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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. 
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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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Karen's tiles

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Investigate how perimeter changes as area changes.
  • Identify the relation between area and perimeter for similar shapes.
  • Pose questions for mathematical exploration.
  • Prove or refute mathematical conjectures.
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Playdough balls

Level Five
Integrated
Problem solving activities
This problem solving activity has a measurement focus.
  • Compare the volume of a sphere and a cylinder by measuring or applying a formula.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
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Tennis ball tubes

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Use the formula for the circumference and diameter of a sphere to solve a problem.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
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Puck's girdle

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Find the circumference of a circle.
  • Understand the relationship between changes in the circumference of a circle and changes in the radius.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
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Penny's box

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Find the volume and surface area of rectangular prisms.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
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Bill's badge

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Construct two intersecting circles where the radius of the second circle is on the circumference of the first.
  • Use Pythagoras’ theorem to find the area of a rhombus.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model).
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A4 containers

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Describe the relationship between the surface area and volume of a container.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use a model).
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Square pegs in round holes

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Draw a diagram to represent a physical situation for a general case.
  • Apply Pythagoras’ theorem to a general situation.
  • Devise and use problem solving strategies to explore situations mathematically.
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Peter's string

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Determine the area of a rectangle with a given perimeter.
  • Pose questions for mathematical exploration.
  • Make conjectures in a mathematical context.
  • Prove or refute mathematical conjectures.
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The chicken run

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Explain the relationship between the area and perimeter of rectangles.
  • Use a table to solve a problem.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a table, make a drawing).