3
Break the number apart
Discover Mathematics P2: Term 2, Lessons 91–100
GoalBreak numbers into tens and ones to subtract and add in your head, and use clusters of related facts.
New words
break apart · split a number into tens and onescluster · numbers that are close to each othermental math · working out an answer in your head
Explanation
We can break a number apart to make a problem easier. To subtract 75 − 32, break 32 into 30 and 2. First 75 − 30 = 45, then 45 − 2 = 43. To add 46 + 38, break both into tens and ones. Add the tens: 40 + 30 = 70. Add the ones: 6 + 8 = 14. Then 70 + 14 = 84. A cluster is a group of numbers that are close to each other. 29 + 31, 30 + 30 and 28 + 32 are all close to 30 + 30, and each one makes 60.
| Break apart | Steps | Answer |
|---|---|---|
| 75 − 32 | 75 − 30 = 45; 45 − 2 | 43 |
| 46 + 38 | 40 + 30 = 70; 6 + 8 = 14; 70 + 14 | 84 |
Worked examples
75 − 32: subtract the tens first, 75 − 30 = 45, then the ones, 45 − 2 = 43.
46 + 38: tens 40 + 30 = 70, ones 6 + 8 = 14, and 70 + 14 = 84.
| Problem | Sum |
|---|---|
| 30 + 30 | 60 |
| 29 + 31 | 60 |
| 28 + 32 | 60 |
Class activity
Break it apart. Write a number such as 48 on a card. On the back write three different ways to break it apart, for example 40 + 8, 30 + 18 and 20 + 28. Then use one of them to solve 48 + 25.
Practice
1
Break apart to find 86 − 23.
86 − 20 = 66, then 66 − 3 = 63.
2
Break apart to find 54 + 27.
50 + 20 = 70, 4 + 7 = 11, and 70 + 11 = 81.
3
Find 90 − 35 by breaking 35 into 30 and 5.
90 − 30 = 60, then 60 − 5 = 55.
4
Find 29 + 31 using a cluster near 30 + 30.
29 is 1 less than 30 and 31 is 1 more, so the sum is 60.
5
Write 123 in two ways as hundreds, tens and ones.
100 + 20 + 3, and 100 + 10 + 13.