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Digit Sums and Divisibility

Discover why you can test for divisibility by 3 and 9 by adding digits, and prove it.

Grade 9Math OlympiadMathNumber SenseLogicAdvanced45 to 75 min3 materials

What you'll learn

  • State and test divisibility rules for 3, 9 and 11
  • Use place value to explain the rules
  • Write a short proof

Objective

Investigate why digit sums reveal divisibility by 3 and 9, and prove the rule using place value.

STEM concepts

Number theoryPatternsProof
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Materials and safety
Step-by-step instructions
Prediction, test sheet and results
Why does it work, challenge and project report

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