Mathematics · Foundation

Active learning ideas

Special Days and Celebrations

Active learning helps students grasp volume and surface area by connecting abstract math to tangible objects from their lives. When students build cake layers, wrap gifts, or design party hats, they physically manipulate shapes and measure in ways that make formulas meaningful.

• ACARA Content Descriptions
• AC9M8M01

• 25–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Placemat Activity
• 45 min · Small Groups

Small Groups: Birthday Cake Builder

Provide unit cubes and straws for students to construct a cake base as a rectangular prism and top as a dome approximated by cubes. Groups count total cubes for volume, then cover with foil squares to count surface area. Record findings on a class chart linked to birthdays.

Can you name a special day that we celebrate in our family?

Facilitation Tip

During Birthday Cake Builder, circulate and ask students to point to the layers they counted to reinforce volume as total space, not just height.

What to look for

Provide students with two simple 3D shapes (e.g., a cube and a rectangular prism). Ask them to combine the shapes to make a new object. Then, ask them to count the unit cubes to find the volume of their new object and explain how they counted.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 02

• Placemat Activity
• 30 min · Pairs

Pairs: Party Hat Designer

Pairs combine a cone (from paper or clay) with a cylinder brim using unit blocks inside for volume. They count blocks for volume and trace the outline on grid paper to count surface area squares. Pairs present to the class, naming the special day inspiration.

What month does your birthday happen in?

Facilitation Tip

In Party Hat Designer, challenge students to predict which shape will need more paper before they wrap, then test their hypothesis.

What to look for

Give each student a picture of a simple combined 3D shape (e.g., a cube on top of a rectangular prism). Ask them to draw unit squares on the visible faces to show how they would calculate the surface area and write down the number of unit squares they drew.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 03

• Placemat Activity
• 50 min · Whole Class

Whole Class: Celebration Composite Gallery

As a class, brainstorm special days from the calendar. Students vote on objects to model, then build shared composites like gift boxes from two prisms. Measure volume by cubes and surface area collectively, discussing combinations on a display wall.

Can you find a special event on our class calendar?

Facilitation Tip

For the Celebration Composite Gallery, provide a checklist of volume and surface area calculations for each model so students self-assess before presenting.

What to look for

Present students with two different combined shapes made from the same number of unit cubes. Ask: 'Which shape do you think has more surface area? Why?' Encourage them to explain their reasoning using the terms 'volume' and 'surface area'.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

Activity 04

• Placemat Activity
• 25 min · Individual

Individual: Personal Present Packer

Each student builds a small gift from two 3D shapes with unit cubes. They calculate volume by counting and surface area by wrapping with stickers. Students label with their birthday month and share one fact about the special day.

Can you name a special day that we celebrate in our family?

Facilitation Tip

During Personal Present Packer, remind students to measure each prism’s dimensions separately before combining to avoid gaps in counting.

What to look for

Provide students with two simple 3D shapes (e.g., a cube and a rectangular prism). Ask them to combine the shapes to make a new object. Then, ask them to count the unit cubes to find the volume of their new object and explain how they counted.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Start with simple shapes to build confidence, then gradually introduce combined forms. Avoid rushing to formulas—let students discover volume and surface area through counting and covering. Research shows hands-on building solidifies understanding more than abstract drills. Use peer teaching to clarify misconceptions as they arise.

Students will work collaboratively to build accurate models of celebration objects, calculate volume by counting unit cubes, and measure surface area by covering shapes with tiles or paper. They will explain their reasoning using precise geometric language.

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Watch Out for These Misconceptions

• During Birthday Cake Builder, watch for students who count only the height of a cake layer instead of the total cubes in all layers.

  Ask students to separate each layer, count the cubes in one layer, then multiply by the number of layers. Have them stack the layers back together to see how volume adds up across dimensions.

• During Party Hat Designer, watch for students who include internal seams or hidden surfaces in their surface area calculations.

  Use colored paper to cover only the visible outer surfaces. Ask students to unfold their hats and count only the squares on the outside, discussing why internal folds don’t count.

• During Celebration Composite Gallery, watch for students who assume combined shapes always add volumes and surface areas in simple ways.

  Have students physically join and separate shapes, measuring before and after to see how volumes add cleanly but surface areas may not. Use their combined models to discuss overlaps and gaps.

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Methods used in this brief

• Placemat Activity