☰ Year plan · Mathematics

Subtracting on a number line and by parts

Week 23 · Subtracting on a number line and by parts · 3 lessons
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 apartStepsAnswer
75 − 3275 − 30 = 45; 45 − 243
46 + 3840 + 30 = 70; 6 + 8 = 14; 70 + 1484
Worked examples
4045505560657075−30−2
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.
ProblemSum
30 + 3060
29 + 3160
28 + 3260
A cluster near 30 + 30: 29 + 31 = 60, 28 + 32 = 60 and 32 + 28 = 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.
2
Break apart to find 54 + 27.
3
Find 90 − 35 by breaking 35 into 30 and 5.
4
Find 29 + 31 using a cluster near 30 + 30.
5
Write 123 in two ways as hundreds, tens and ones.