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Problem solving activities

The Ministry is migrating nzmaths content to Tāhurangi.           
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. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

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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Triangular numbers

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Continue a pattern.
  • Use a table where appropriate.
  • Find a relation between successive members of a pattern.
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Multiples of a

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Perform calculations with algebraic quantities.
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Number plates

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Express numbers in a variety of ways.
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Sara's table

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe number patterns.
  • Solve problems involving patterns.
  • Devise and use problem solving strategies (guess and check, make a table, look for patterns).
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The farmer's sheep

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Devise and use problem solving strategies to explore situations mathematically.
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Take two

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Select and use a problem solving strategy (e.g. use equipment, work backwards, draw a picture).
  • Identify patterns used in solving the problem (multiples of 3).
  • Devise and use problem solving strategies (draw a picture, use equipment, think, work backwards).
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Race to 100

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe number patterns in words.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a drawing, use equipment).
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Toothpick squares

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • State the general rule for a practical situation.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a drawing, use equipment, make a table).
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Shaking hands

Level Three
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe in words the rules for the pattern.
  • Identify the pattern of triangular numbers.
  • Devise and use problem solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).
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Jo's table

Level Two
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Continue patterns.
  • Describe number patterns.
  • Devise and use problem solving strategies (guess and check, make a table, look for patterns).