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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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Three in a line

Level Two
Integrated
Problem solving activities
This problem solving activity has a logic and reasoning focus.
  • Rotate pattern pieces through quarter and half turns.
  • Be systematic and count possibilities.
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Strawberry and Chocolate Milk

Level One
Integrated
Problem solving activities
This problem solving activity has a logic and reasoning focus.
  • Rotate patterns through quarter and half turns.
  • Count possibilities.
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Strawberry Milk

Level One
Integrated
Problem solving activities
This problem solving activity has a logic and reasoning focus.
  • Rotate patterns through quarter and half turns.
  • Count possibilities.
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Not enough drawers

Level One
Statistics
Problem solving activities
This problem solving activity has a statistics focus.
  • Describe three different categories to sort clothes into.
  • Sort clothes into three chosen categories.
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Tripods

Level One
Number and Algebra
Problem solving activities
This problem solving activity has a number (multiplication and division) focus.
  • Model and explain addition of sets of three and/or subtraction of sets of three.
  • Count forward or back in threes.
  • Devise and use problem solving strategies (act it out, draw a picture, use equipment appropriately).
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Difference magic squares

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Use algebra when necessary.
  • Construct 3 by 3 arrays of numbers according to a given rule.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Weighing time

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Solve simultaneous equations.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment, draw a diagram, use smaller cases, use algebra).
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Ten tiles III

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Identify numbers divisible by 9.
  • Count large but relatively straightforward sets.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, think).
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Ten tiles II

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Identify numbers divisible by 5.
  • Count large but relatively straightforward sets.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, think, draw a diagram).
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Nine tiles

Level Six
Number and Algebra
Problem solving activities
This problem solving activity has a number and algebra (patterns and relationships) focus.
  • Guess and check the solution to a number problem.
  • Explain the effect of "carry-overs" in addition problems.