Mathematics · Primary 2

Active learning ideas

Halves and Quarters

Active learning helps students grasp halves and quarters because hands-on work with physical materials builds spatial reasoning and visual memory. When children fold paper or share objects, they connect abstract symbols like ½ and ¼ to real experiences, making fractions meaningful and memorable.

• MOE Syllabus Outcomes
• MOE: Numbers and Algebra - P2
• MOE: Fractions - P2

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 20 min · Pairs

Pairs: Paper Folding Halves

Give each pair square and circular papers. Instruct them to fold each into two equal halves, crease firmly, and label ½ on each part. Then unfold and discuss why the folds create equal areas. Pairs compare results with neighbors.

What does it mean for the parts of a shape to be equal?

Facilitation Tip

During Pairs: Paper Folding Halves, circulate to ensure students align edges precisely when folding to avoid partial overlaps or gaps.

What to look for

Provide students with a worksheet showing several shapes and sets. Ask them to circle the shapes/sets divided into equal halves and write '½' on them. Then, ask them to circle the shapes/sets divided into equal quarters and write '¼' on them.

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

Activity 02

• Experiential Learning
• 30 min · Small Groups

Small Groups: Sharing Sets into Quarters

Provide groups with 12 items like buttons or straws. First, divide into two equal halves and notate ½. Then repartition into four equal quarters, drawing each ¼. Groups justify equality by matching parts side by side.

Why are two halves the same as one whole?

What to look for

Hold up a paper circle folded in half. Ask: 'How many equal parts do you see?' (Two). 'What do we call each part?' (A half). Repeat with a circle folded into quarters.

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

Activity 03

• Experiential Learning
• 25 min · Whole Class

Whole Class: Fraction Strips Comparison

Distribute precut strips to represent wholes, halves, and quarters. As a class, layer two ½ strips over four ¼ strips to show equivalence. Students record observations and notate matches on worksheets.

How is one quarter related to one half?

What to look for

Show a picture of a pizza cut into 4 unequal slices and another cut into 4 equal slices. Ask: 'Which pizza is cut into quarters? Why?' Guide students to explain the importance of equal parts.

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

Activity 04

• Experiential Learning
• 15 min · Individual

Individual: Shape Partitioning Drawings

Each student draws rectangles and circles, then shades halves and quarters accurately. They label with ½ and ¼, self-check by folding drawings, and note if parts are equal.

What does it mean for the parts of a shape to be equal?

What to look for

Provide students with a worksheet showing several shapes and sets. Ask them to circle the shapes/sets divided into equal halves and write '½' on them. Then, ask them to circle the shapes/sets divided into equal quarters and write '¼' on them.

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

A few notes on teaching this unit

Teachers should start with concrete materials before moving to drawings, as research shows that tactile experiences strengthen fraction sense. Avoid rushing to symbols; instead, build vocabulary and notation gradually through repeated exposure and guided practice. Emphasize the language of fractions by modeling phrases like 'one of two equal parts' to reinforce meaning.

Students will confidently divide shapes and sets into equal halves and quarters, name each part correctly, and use ½ and ¼ notation. They will explain why parts must be equal and how two halves or four quarters form a whole, showing both oral and written evidence of understanding.

---

Watch Out for These Misconceptions

• During Pairs: Paper Folding Halves, watch for students who create two parts that look different in size.

  Have students overlay their folded halves to check for exact matching edges. If they don’t match, guide them to refold carefully, emphasizing that halves must be identical in size and shape.

• During Small Groups: Sharing Sets into Quarters, watch for students who divide objects unevenly.

  Ask them to recount the objects in each group and verify totals match the original set. Use grid paper to arrange objects in rows of four to highlight equal distribution.

• During Whole Class: Fraction Strips Comparison, watch for students who confuse the size of quarters and halves based on visual length.

  Have students place a half strip next to a quarter strip and cover both with identical unit squares to show how four quarters fill the same space as two halves.

---

Methods used in this brief

• Experiential Learning