Year 6 Mathematics · AC9M6M02

Establishing and Applying the Rectangle Area Formula

Connect arrays, multiplication, units and composite practical regions

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students derive area from rows and columns of square units, explain A = length × width and apply it to missing dimensions, composite spaces and material estimates.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: establish the formula for the area of a rectangle and use it to solve practical problems
Key conceptTeach from the board

Derive A = l × w from a square-unit array

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

rectanglerowssquares per rowarea6 cm × 4 cm4624 cm²l × ww rowsl per rowlw square units

The formula summarises repeated counting of square units. Units are squared because area measures two-dimensional coverage.

Solve practical and missing-dimension problems

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

floor 8 m × 5.5 m44 m²
area 72 m², width 8 mlength = 9 m
L-shapelarge rectangle − missing rectangle
tilesarea ÷ tile area; round for whole tiles and waste

Check dimensions use compatible units and distinguish area, perimeter and material quantity.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6M02 - Establishing and Applying the Rectangle Area Formula
Example 1

rectangle rows squares per row area 6 cm × 4 cm 4 6 24 cm² l × w w rows l per row lw square units

Example 2

: using one centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area

Example 3

: using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides

Example 4

: solving problems involving the comparison of lengths and areas using appropriate units

Curriculum examplesCopied content

AC9M6M02: establish the formula for the area of a rectangle and use it to solve practical problems

  • E1: using one centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area
  • E2: using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides
  • E3: solving problems involving the comparison of lengths and areas using appropriate units
  • E4: investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Derive 6×4 area.
  • Find a missing dimension.
  • Decompose an L-shape.
  • Convert before area.
  • Interpret tile count.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Perimeter formula usedArea counts covering; perimeter traces boundary.
Units not squaredUse cm², m² and related square units.
Length and width in different unitsConvert before multiplying.
Tile count left fractionalInterpret whole items and allowance.
Curriculum alignmentStart here

Learning goal

Students derive area from rows and columns of square units, explain A = length × width and apply it to missing dimensions, composite spaces and material estimates.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: establish the formula for the area of a rectangle and use it to solve practical problems
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