Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Area of Parallelograms and Trapezoids

Active learning helps young students build a strong foundation in geometric reasoning. By moving, stacking, and covering shapes with their hands, children connect abstract area formulas to real, touchable experiences. This tactile work makes invisible concepts like conservation of area visible and memorable for junior infants.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Measurement - M.1.3

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Peer Teaching
• 25 min · Pairs

Shape Shift: Parallelogram Push

Give each pair playdough or paper cutouts of rectangles. Children push one side to form parallelograms, then cover both with counters. Discuss why the number of counters matches. Extend by drawing around shapes.

Explain how the area formula for a parallelogram relates to that of a rectangle.

Facilitation Tip

During Shape Shift: Parallelogram Push, remind children to press gently on the playdough to avoid distorting the base and height.

What to look for

Provide students with pre-drawn parallelograms on grid paper. Ask them to count the unit squares to find the area, then measure the base and height and multiply them. Ask: 'Does the base times height give you the same answer as counting the squares? Why do you think that is?'

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

Activity 02

• Peer Teaching
• 30 min · Small Groups

Trapezoid Tile Challenge

Provide trapezoid outlines on mats. In small groups, children fill with unit squares or blocks, count coverings, and compare to rectangle mats of same tiles. Record with drawings.

Analyse the components of the trapezoid area formula.

Facilitation Tip

For Trapezoid Tile Challenge, model how to rotate trapezoids so their parallel sides align before tiling.

What to look for

Give each student a card showing a simple trapezoid with its parallel bases and perpendicular height labeled. Ask them to write one sentence explaining how they might find the area of this shape, and one place they might see a shape like this.

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

Activity 03

• Peer Teaching
• 35 min · Whole Class

Playground Patchwork

Draw large parallelogram and trapezoid shapes on paper as 'fields'. Whole class adds square stickers or tiles to cover, then cuts and rearranges into rectangles. Share findings.

Construct a real-world problem requiring the calculation of a trapezoid's area.

Facilitation Tip

In Playground Patchwork, encourage students to name the shapes they create with blocks to reinforce vocabulary.

What to look for

Show students a rectangle and a parallelogram that have the same base and height. Ask: 'How are these shapes similar? How are they different? If I cut the parallelogram and rearranged the pieces, could I make a rectangle? What does this tell us about their areas?'

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

Activity 04

• Peer Teaching
• 20 min · Pairs

Block Balance

Pairs build matching parallelograms and trapezoids with multilink cubes. Cover with flat tiles and balance on scales to compare areas visually. Note equal coverings.

Explain how the area formula for a parallelogram relates to that of a rectangle.

Facilitation Tip

During Block Balance, ask guiding questions like 'What happens if we make the base longer?' to prompt comparisons.

What to look for

Provide students with pre-drawn parallelograms on grid paper. Ask them to count the unit squares to find the area, then measure the base and height and multiply them. Ask: 'Does the base times height give you the same answer as counting the squares? Why do you think that is?'

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

A few notes on teaching this unit

Teachers should start with rectangles because children already understand their area. Use guided questions to help students notice that rearranging a rectangle into a parallelogram with the same base and height does not change the tile count. Avoid rushing to formulas; focus on the conservation principle first. Research shows that physical manipulation leads to stronger conceptual understanding than abstract rules alone.

Success looks like students confidently stating that pushing a rectangle into a parallelogram does not change its area. They should use tiles to compare shapes and explain how base and height determine area, not just the shape's name or outline.

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Watch Out for These Misconceptions

• During Shape Shift: Parallelogram Push, watch for students who believe the area changes when the shape is pushed.

  Have students cover both the rectangle and the parallelogram with identical tiles and count them side-by-side. Lead a group discussion where students compare the counts and explain why the number stays the same.

• During Trapezoid Tile Challenge, watch for students who assume all trapezoids have larger areas than parallelograms.

  Provide trapezoids and parallelograms of varying sizes and ask students to tile them. Guide them to observe that area depends on base, height, and width, not the shape's name.

• During Playground Patchwork, watch for students who confuse area with the outline length.

  Ask students to trace the inside of shapes with their fingers and fill them with blocks. Use phrases like 'the space inside the lines' to emphasize the difference between area and perimeter.

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Methods used in this brief

• Peer Teaching