ELPSA Lesson Plan

Area and Perimeter through Arrays and Partitioning

Students build understanding of multiplication, area and perimeter by noticing patterns in arrays, partitioning rectangles efficiently, and exploring how removing sections changes or preserves perimeter.

Stage / Year
Upper Primary or early Stage 4
Duration
Approximately 60 minutes
Focus
Area, perimeter, multiplication and partitioning
Resource
Area Model Splitter

Learning Intentions

  • Understand area as the number of square units covering a region.
  • Understand perimeter as the distance around a shape.
  • Use arrays and partitioning to support efficient multiplication strategies.
  • Explore how removing parts of a shape can change area and sometimes change or preserve perimeter.

Success Criteria

  • I can explain the difference between area and perimeter.
  • I can use an array to represent multiplication.
  • I can partition a rectangle to make calculations easier.
  • I can explain what happens to perimeter when sections are removed.

Materials

  • Area Model Splitter digital tool
  • Mini-whiteboards and markers
  • Student devices if available
  • Student Quiz with differentiated levels: Sweet to Extra Hot
  • Worksheet Creator for follow-up practice

Lesson Overview

The lesson begins with a multiplication number talk to activate partitioning strategies. Students then discuss where they have heard the terms area and perimeter and contribute examples from everyday life. The class uses the Area Model Splitter to notice how partitioning arrays supports efficient multiplication and to distinguish between the structure of area and the boundary of perimeter. Later, students explore shapes with removed sections and reason about when perimeter stays the same and when it changes.

Teacher move: Use mini-whiteboards throughout the lesson so students commit to dimensions, predictions and explanations before class discussion.

ELPSA Sequence

E — Experience

Begin with a short number talk using a multiplication expression such as 15 × 18, adjusted to suit student readiness. Students solve mentally and share different strategies.

Record student thinking such as:

  • 15 × 10 + 15 × 8
  • 18 × 10 + 18 × 5
  • 15 × 20 − 15 × 2

Then ask students where they have heard the words area and perimeter. Record examples from the class, such as fencing, carpet, paint, floor plans, gardens or sports courts.

Teacher prompts
  • How did you work that out?
  • Which part was easy to calculate first?
  • Where have you heard the word perimeter before?
  • Where might area matter in real life?

L — Language

Develop clear language for the mathematical ideas before formalising procedures.

  • Area: the amount of surface covered, measured in square units.
  • Perimeter: the total distance around the outside of a shape.
  • Array: an arrangement in rows and columns.
  • Partition: splitting a number or shape into useful parts.
  • Dimension: the side lengths of the rectangle.
  • Shaded region: the part of the figure we are considering.

Explicitly contrast the phrases covering the inside and going around the outside.

Language prompts
  • Which part shows area: the inside or the outside?
  • What do the individual squares represent?
  • What does the boundary tell us?
  • Why does partitioning help with multiplication?

P — Pictorial

Open the Area Model Splitter and lead a series of notice-and-wonder routines. Start with products of 10 and split vertically to highlight halving and partitioning strategies.

  • Use examples such as 10 × 18, 10 × 24 or 30 × 40.
  • Split vertically to show how 10 can become 5 + 5.
  • Discuss how the tool shows area as a collection of individual square units.
  • Use the perimeter feature to show the distance around the outside boundary.
  • Demonstrate that partitioning can make calculations easier by collecting tens or hundreds.
  • Use repeat partitions to explore structures such as 30 × 40 as 12 groups of 100, not just 3 × 4 with two zeros added.
Notice and wonder prompts
  • What do you notice when the array is split in half?
  • What stays the same after partitioning?
  • What changes visually?
  • How does the tool help us see tens or hundreds more clearly?

S — Symbolic

Link the visual model to equations and symbolic recording.

  • 15 × 18 = (10 × 18) + (5 × 18)
  • 30 × 40 = 12 × 100 = 1200 when viewed as repeated partitions of hundreds
  • A = l × w
  • P = l + w + l + w or P = 2l + 2w for rectangles

Make the connection that partitioning does not change the total area of the full rectangle, but it can make the total easier to calculate. Students can record matching diagrams and equations on mini-whiteboards.

