Mathematics · Foundation

Active learning ideas

Covering Space: Which Covers More?

Active learning works for this topic because young students need to physically manipulate objects to grasp the abstract concept of area. Covering shapes with tiles or counters provides a concrete experience that builds foundational measurement understanding before moving to symbolic representations.

• ACARA Content Descriptions
• AC9M6M02

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Shape Covering Stations

Prepare stations with rectangles, triangles, and mixed shapes on mats. Students cover each with square tiles, count units used, and note patterns. Groups rotate every 10 minutes, then share findings.

Can you cover this shape with tiles , how many do you need?

Facilitation Tip

During Shape Covering Stations, circulate and ask guiding questions like 'How did you decide this shape needs more tiles?' to prompt deeper thinking.

What to look for

Provide students with two different-sized rectangles made of grid paper. Ask them to count the number of squares in each and write down which one has more squares. Then, ask them to explain their answer using the word 'area'.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Experiential Learning
• 25 min · Pairs

Pairs Challenge: Table Coverage Compare

Give pairs two shapes cut from paper. They cover a table section with each shape using tiles, count tiles, and decide which covers more. Pairs explain their reasoning to the class.

Which shape covers more of the table , the big one or the small one?

Facilitation Tip

For Table Coverage Compare, model how to align books flush against the edge to avoid gaps before students begin their challenge.

What to look for

Give each student a small shape drawn on paper (e.g., a small rectangle or triangle). Ask them to draw square units inside the shape to cover it completely. On the back, they should write how many square units they used and if this shape is bigger or smaller than another shape they covered today.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 35 min · Whole Class

Whole Class: Book Layout Puzzle

Display a large outline on the floor. Students suggest and test laying flat books or blocks to cover it without overlaps. Class votes on best coverage and counts total units.

Can you lay books flat to cover this space?

Facilitation Tip

In the Book Layout Puzzle, demonstrate how to rotate books to test different arrangements before finalizing the cover.

What to look for

Present two objects of different sizes on a table, like a placemat and a small rug. Ask students: 'Which object covers more of the table? How do you know?' Encourage them to use terms like 'area' and 'square units' in their explanations.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Personal Space Tiles

Each student gets grid paper shapes and counters. They cover shapes, count squares, and draw their tiling. Collect for a class display comparing areas.

Can you cover this shape with tiles , how many do you need?

Facilitation Tip

For Personal Space Tiles, provide students with a variety of tile sizes to encourage discussion about unit consistency.

What to look for

Provide students with two different-sized rectangles made of grid paper. Ask them to count the number of squares in each and write down which one has more squares. Then, ask them to explain their answer using the word 'area'.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teachers approach this topic by starting with simple, relatable shapes and gradually introducing complexity. Avoid rushing to formulas by letting students discover that area depends on interior space, not just outline length. Research shows that repeated hands-on experiences with direct comparison strengthen spatial reasoning and measurement vocabulary in young learners.

Successful learning looks like students accurately covering shapes without gaps or overlaps, counting units precisely, and confidently comparing which shape covers more space. They should use language such as 'area' and 'square units' when explaining their reasoning to peers.

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Watch Out for These Misconceptions

• During Shape Covering Stations, watch for students assuming a long, skinny rectangle covers more area because it's longer.

  Have students recount the tiles in both the long rectangle and a compact shape with the same perimeter, then ask them to physically rearrange the tiles to test their assumption.

• During Shape Covering Stations, watch for students leaving gaps or overlapping tiles when counting area.

  Pause the activity and remind students to check for complete coverage by holding up their shapes to the light to spot gaps or overlaps before recounting.

• During Table Coverage Compare, watch for students believing that shapes with the same outline length have equal area.

  Provide students with two books of the same perimeter but different shapes, then ask them to cover each with identical square tiles to count and compare the areas directly.

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Methods used in this brief

• Stations Rotation
• Experiential Learning