Speed calculation · lesson 10 of 25 · free

Squares next to a ten — Speed Calculation

Squares of round numbers are easy: 70² = 4900. A number ending in 1 or 9 sits right next to one. To step up by one, add the two numbers; to step down by one, take them away.

The fast method

Step from a neighbour — “square the round number, then step up or down one”

  1. Find the round neighbour and square it: 70² = 7 × 7 = 49, then two 0s → 4900.
  2. Ends in 1 (one more)? Add the round number and the number: 4900 + 70 + 71.
  3. Ends in 9 (one less)? Take them away: 69² = 4900 − 70 − 69 = 4761.

Use it for: Areas of squares, Pythagoras in Class 7–9, and checking square tables.

Worked example: 71² = 5041

  1. 70² = 4900.
  2. 71 is one more, so add 70 and 71.
  3. 4900 + 70 + 71 = 5041.

Check: 71 × 71 = 70 × 71 + 71 = 4970 + 71 = 5041 ✓

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🏁 Lesson 10 test

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🖨️ Squares Trick Worksheet

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