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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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Pizza toppings 2

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (equations and expressions) focus.
  • Generate linear and quadratic patterns.
  • Make predictions using a rule.
  • Use a systematic method to solve a problem.
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Rectangular milk bottle crates

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (equations and expressions) focus.
  • Find and use patterns to solve a problem (algebraically or by using a table).
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Square milk bottle crates

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (equations and expressions) focus.
  • Find a rule for a quadratic pattern.
  • Explain the rule for a quadratic pattern.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a table, use algebra).
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Pigs, goats and sheep

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (equations and expressions) focus.
  • Use algebraic skills to solve a problem involving three variables.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
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Ten tiles I

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Identify numbers divisible by 10.
  • Count large but relatively straightforward sets.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, think, use a simpler case, draw a digram).
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Transforming a square

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Solve problems involving percentage increases and decreases
  • Apply the area formulas for squares and rectangles.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use a diagram).
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Square and triangular numbers

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Give a general expression for the nth term of a pattern.
  • Describe the links between different patterns.
  • Devise and use problem solving strategies to explore situations mathematically.
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The painting triplets

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Form and solve linear equations.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
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Rows of numbers

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Generate patterns from a structured situation.
  • Find a rule for the general term (extension problem).
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, guess and check, make a table, look for a pattern).
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Olympic training

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has an algebra focus.
  • Form and solve linear equations.
  • Use ratios.
  • Devise and use problem solving strategies to explore situations mathematically (draw a diagram).