Introduction to Fractions: Quarters of Shapes

Active learning works for quarters of shapes because young students need to physically interact with materials to grasp abstract equal-part relationships. Hands-on folding and cutting create immediate visual feedback, helping children correct their own partitioning errors and build confidence in their spatial reasoning.

• Year 1
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Identify shapes divided into four equal parts.
2. Explain why all four parts of a shape must be equal to be called quarters.
3. Compare a quarter of a shape to a half of a shape.
4. Construct a representation of a quarter of a circle by folding or drawing.

Stations Rotation

⏱ 35 min·Small Groups

Stations Rotation: Quarter Folding Stations

Prepare stations with paper circles, squares, and rectangles. Students fold each shape into quarters, check equality by overlaying parts, and label them. Rotate groups every 7 minutes, then share one method per group with the class.

Prepare & details

Explain the difference between a half and a quarter of a shape.

Facilitation Tip: At the Quarter Folding Stations, circulate with a transparency overlay to check each student’s fold lines for accuracy before they proceed to the next shape.

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

Experiential Learning

⏱ 25 min·Pairs

Playdough Partitioning: Equal Quarters

Give each pair playdough and shape cutters. Roll flat, cut into four, then adjust until parts match exactly by stacking. Discuss why changes were needed and draw results on mini-whiteboards.

Prepare & details

Construct a way to show a quarter of a circle.

Facilitation Tip: During Playdough Partitioning, ask students to press a ruler along their cuts to verify that all four pieces lift cleanly and match in weight.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Experiential Learning

⏱ 30 min·Whole Class

Shape Sharing Circle: Whole Class Demo

Display a large shape on the floor. Students suggest ways to divide into quarters using string or chalk, vote on best method, then verify by comparing parts. Record class findings on a chart.

Prepare & details

Analyze why all four parts must be equal to be called quarters.

Facilitation Tip: In the Shape Sharing Circle, deliberately fold one paper shape incorrectly to prompt students to identify and articulate the error in groups.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Experiential Learning

⏱ 20 min·Individual

Individual Matching: Quarter Puzzles

Provide printed shapes pre-cut into quarters, some equal, some not. Students sort into 'quarter sets' or 'not quarters,' explain choices to a partner, then create their own puzzle.

Prepare & details

Explain the difference between a half and a quarter of a shape.

Facilitation Tip: For Individual Matching Quarter Puzzles, provide a reference strip that shows a quarter marked on the side of their page to guide their cutting.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Teaching This Topic

Start with real-world connections, like cutting a sandwich into quarters for sharing, to anchor the concept in lived experience. Avoid premature symbolic notation; let students describe quarters in their own words first. Research shows that blending folding (manipulating halves) with cutting (producing quarters) accelerates the shift from additive to multiplicative thinking. Stay alert to the tendency to over-emphasize rectangles, and rotate triangle and circle tasks early to prevent shape bias.

What to Expect

Students will confidently partition shapes into four equal quarters and explain why parts must match in size and shape. They will compare quarters to halves and recognize quarters in both straight-edged and curved shapes without relying on counting alone.

Watch Out for These Misconceptions

Common Misconception

During Quarter Folding Stations, students often divide shapes unevenly and call them quarters.

What to Teach Instead

Ask each pair to place their folded quarters on a light box and overlap identical shapes to reveal any gaps or overlaps. Prompt them to re-fold until all edges align perfectly before labeling the parts.

Common Misconception

During Playdough Partitioning, children may avoid circles or triangles, thinking quarters need straight lines.

What to Teach Instead

Provide a set of curved and straight-edged cutters, and ask students to choose any shape to divide. After cutting, have them trace each part on paper and compare the outlines to see that quarters can be curved or angular.

Common Misconception

During Individual Matching Quarter Puzzles, some confuse quarters with smaller divisions like eighths.

What to Teach Instead

Ask students to set aside three puzzle pieces and check the remaining piece’s size against their reference strip. If it’s smaller than a quarter, they must trim it until it matches the strip exactly.

Assessment Ideas

Exit Ticket

After Individual Matching Quarter Puzzles, give each student a card with a square and a circle divided into four parts, some equal and some not. Ask them to circle only the shapes with true quarters and write, ‘I know because ______.’

Discussion Prompt

During Shape Sharing Circle, show one shape divided into four equal quarters and another divided into four unequal parts. Ask, ‘Which is divided into quarters? How do you know? What tells you the parts are equal?’

Quick Check

After Quarter Folding Stations, hand out paper circles and ask students to fold one quarter. Circulate with a checklist: Did they fold through the center? Did they verify all four flaps match when overlapped? Ask each student to explain how they confirmed their quarter was correct.

Extensions & Scaffolding

• Challenge: Provide hexagons and ask students to find multiple ways to partition into quarters, documenting each method with sketches.
• Scaffolding: Give students dotted lines lightly pre-printed on paper circles to guide their first fold.
• Deeper exploration: Introduce area puzzles where students must cover a shape with exactly four identical smaller shapes, not just cut it into four parts.

Key Vocabulary

quarter	One of four equal parts of a whole shape or object.
equal parts	Sections of a shape that are exactly the same size and shape.
whole	The entire shape or object before it is divided into parts.
partition	To divide a shape into smaller, equal parts.