because 7 × 3 = 21 is close.” Explain why close is not enough here.
Show answer
Seven groups use only 21 counters and leave three. Eight equal groups of three use all 24, so 24÷3 = 8.
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