AC9M4M02 • Year 4 Maths
Recognise ways of measuring and approximating perimeter and area using appropriate formal and informal units.
Perimeter measures distance around a boundary in length units. Area measures surface coverage in square units. Shapes can share an area but have different perimeters, or share a perimeter but have different areas.
Learning intention: Choose and use formal and informal units to measure or approximate the perimeter and area of shapes and enclosed spaces.
Learning routine: Decide boundary or surface → choose and define a unit → measure or cover → combine full and part units → record units and any approximation → compare.
Worked example: The 4 by 6 rectangle covers four rows of six squares: 24 square units. Its perimeter is the four boundary lengths: 4 + 6 + 4 + 6 = 20 units. The internal grid lines do not contribute to perimeter.
Teacher asks: “Which number helps buy edging? Which helps choose surface covering?” Expected response: perimeter for edging, area for covering. Trace the edge, then shade the surface if the learner confuses them.
Worked example: Both rectangles cover 12 cm². A has perimeter 4 + 3 + 4 + 3 = 14 cm. B has perimeter 6 + 2 + 6 + 2 = 16 cm. Equal area does not force equal perimeter.
Preserved rectangle investigation: With 24 square tiles, 1 by 24 has perimeter 50 units; 2 by 12 has 28; 3 by 8 has 22; 4 by 6 has 20. Adding four side lengths is more efficient than counting every short boundary edge.
Worked example: The rows cover 4 + 2 + 2 = 8 cm². Tracing clockwise from the upper-left corner gives boundary lengths 4 + 1 + 2 + 2 + 2 + 3 = 14 cm. Both edges of the inward step belong to the boundary.
Worked method: Place string once around the full boundary without stretching it. Mark where its ends meet, straighten it, and measure between the marks with a ruler or tape. Repeat to check. Example readings 81 cm and 83 cm support about 82 cm; these are measuring approximations, not exact shape facts.
Informal comparison: The same edge might measure 24 short-stick lengths or 12 long-stick lengths. If each set uses one fixed unit, a long stick is twice the short stick’s length. For the same boundary, smaller units give a larger count.
Worked example: The triangle covers six full squares and four half squares. Four halves make two wholes, so its area is 6 + 2 = 8 square units. Counting each half as one would overcount; ignoring the halves would undercount.
Another model: Six whole squares plus one quarter and three quarters make 7 square units. Fractional pieces must belong to the same-size square unit before combining them.
Worked method: Put one paper square at a corner. Trace its position, move it directly beside the trace and number the next placement. Continue across rows. Include part units at the edge. A 4 by 3 rectangle takes 12 full placements of a matching square: 12 square units.
Why it works: The same square provides an equal unit each time. Gaps omit surface; overlaps count some surface twice. Do the same with a triangle and combine or estimate the fractional edge pieces.
Worked example: This is an invented map. A covers 3 columns by 4 rows: 12 equal area units. B covers 3 by 3: 9 equal area units. A covers 3 more area units. No real site or Ranger measurement is represented.
Limit: An area comparison alone cannot decide where or when a real burn should occur. The public Ranger source below gives a specific example of mapping within a wider decision process.
Content description: recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units
E1: recognising that perimeter is the sum of the lengths that form the boundary of a shape or enclosed space; choosing suitable units from a range of objects to measure around the boundary of a shape such as a garden bed; comparing the results to say which unit was an appropriate choice for the context; using a piece of string or rope to measure the perimeter of irregular shapes and enclosed spaces, including those that have curved sections
Teach and measure: Walk a finger once around a rectangle, adding all boundary sides. Choose a fixed informal length unit for a garden-bed model, then compare with centimetres or metres. For a curved or irregular edge, fit string or rope around it, mark the meeting point, straighten and measure. Repeat and explain an approximate result. Evidence: actual full-boundary measuring, a suitable unit and a method that includes curved sections.
E2: creating a range of rectangles representing “paddocks” on grid paper and establishing different methods of working out the length of the boundary fences; explaining that the more efficient methods involve adding the side lengths rather than counting squares
Create paddocks: Draw rectangles on grid paper using different side-length pairs. For area 24 square units, compare the 1 by 24, 2 by 12, 3 by 8 and 4 by 6 examples above. Label the four sides and calculate each boundary sum. Teacher asks: “Why is adding 4 + 6 + 4 + 6 quicker than counting twenty short edges?” Evidence: actual drawings, correctly labelled boundaries and explained efficient addition.
E3: recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes, using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; comparing the total areas by combining the fractional parts to make whole units
Cover and combine: Use equal paper tiles to cover a rectangle and a shape with a sloping edge. A triangle may cover six whole squares and four halves, making eight square units. Pair halves or combine quarters from the same unit. Compare: seven whole squares plus two halves equals six whole plus four halves: both are eight square units. Look for: complete surface coverage and recorded full/part totals.
E4: demonstrating how to use one unit repeatedly to measure the area of a shape; for example, using one paper square to measure and compare the area of a rectangle and a triangle; recording and explaining how they used part units to give a more accurate measure, and why they needed to ensure there were no gaps or overlaps
Use one unit repeatedly: Give each learner only one paper square. They move, trace and number its positions on a rectangle, then a triangle. Record the full-square count and combined part count; show why no surface is skipped or counted twice. Evidence: actual repeated placement, marked positions, a stated unit and a justified total. Choosing a multiple-choice method alone does not demonstrate this practical skill.
