Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Comparing Fractions , Halves and Quarters

Active learning helps students grasp the size of fractions by connecting abstract symbols to tangible experiences. When children fold paper or share real snacks, they physically see that a half covers more space than a quarter of the same whole, building lasting understanding beyond rote comparison.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.9

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

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Paper Folding: Halves vs Quarters

Give each pair a square of paper. Fold one into halves, shade one half; fold another into quarters, shade one quarter. Compare shaded areas by overlaying. Pairs discuss and record which is larger.

Which is bigger: one half or one quarter of the same thing?

Facilitation Tip

During Paper Folding: Halves vs Quarters, circulate to ensure students fold their paper strips exactly in half first, then fold each half in half again to create quarters, reinforcing equal parts.

What to look for

Provide students with two identical rectangles, one divided into two equal parts and one into four equal parts. Ask them to shade one part of each rectangle and write which shaded part is bigger and why.

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

Activity 02

• Think-Pair-Share
• 35 min · Small Groups

Fraction Tiles: Ordering Line

Distribute fraction tiles for halves and quarters. In small groups, arrange tiles from smallest to largest piece. Groups explain their order to the class and justify with drawings.

How can you use pictures or diagrams to compare halves and quarters?

Facilitation Tip

For Fraction Tiles: Ordering Line, ask students to explain their placement of tiles aloud so peers hear reasoning about size and equivalence, not just order.

What to look for

Hold up fraction cards showing 1/2 and 1/4 (using pictures). Ask students to give a thumbs up if they think 1/2 is bigger, thumbs down if they think 1/4 is bigger, and a thumbs sideways if they are unsure. Discuss the results.

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

Activity 03

• Think-Pair-Share
• 30 min · Pairs

Sharing Snacks: Real Fractions

Provide oranges or playdough balls. Pairs divide into halves and quarters, compare piece sizes visually and by feel. Record comparisons on worksheets with sketches.

Can you put halves and quarters in order and explain which is the greatest?

Facilitation Tip

In Sharing Snacks: Real Fractions, let students use real crackers or chocolate bars to model fractions, which builds immediate relevance and reduces confusion about abstract symbols.

What to look for

Present students with a scenario: 'Imagine you have one chocolate bar. Would you rather have one half of the bar or one quarter of the bar? Explain your choice using words or drawings.'

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

Activity 04

• Think-Pair-Share
• 20 min · Whole Class

Diagram Match: Whole Class Sort

Project shapes divided into halves and quarters. Class votes on which is larger in pairs of diagrams, then sorts cards into order as a group.

Which is bigger: one half or one quarter of the same thing?

What to look for

Provide students with two identical rectangles, one divided into two equal parts and one into four equal parts. Ask them to shade one part of each rectangle and write which shaded part is bigger and why.

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

A few notes on teaching this unit

Teach through guided discovery with hands-on materials so students see fractions as parts of a whole, not just numbers. Avoid rushing to symbols; let children verbalize their observations using words like ‘more’ and ‘less’ before introducing fraction notation. Research shows concrete experiences strengthen fraction sense in early grades, so prioritize visual and tactile learning before abstract tasks.

Students will confidently state that one half is larger than one quarter of the same whole and explain why. They will use materials to demonstrate equivalence between two quarters and one half, and order halves and quarters from least to greatest with clear reasoning.

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Watch Out for These Misconceptions

• During Paper Folding: Halves vs Quarters, watch for students who fold paper unevenly or assume all pieces are equal by size alone.

  Have students use a ruler to measure folded edges or refold to check equal parts before shading, reinforcing the need for equal shares in fractions.

• During Fraction Tiles: Ordering Line, watch for students who order tiles by the number of pieces rather than the size of each piece.

  Ask students to place tiles on top of each other to compare physical size directly, forcing them to see that two quarters fit exactly over one half.

• During Sharing Snacks: Real Fractions, watch for students who claim quarters are always bigger because there are more pieces.

  Give each student the same-sized snack to divide, then compare one quarter piece to one half piece side by side to show the difference in size.

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Methods used in this brief

• Think-Pair-Share