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MathidiaMathematics Academy
Calculations and problem solving
Lesson 11 of 75
Introduction

Mental calculation strategies

Objective. Use compensation, partitioning and known facts efficiently.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Mental calculation strategies make sums easier to do in your head. Partitioning splits a number into parts: 47 + 38 = 47 + 30 + 8 = 85. Compensation rounds to a friendly number then adjusts: 56 + 29 = 56 + 30 − 1 = 85. Known facts help too: if 7 × 8 = 56, then 70 × 8 = 560. Choose the strategy that suits the numbers.

Worked example

Use a mental calculation strategy (compensation) to work out 56 + 29.

56 … 29
Illustrated card showing 56 … 29
  1. 129 is close to 30, which is easier to add.
  2. 256 + 30 = 86.
  3. 3You added 1 too many, so subtract 1.
  4. 486 − 1 = 85.

Answer: 85

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. When using compensation, pupils often adjust the wrong way, for example 56 + 29 = 56 + 30 + 1 = 87. You added 1 too many, so you must take 1 off.

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