Area of Rectangles by Tiling

Active learning through tiling gives students a tangible way to grasp area as a countable concept. When students physically place unit squares on rectangles, they build spatial reasoning that connects to multiplication, moving beyond abstract formulas to concrete understanding.

• Grade 3
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the area of a rectangle by counting unit squares arranged in rows and columns.
2. Compare the areas of different rectangles by tiling them with unit squares.
3. Explain the relationship between the number of unit squares along the length and width of a rectangle and its total area.
4. Construct a formula for the area of a rectangle using the measurements of its sides.
5. Identify rectangles with equal areas but different dimensions through tiling and calculation.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Tiling Challenges

Prepare four stations with grid paper rectangles of varying sizes and square tiles. Students tile each rectangle, record the area, and calculate length x width to check. Groups rotate every 10 minutes, then share one insight as a class.

Prepare & details

Explain how tiling a rectangle with unit squares helps us understand its area.

Facilitation Tip: During Station Rotation: Tiling Challenges, provide a mix of rectangle sizes and unit square sets to push flexible thinking about area.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Problem-Based Learning

⏱ 30 min·Pairs

Pairs Build: Target Area Rectangles

Give pairs a target area number and square tiles. They build as many different rectangles as possible that tile to that area, measure side lengths, and list multiplication sentences. Pairs swap builds to verify areas.

Prepare & details

Analyze the relationship between the side lengths of a rectangle and its area.

Facilitation Tip: For Pairs Build: Target Area Rectangles, model how to agree on dimensions before building, reinforcing measurement and collaboration.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Whole Class

Whole Class: Rectangle Design Contest

Students design a rectangle on grid paper for a playground or garden with a given area. They tile to confirm, label dimensions and multiplication fact, then vote on the most creative design that matches.

Prepare & details

Construct a formula for finding the area of any rectangle.

Facilitation Tip: In Whole Class: Rectangle Design Contest, invite students to explain their designs to peers, using math vocabulary like ‘rows’ and ‘columns’ intentionally.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 25 min·Individual

Individual: Virtual Tiling Exploration

Using online grid tools or apps, students create rectangles, tile digitally, and record areas with side lengths. They experiment with changing one side and predict area changes before tiling.

Prepare & details

Explain how tiling a rectangle with unit squares helps us understand its area.

Facilitation Tip: With Individual: Virtual Tiling Exploration, circulate to ask guiding questions such as ‘How do you know your rectangle has the right area?’ to assess reasoning.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Teach this topic by having students alternate between hands-on tiling and abstract recording. Avoid rushing to formulas; instead, let students discover the length x width pattern through repeated tiling. Research shows that students who physically tile and count are more likely to retain the concept and apply it correctly in new contexts.

What to Expect

Successful students will tile rectangles accurately without gaps or overlaps, count tiles to find area, and write matching multiplication sentences. They will explain how the number of rows times columns matches the total tiles, showing confidence in both visual and numerical representations.

Watch Out for These Misconceptions

Common Misconception

During Station Rotation: Tiling Challenges, watch for students who trace the perimeter of tiles instead of counting the interior squares.

What to Teach Instead

Ask students to trace the outside edge of the rectangle with one finger while counting interior tiles, then compare the two counts to clarify the difference.

Common Misconception

During Station Rotation: Tiling Challenges, watch for students who leave gaps or overlap tiles when tiling.

What to Teach Instead

Set a rule that tiles must fit edge-to-edge and provide a peer checker to verify coverage before counting area.

Common Misconception

During Pairs Build: Target Area Rectangles, watch for students who assume area depends on shape rather than dimensions.

What to Teach Instead

Have pairs build multiple rectangles with the same area but different dimensions, then discuss how the count of tiles remains constant despite different looks.

Assessment Ideas

Quick Check

After Pairs Build: Target Area Rectangles, ask each pair to present one rectangle they built. Have them display the tiles and explain how the count matches their multiplication sentence (length x width = area).

Discussion Prompt

During Whole Class: Rectangle Design Contest, display two rectangles with area 16 but different dimensions (e.g., 4x4 and 2x8). Ask students to show their tiling and explain why both have the same area, using unit squares as evidence.

Exit Ticket

After Station Rotation: Tiling Challenges, collect each student’s completed tiling sheet. Ask them to count the unit squares, write the multiplication sentence, and explain in one sentence how tiling shows area.

Extensions & Scaffolding

• Challenge early finishers to tile irregular rectangles made by combining two smaller rectangles, then find the total area.
• Scaffolding for struggling students: Provide rectangles pre-divided into rows or columns, letting them count without building from scratch.
• Deeper exploration: Ask students to compare areas of rectangles with the same perimeter, prompting them to notice how area changes with different dimensions.

Key Vocabulary

Unit Square	A square with sides that are one unit long, used to measure area. It has an area of 1 square unit.
Tiling	Covering a surface or shape completely with unit squares without any gaps or overlaps. This process is used to measure area.
Area	The amount of two-dimensional space a shape covers. It is measured in square units.
Square Unit	A standard unit for measuring area, such as a square centimeter or a square inch. It represents the area of a unit square.