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Problem solving activities

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Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
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For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Problems for students to solve, accompanied by a suggested teaching sequence, extensions to the problem, and the problem’s solution.

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How many numbers?

Level Six
Number and Algebra
Problem solving activities
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a list).
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All the ones

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Use a calculator efficiently.
  • Devise a strategy to solve a number problem involving remainders.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Adding ten tiles II

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Use the numbers facts with digits to solve a problem.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, think, use algebra).
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Working backwards

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use their mathematical knowledge to invent problems.
  • Devise and use problem solving strategies to explore situations mathematically.
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My son is naughty

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Find factors of numbers.
  • Work systematically.
  • Use logic to explain away certain possible number combinations.
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The magic squares

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use algebra as required.
  • Construct magic squares.
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Doubling up

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Perform calculations with powers of numbers and square roots.
  • Explain the relation between a square root and a square.
  • Devise and use problem solving strategies to explore situations mathematically. This problem uses be systematic, draw a picture, and think.
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Spheres

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use powers.
  • Identify square and cube roots (with or without a calculator).
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use smaller cases).
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Time problems

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Understand how positive and negative numbers can be used in an unusual practical problem.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, use algebra).
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Base 3

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Write numbers in base 3.
  • Do arithmetic in base 3.
  • Explain the "links" between base 3 and decimal numbers.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).