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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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Jackson's consecutive numbers

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe a rule for the general term.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Displaying postcards

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Apply algebra to the solution of a problem.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use a table, use algebra).
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Can stack

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Find the rule for summing consecutive numbers.
  • Identify the pattern of triangular numbers.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
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Counting pills

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Express rules in words.
  • See more than one rule for a given pattern.
  • Devise and use problem solving strategies to explore situations mathematically.
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Still more lollies

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Solve multi-step problems that involve simple linear relationships.
  • Write simple linear expressions.
  • Devise and use problem-solving strategies to explore situations mathematically.
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The farmer's sheep II

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Describe a number pattern in words.
  • Devise and use problem solving strategies to explore situations mathematically.
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Take three or fewer

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Identify patterns used in solving the problem (multiples of 3).
  • Devise and use problem solving strategies (draw a picture, use equipment, work backwards).
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QwikQure medicine

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Use the graph to describe the relationship.
  • Devise and use problem solving strategies (draw a picture, make a table).
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Paul's patterns

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Find a rule to describe any member of a number sequence and express it in words.
  • Devise and use problem solving strategies to explore situations mathematically (systematic, guess and check).
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Topsy-turvy twins

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Use a graph to describe a rule for continuing a number sequence.
  • Use a graph to compare two number sequences.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a drawing).