Year 5 Mathematics · AC9M5M02

Solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units

Students distinguish boundary length from surface coverage, calculate regular shapes, decompose composite regions and approximate irregular spaces with stated assumptions…

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Learning goalsSay it simply

Students distinguish boundary length from surface coverage, calculate regular shapes, decompose composite regions and approximate irregular spaces with stated assumptions and metric units.

Perimeter uses linear units around a boundary; area uses square units covering a region.

For area, subtract the missing rectangle. For perimeter, trace only the outer boundary and include the new internal corner edges.

An approximation is defensible when the grid scale, partial-square rule and uncertainty are stated.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

  • Represent accurately
  • Explain the relationship
  • Choose a suitable method or unit
  • Apply in context
  • Check and justify
Key conceptTeach from the board

Calculate a composite L-shaped garden

decompositiondimensionsarealarge rectangle8 m × 6 m48 m²removed rectangle3 m × 2 m6 m²garden area48 − 642 m²perimetersum outer edges24 m

For area, subtract the missing rectangle. For perimeter, trace only the outer boundary and include the new internal corner edges.

  1. Read every label and identify the quantities, parts or evidence.
  2. Explain the relationship shown—not just the final answer.
  3. Check the conclusion against the original question and units.

Approximate an irregular area on a grid

whole squarescount exactly
partial squarescombine halves or use a consistent threshold
perimetertrace boundary and estimate curved segments
reportstate approximately and give unit/range

An approximation is defensible when the grid scale, partial-square rule and uncertainty are stated.

Now transfer the same relationship to a new situation and justify the result with precise vocabulary.

Clean visual examplesOne-page board

Clean one-page examples

AC9M5M02 - Solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
Example 1

decomposition dimensions area large rectangle 8 m × 6 m 48 m² removed rectangle 3 m × 2 m 6 m² garden area 48 − 6 42 m² perimeter sum outer edges 24 m

Example 2

whole squares count exactly

Example 3

decomposition dimensions area large rectangle 8 m × 6 m 48 m² removed rectangle 3 m × 2 m 6 m² garden area 48 − 6 42 m² perimeter sum outer edges 24 m

Example 4

whole squares count exactly

Curriculum examplesCopied content

Content description: solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units.

  • E1: investigating problem situations involving perimeter; for example, “How many metres of fencing are required around a paddock, or around a festival event?”
  • E2: using efficient ways to calculate the perimeters of rectangles, such as adding the length and width together and doubling the result
  • E3: solving measurement problems, such as “How much carpet would be needed to cover the entire floor of the classroom”, using square metre templates to directly measure the floor space
  • E4: creating a model of a permaculture garden, dividing the area up to provide the most efficient use of space for gardens and walkways, labelling the measure of each area, and calculating the amount of resources needed; for example, compost to cover the vegetable garden
  • E5: using a physical or a virtual “geoboard app” to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter
  • E6: exploring the designs of fishing nets and dwellings of First Nations Australians, investigating the perimeter, area and purpose of the shapes within the designs
Questions and answersWith answers

Core idea: Perimeter uses linear units around a boundary; area uses square units covering a region.

Remember

  • Represent accurately
  • Explain the relationship
  • Choose a suitable method or unit
  • Apply in context
  • Check and justify

Important questions

  • Find area of an L-shape. Explain using the model or evidence above.
  • Trace a composite perimeter. Explain using the model or evidence above.
  • Choose m² for a garden. Explain using the model or evidence above.
  • Approximate partial squares. Explain using the model or evidence above.
  • Explain perimeter versus area. Explain using the model or evidence above.
Practice and reviewReady for practice
  • Interior grid lines included in perimeter — Trace only the external boundary.
  • Linear units used for area — Write cm² or m².
  • Missing rectangle added instead of removed — Check the physical region represented.
  • Approximation reported as exact — State method and uncertainty.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Curriculum alignmentStart here

Students distinguish boundary length from surface coverage, calculate regular shapes, decompose composite regions and approximate irregular spaces with stated assumptions and metric units.

Perimeter uses linear units around a boundary; area uses square units covering a region.

For area, subtract the missing rectangle. For perimeter, trace only the outer boundary and include the new internal corner edges.

An approximation is defensible when the grid scale, partial-square rule and uncertainty are stated.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

  • Represent accurately
  • Explain the relationship
  • Choose a suitable method or unit
  • Apply in context
  • Check and justify
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