Symbolic prompts
  • How would you record this split as a number sentence?
  • Which partial products can you see?
  • How does the area formula connect to the array?
  • Why is the perimeter not found by counting all the inside squares?

A — Application

Move to the feature where sections can be removed. Explore how the shape changes and ask students to predict what happens to area and perimeter before revealing the result.

  • Remove a corner piece and discuss when the perimeter can remain unchanged.
  • Remove an interior section or a section that creates an indentation and discuss why the perimeter changes because the new boundary must also be measured.
  • Use the pointer tool to focus on selected parts and justify reasoning.
  • Students then complete differentiated practice in the Student Quiz from Sweet to Extra Hot.
  • Use the Worksheet Creator for independent follow-up, revision or homework.
Application prompts
  • If this corner is removed, what do you predict will happen to the perimeter?
  • Why does removing an interior section change the fencing needed?
  • Can the area change while the perimeter stays the same?
  • Can the perimeter change while the area decreases?

Suggested Lesson Flow

Time Teacher actions Student actions Purpose
5–8 min Run a multiplication number talk such as 15 × 18. Share mental strategies on mini-whiteboards and orally justify methods. Activate multiplicative thinking and partitioning strategies.
5–7 min Ask where students have heard the words area and perimeter. Record examples. Contribute everyday contexts and prior understandings. Build relevance and surface prior knowledge.
12–15 min Demonstrate the tool with arrays, splits and repeat partitions. Lead notice-and-wonder discussion. Observe, notice patterns, predict totals and discuss how partitioning helps. Build visual understanding of area and multiplication structure.
10–12 min Reveal area and perimeter in the tool. Compare inside coverage and outside boundary. Explain the difference between the two measures using the model. Strengthen conceptual distinction between area and perimeter.
10–12 min Remove sections from shapes and ask students to predict effects on area and perimeter. Make predictions, justify reasoning, then test ideas using the tool. Develop reasoning about boundary changes.
10–15 min Set differentiated student practice using the Student Quiz or Worksheet Creator. Complete tasks at an appropriate level and explain solutions. Apply and consolidate learning.

Differentiation

Sweet

  • Rectangles from 5–10 by 5–10.
  • Students focus on straightforward rectangular arrays with no removed sections.
  • Suitable for building confidence with counting square units, linking multiplication to area, and using P = 2l + 2w for perimeter.

Mild

  • Rectangles from 10–20 by 10–20.
  • Students continue working with full rectangles, but with larger dimensions and more need for efficient partitioning strategies.
  • Encourage splitting into friendly parts to support multiplication and perimeter reasoning.

Medium

  • Rectangles from 10–50 by 10–50.
  • Students work with larger arrays where direct counting is impractical.
  • This level emphasises strategic partitioning, repeated partitions, and seeing structures such as tens, factors and groups of hundreds.

Spicy

  • Rectangles from 10–20 by 10–20 with up to 2 removed sections.
  • Students find the area and perimeter of the shaded region, rather than the full rectangle.
  • This supports discussion about how removing parts changes area, and how perimeter may stay the same or change depending on where the section is removed.

Extra Hot

  • Rectangles from 10–20 by 10–20 with up to 6 separate removed sections.
  • Students reason about more complex composite shapes with multiple missing parts.
  • This level is designed for deeper reasoning about internal edges, notches, preserved perimeter, and how the boundary of the shaded region must be traced carefully.

Assessment Opportunities

  • Listen to strategies during the opening number talk.
  • Check mini-whiteboards for accurate language and symbolic recording.
  • Ask students to justify whether area, perimeter or both change in each example.
  • Use student quiz data or completed worksheets as evidence of understanding.

Reflection / Exit Ticket

Ask students to respond to one or more of the following:

  • Explain the difference between area and perimeter in your own words.
  • How does partitioning help you solve multiplication more efficiently?
  • Describe a time when removing part of a shape changes the area but not the perimeter.
  • Give an example of a shape where the perimeter changes because the boundary now includes an inside edge.
Designed as an ELPSA-style lesson sequence using the Area Model Splitter tool, student discussion, and mini-whiteboards to connect experience, language, visual structure, symbolic representation and application.