Mathematics · 2nd Class

Active learning ideas

Quarters: Equal Parts of a Whole

Active learning with quarters works because students need to physically manipulate and visualize equal parts before abstract reasoning can take hold. Folding, sorting, and drawing give children concrete evidence of how four quarters make a whole, which builds lasting fraction understanding.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Measurement - M.1.1

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

Activity 01

• Experiential Learning
• 25 min · Pairs

Paper Folding: Quarter Circles

Give each pair a circle of paper. Students fold it in half twice to create four equal quarters, then label and shade one or three quarters. Discuss how the folds confirm equal parts. Pairs share with the class using a document camera.

What does it mean to split something into four equal quarters?

Facilitation Tip

During Paper Folding: Quarter Circles, remind students to align edges precisely to avoid overlapping folds that create unequal parts.

What to look for

Give each student a paper circle. Ask them to fold it into four equal quarters and shade one quarter. Then, ask them to draw a set of 8 counters and circle three quarters of the counters.

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

Activity 02

• Experiential Learning
• 30 min · Small Groups

Object Sharing: Quarter Counters

Provide small groups with 12 counters or blocks. Students divide into four equal groups of three, then remove one group to show one quarter. Rotate roles: one divides, one checks equality, one records. Groups present findings on mini-whiteboards.

How is one quarter different from one half?

Facilitation Tip

While doing Object Sharing: Quarter Counters, circulate and support groups by asking them to trade objects until each pile has the same number.

What to look for

Present students with two images: one showing a shape divided into four equal quarters, and another showing a shape divided into four unequal pieces. Ask: 'Which shape is divided into quarters? How do you know? What is the difference between these two ways of dividing?'

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

Activity 03

• Experiential Learning
• 35 min · individual then pairs

Shape Partitioning: Draw and Shade

Individually, students draw rectangles or circles and partition into quarters using lines or folds. Shade specified amounts like two quarters. Pairs swap drawings to verify equality. Whole class gallery walk to spot patterns.

Can you show one quarter and three quarters of a shape or a group of objects?

Facilitation Tip

For Shape Partitioning: Draw and Shade, model how to use a ruler to draw straight lines that split shapes exactly into four equal areas.

What to look for

Hold up a set of 12 building blocks. Ask students to show you one quarter of the blocks. Then ask them to show you three quarters of the blocks. Observe if they can create equal groups of three.

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

Activity 04

• Experiential Learning
• 20 min · Whole Class

Whole Class: Quarter Story Problems

Pose problems like 'Share 16 sweets into quarters.' Students use personal tens frames or drawings to model. Think-pair-share solutions before whole class vote on strategies. Record correct methods on chart paper.

What does it mean to split something into four equal quarters?

Facilitation Tip

In Whole Class: Quarter Story Problems, ask students to act out the sharing scenarios with props to deepen understanding.

What to look for

Give each student a paper circle. Ask them to fold it into four equal quarters and shade one quarter. Then, ask them to draw a set of 8 counters and circle three quarters of the counters.

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

A few notes on teaching this unit

Teach quarters by starting with familiar halves, then show how a half can be split in half again to make quarters. Avoid rushing to symbols; let students describe quarters in their own words first. Research shows that young learners grasp fractions better when they can fold, cut, or rearrange materials before recording fractions with numbers or symbols.

Students will confidently fold shapes into four equal quarters, sort objects into four equal groups, and identify one quarter, three quarters, and the whole. They will explain why pieces must be equal and use this language in discussions with peers.

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Watch Out for These Misconceptions

• During Paper Folding: Quarter Circles, watch for students who fold unevenly or who think any small piece is a quarter.

  Have them unfold and refold, then overlay the quarters to check for matching sizes. Ask peers to verify by comparing their folded quarters side by side.

• During Paper Folding: Quarter Circles, watch for students who believe one quarter is larger than one half.

  Provide a pre-folded half-circle and ask them to split it into two equal quarters. Have them stack the two quarters against the half to see the halves relationship.

• During Object Sharing: Quarter Counters, watch for students who create unequal groups when dividing counters into quarters.

  Ask them to trade objects until all groups are equal. Have them count each group aloud and compare totals to the whole set.

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Methods used in this brief

• Experiential Learning