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Problem solving activities

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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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Poppy meets Pythagoras

Level Five
Integrated
Problem solving activities
This problem solving activity has a geometry focus.
  • Find connections between numbers in a table.
  • Use Pythagoras’ theorem in a general algebraic form.
  • Measure accurately from a scale drawing.
  • devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
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Flip's flag

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the angle properties of squares, rectangles and triangles.
  • Use fractions to express the relationships between the areas of rectangles, squares and triangles.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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The clumsy tiler A

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Recognise and invent patterns with reflection symmetry.
  • Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).
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Castles on the ground

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Construct 3D shapes from 2D drawings.
  • Describe the symmetries of 3D shapes.
  • Draw 3D shapes on isometric paper.
  • Interpret information and results in context; make conjectures in a mathematical context.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, use...
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Robots

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Follow grid references.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
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The castle

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Construct 3-D shapes from 2-D drawings.
  • Describe the symmetries of 3-D shapes.
  • Draw 3-D shapes on isometric paper.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, use equipment).
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Circles and oblongs

Level One
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Give a sequence of instructions related to movement and position (forwards, backwards, sidewards, left, right).
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
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Noughts

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Use symmetry as a game strategy.
  • Apply problem solving strategies to a game context.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
  • Make conjectures in a mathematical context.
  • Critically follow a chain of reasoning.
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More of Carrie's cubes

Level Four
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the properties of 3-D objects to solve a problem.
  • Visualise 3-D objects.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Carrie's first cubes

Level Four
Integrated
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the properties of 3-D shapes to solve a problem.
  • Visualise 3-D objects.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).