E5: investigating the ways First Nations Ranger Groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place
Public context: The ALFA (NT) 2020 annual report, pages 56–57, describes Mimal Rangers mapping patches of unburnt land to assess wildfire risk, with GIS and mapped information alongside local Indigenous knowledge. This is a specific published example of mapped areas contributing to fire-related decisions about caring for Country/Place.
Classroom investigation: Read the account with an adult, discuss why the amount and location of land matters, then make an invented equal-square map like the one above. Compare covered areas, including parts of squares. State which comparison the model supports and what it cannot establish. Do not invent cultural meanings, reproduce restricted knowledge or use classroom maps to plan a real burn.
Use reliable, community-approved sources and identify the specific Nation, People or community where the source does. Do not present diverse First Nations knowledges as one generic tradition. Follow local cultural and intellectual property protocols before reproducing cultural material or inviting community participation.
Answer: 1 by 24: 50 units; 2 by 12: 28; 3 by 8: 22; 4 by 6: 20. All have area 24 square units. Require actual arrangements or drawings, full side sums and correct units.
Answer: Actual records vary. The string measures perimeter in length units; tiles measure area in square units. Require the complete boundary and coverage without gaps or overlaps.
Answer: Count every full square as one. Group the partial coverage into approximately whole units and state the method. If 12 squares are wholly inside and 7 more are only partly covered, the area is more than 12 and less than 19 square units. If the parts combine to about 4, estimate about 16 square units. Do not automatically drop all small parts.
Answer: Trace and number each placement; record the full-square count and combined part count for both shapes. Inspect real repeated placement and a justified area total or estimate. Accept valid alternative shapes and reasonable fractional estimates.
Teacher action: First trace an edge and cover a surface; then ask students to distinguish the two. If a learner counts internal grid lines for perimeter, retrace only the outer edge. If area placements overlap, demonstrate moving a single tile directly to the next uncovered position.
Answer: Area: 5 rows of 7 = 35 cm². Perimeter: 5 + 7 + 5 + 7 = 24 cm.
Answer: The same number of tiles can be arranged with different side lengths; 3 by 4 and 2 by 6 each cover 12 cm² but have perimeters 14 cm and 16 cm.
Answer: Square metres, or a clearly defined equal square floor tile as an informal unit.
Answer: Combine edge pieces into approximate whole square units, add the complete inside squares, and describe the method. Keep an estimate labelled about.
Answer: A centimetre is a length unit. A square centimetre is the area of a 1 cm by 1 cm square.
Review hint: Add each of the four sides once. Answer: 9 + 4 + 9 + 4 = 26 m. The boundary is length, so the unit is metres.
Review hint: Combine equal-unit parts before adding. Answer: Six halves make three whole squares; 7 + 3 = 10 square units.
Review hint: Trace the unit before moving it. Answer: Inspect the real triangle, marked placements, whole/part counts, total or estimate, and explanation of no gaps or overlaps. Results vary with the drawing.
Materials and timing: Allow two or more lessons for boundary/area comparisons and practical investigations. Use grid paper, one paper square per learner, extra tiles for arrays, rulers, paper strips and string.
Prerequisites: repeated equal units, addition of lengths and halves/quarters. Support: trace boundaries in one colour; cover simple rectangles with equal tiles. Core: measure, draw and compare rectangles and irregular/curved shapes; combine fractional square units. Extend: create equal-area or equal-perimeter rectangle pairs, or improve and justify an irregular-area estimate.
Boundary: Derive boundary sums and use square-unit coverage. Circle circumference formulas, triangle-area formulas and formal square-unit conversion algorithms are not required. Use rows and columns to organise a count without replacing the idea of covering.
Answer: Perimeter 6 + 3 + 6 + 3 = 18 units; area 18 square units. The numerical counts happen to match but measure different attributes.
Answer: Four halves make two wholes, so the area is 6 square units.
Answer: Require actual measuring evidence, the complete boundary or surface, correctly interpreted units and a sound treatment of curved edges or fractional area parts. Different valid constructions are accepted.
Mastery evidence: The learner can distinguish attributes, choose units, measure curved boundaries and move a square unit repeatedly, including parts without gaps or overlaps. Correct numerical answers alone do not establish these practical skills.
Use the Topic Guide and native Classroom View for instruction, then move to the written worksheet, supported Practice and Test resources.
Teacher resource
Project the native Classroom View one teaching section at a time, using the same worked models and answers as this Topic Guide.
Open Classroom View| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M4M02 |
| Victoria | Victorian Curriculum F–10 | Year 4 Measurement: perimeter and area. |
| NSW | NSW Curriculum | Stage 2 Mathematics: length, perimeter and area. |
| United States | Common Core | Grade 4 measurement and geometric measurement. |
| England / UK | National Curriculum | Year 4 measurement: perimeter and area. |
| New Zealand | New Zealand Curriculum | Level 2 measurement. |
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Khan Academy — Split a gridded shape into rectangles to find its area in square units.
As you watch: How can you split the shape without counting any square twice?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Draw an L-shaped region on squared paper. Split it into two rectangles and check its area by counting squares.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
Math Antics — Distinguish the distance around a shape from the area inside it.
As you watch: Which lengths belong in a perimeter calculation?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Use a ruler to find the perimeter of a small rectangular book cover. State the unit.
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Mapped skill: recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M4M02 · Year 4 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M4M02 · Level 4 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA2-2DS-03 + MA2-GM-02 · Stage 2 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 4 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 4 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 5, Key Stage 2 |
| India | NCERT / CBSE — Mathematics | Class 4 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M4M02 — AC9M4M02: Perimeter and area of shapes and enclosed spaces
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