Joining, Taking Away and Equal Groups
What this lesson covers
- When you take away, the order of the numbers matters.
- Multiplying is putting equal groups together.
- Dividing is sharing into equal groups.
- Counting equal groups helps you multiply and divide.
Join and split up to 20
- To add 9 + 6, make 10 first: 9 + 1 = 10, then 5 more is 15.
- For 7 + __ = 11, count on from 7 to 11.
- To take away, count back.
| Problem | Think | Answer |
|---|---|---|
| 9 + 6 | 9 + 1 = 10, then 5 more | 15 |
| 7 + __ = 11 | 8, 9, 10, 11 is 4 hops | 4 |
| 14 − 5 | back 4 to 10, then 1 more | 9 |
| 13 + 4 | 14, 15, 16, 17 | 17 |
Try it: join and split on a number line
Order matters when taking away
- 8 − 3 = 5. You have 8 apples and eat 3.
- 3 − 8 is not the same. You cannot eat 8 apples if you only have 3.
- Adding can swap. Taking away cannot.
Adding ten
- Put one ten with some ones.
- 10 + 6 = 16: one ten and six ones.
- The ones digit stays the same.
| Sum | Tens and ones | Answer |
|---|---|---|
| 10 + 6 | 1 ten, 6 ones | 16 |
| 4 + 10 | 1 ten, 4 ones | 14 |
| 10 + 9 | 1 ten, 9 ones | 19 |
| 10 + 0 | 1 ten, 0 ones | 10 |
Story problems
- Read the story. Are things joining or going away?
- Draw it or use counters.
- Then write the number sentence.
| Story | Number sentence | Answer |
|---|---|---|
| Mia has 8 pāua shells and finds 5 more. | 8 + 5 | 13 |
| 15 apples are in a box. 6 are eaten. | 15 − 6 | 9 |
| Tama has 11 stickers. He wants 20. | 11 + __ = 20 | 9 more |
Equal groups
- Multiplying means putting equal groups together.
- 3 groups of 4 strawberries: count 4, 8, 12.
- Every group must have the same number.
| Groups | In each | Count | Total |
|---|---|---|---|
| 2 | 5 | 5, 10 | 10 |
| 3 | 4 | 4, 8, 12 | 12 |
| 4 | 2 | 2, 4, 6, 8 | 8 |
| 5 | 3 | 3, 6, 9, 12, 15 | 15 |
Sharing fairly
- Dividing means sharing so every group gets the same.
- Share 12 strawberries between 3 children: one each, again and again, until none are left. Each gets 4.
- Or make groups: 10 socks in pairs is 5 pairs.
| Share | Between | Each gets |
|---|---|---|
| 12 | 3 | 4 |
| 20 | 4 | 5 |
| 10 | 2 | 5 |
| 18 | 3 | 6 |
Try it: share it fairly
Common mistakes
- 8 − 3 is the same as 3 − 8.Order matters when taking away. 8 − 3 = 5, but you cannot take 8 from 3 apples.
- 3 groups of 4 is 7.That is 3 + 4. Three groups of 4 is 4, 8, 12, so 12.
- Sharing 12 so one child gets 6 and two get 3 is fair.Fair sharing means the same for everyone: 4 each.
- 7 + __ = 11, so the answer is 18.The total is 11. Count on from 7 to 11: the missing number is 4.
Your turn
1
9 + 6 = __
2
7 + __ = 11
3
10 + 8 = __
4
How many in 4 groups of 5?
5
Share 14 grapes between 2 children. How many does each child get?
Show answer
1. 15 2. 4 3. 18 4. 20 5. 7
What to take away
- Make 10 to help you add.
- Order matters when taking away.
- Multiplying is equal groups put together.
- Dividing is sharing fairly.
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More in Number
Counting to 100 and Place ValueNotes1st, 2nd, 3rd, Te Reo Numbers and Number LinesNotesGroups, Pairs and Counting in 2s and 10sNotesNumber Facts to 10, Doubles and Adding to 20NotesJoining, Taking Away and Equal GroupsNotesHalves and QuartersNotesSharing Fairly: From Halves to QuartersNotesNew Zealand Coins and NotesNotes
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