Mathematics · Year 1 · Fractions and Sharing · Term 4

Quarters of Shapes and Objects

Dividing shapes and objects into four equal parts and identifying quarters.

• ACARA Content Descriptions
• AC9M1N05

About This Topic

Quarters mean dividing a shape or object into four equal parts. Year 1 students practise this by partitioning circles, squares, rectangles, and familiar items like cakes or oranges. They see that two quarters form a half, fold paper to create quarters, and check if parts match in size and area. This builds from halving work and prepares for fraction equivalence.

Aligned to AC9M1N05, the topic strengthens number partitioning and geometric reasoning. Students construct divided shapes, justify equal shares, and link quarters to fair division in sharing scenarios. Spatial awareness grows as they compare whole shapes to parts, supporting later fraction models and proportional thinking.

Active learning suits quarters perfectly since equality is best felt through manipulation. When students cut clay models or sort quartered fruits in groups, they test divisions hands-on and debate fairness with peers. These experiences turn abstract equality into visible, touchable reality, boosting confidence and retention.

Key Questions

1. Analyze the relationship between halves and quarters of a whole.
2. Construct a shape that is divided into four equal quarters.
3. Justify why four unequal parts do not make quarters.

Learning Objectives

• Identify shapes and objects divided into four equal parts.
• Construct a shape divided into four equal quarters.
• Compare two quarters to one half of a whole shape.
• Explain why four unequal parts do not represent quarters.

Before You Start

Halves of Shapes and Objects

Why: Students need to understand the concept of dividing a whole into two equal parts before they can divide it into four equal parts.

Identifying Equal and Unequal Parts

Why: A foundational understanding of what constitutes 'equal' is necessary to grasp the definition of quarters.

Key Vocabulary

Quarter	One of four equal parts of a whole shape or object.
Equal parts	Pieces that are exactly the same size and shape.
Whole	The entire shape or object before it is divided.
Partition	To divide a shape or object into parts.

Watch Out for These Misconceptions

Common Misconception

Any four parts of a shape are quarters.

What to Teach Instead

Quarters must be equal in size and area. Group sorting of quartered vs. unequal images lets students measure with strings or overlay parts, revealing mismatches through direct comparison and peer feedback.

Common Misconception

Quarters always look the same shape as each other.

What to Teach Instead

Equal quarters can vary in shape if areas match, like pizza slices. Hands-on cutting activities with playdough help students test area equality by stacking pieces, shifting focus from looks to measurement.

Common Misconception

Four small pieces make quarters even if the whole is not filled.

What to Teach Instead

Quarters partition the entire whole equally. Collaborative puzzles where groups fit quarters into outlines expose gaps, prompting discussions on complete coverage and equal shares.

Active Learning Ideas

Pairs: Paper Folding Quarters

Give each pair square paper. Fold in half vertically, then horizontally to form four equal rectangles. Students unfold, color one quarter, and explain to partners why all parts match. Pairs swap papers to check equality.

20 min·Pairs

Small Groups: Clay Shape Quarters

Provide modeling clay and cutters for circles or squares. Groups divide each shape into four equal parts using strings or knives. They reassemble to verify wholeness and trade pieces to compare sizes visually and by touch.

30 min·Small Groups

Whole Class: Quartered Object Sort

Display images or real objects like quartered apples or pies. Class votes if each shows true quarters, discussing unequal examples. Students draw their own divided shapes on whiteboards to share justifications.

25 min·Whole Class

Individual: Draw and Divide

Students draw a shape, divide into four equal quarters with lines, shade one, and label. They self-check by cutting out and comparing parts for equal size before gluing back together.

15 min·Individual

Real-World Connections

• Bakers cut cakes into quarters to serve portions. Customers expect each quarter to be the same size for a fair share.
• When sharing a pizza, people often divide it into four equal slices, or quarters, so everyone receives a similar amount.

Assessment Ideas

Exit Ticket

Give students a circle and a square. Ask them to draw lines to divide each shape into four equal quarters. Collect and check if the parts are equal in size.

Quick Check

Show students several shapes: one divided into four equal quarters, one divided into four unequal parts, and one divided into two halves. Ask students to point to the shape that shows quarters and explain why the other shapes are not quarters.

Discussion Prompt

Present a shape divided into two halves and another shape divided into four quarters. Ask: 'How many quarters do you need to make one half? How do you know?' Encourage students to use their hands or draw to demonstrate.

Frequently Asked Questions

How do I teach quarters to Year 1 students?

Start with familiar objects like dividing a sandwich into four equal bites. Use folding and cutting paper shapes to show equality. Link to halves by combining two quarters, and have students justify divisions in sharing games. Visual aids and real items keep engagement high across lessons.

What activities recognise quarters in shapes?

Try clay partitioning where students divide and reassemble shapes, or paper folding to crease quarters. Object hunts with quartered fruits build recognition. Drawing tasks let them create and label quarters, reinforcing through repetition and variety for different learning styles.

How can active learning help teach quarters?

Active methods like group clay dividing or pair folding make equality tangible through touch and collaboration. Students test parts by stacking or measuring, correcting ideas instantly via peer talk. This beats worksheets, as physical manipulation and shared justifications deepen understanding and make fairness intuitive.

Common misconceptions about quarters in Year 1?

Students often think any four parts count as quarters or that shapes must match exactly. Address with hands-on sorts and cuts to compare areas. Emphasise whole coverage and equality through group debates, turning errors into learning moments with visual proofs.