☰ Year plan · Mathematics

Addition properties and mental strategies

Week 3 · Addition properties and mental strategies · 3 lessons
2

Mental math with tens and hundreds

Discover Mathematics P4: Term 1, Unit 2, Lessons 1–4
GoalAdd in my head by breaking numbers apart, using friendly numbers and adjusting (compensation).
New words
break apart · to split a number into tens and ones to add part by partfriendly number · a number like 10, 100 or 1,000 that is easy to addcompensation · changing a number to a friendly one and then fixing the answer
Explanation

You can add in your head with three ideas. Break apart: split one number into tens and ones and add the parts one at a time, 58 + 37 = 58 + 30 + 7 = 88 + 7 = 95. Friendly numbers: when numbers are near a hundred, think of the hundred. Compensation: change one number to a friendly one, add, then fix. For 398 + 245, add 2 to make 400. 400 + 245 = 645. Then take 2 away, because we added 2 too many: 645 − 2 = 643. For round numbers use place value: 2,600 + 1,700 is 26 hundreds + 17 hundreds = 43 hundreds = 4,300.

StrategyExample
Break apart58 + 37 = 58 + 30 + 7 = 95
Compensation398 + 245 = 400 + 245 − 2 = 643
Place value2,600 + 1,700 = 26 + 17 = 43 → 4,300
Worked examples
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Omar needs 58 + 37 for the price of two toys. He breaks 37 into 30 and 7. 58 + 30 = 88 and 88 + 7 = 95. The two toys cost 95 LE.
StepWork
1398 + 2 = 400
2400 + 245 = 645
3645 − 2 = 643
Add 398 + 245 with compensation. 398 is 2 less than 400. Add 400 + 245 = 645. We used 2 too many, so subtract 2: 645 − 2 = 643. Check by breaking apart: 398 + 245 = 300 + 200 + 98 + 45 = 500 + 143 = 643.
A school has 2,600 books in one library and 1,700 books in another. Think of hundreds: 26 hundreds + 17 hundreds = 43 hundreds. So there are 4,300 books in all.
Class activity

Mental math race. A grown-up says two numbers, for example 47 and 36. The child adds them without paper and explains the way: break apart, friendly number or compensation. Then change places. Try numbers near 100 and near 1,000.

Practice
1
Add 46 + 38 in your head by breaking apart.
2
Add 499 + 327 with compensation.
3
Add 3,400 + 2,900 using hundreds.
4
Hana pays 18 LE for a pack of bus tickets and 27 LE for a pack of water bottles. How much does she pay in all?
5
Is 297 + 156 equal to 453? Check with compensation.