Mathematics · Year 1 · Multiplicative Thinking and Data · Summer Term

Introduction to Fractions: Quarters of Shapes

Understanding quarters of shapes and identifying when a shape is divided into four equal parts.

• National Curriculum Attainment Targets
• KS1: Mathematics - Fractions

About This Topic

In Year 1, students begin exploring fractions by recognising quarters of shapes, building on their understanding of halves. They identify when a shape, such as a circle, square, or rectangle, is divided into four equal parts. This involves partitioning shapes fairly and explaining why all parts must be the same size and shape to count as quarters. Key skills include comparing quarters to halves and constructing representations, like folding a circle into quarters.

This topic sits within the fractions strand of the National Curriculum for KS1 Mathematics, specifically supporting early multiplicative thinking. Students practise partitioning numbers and shapes, which lays groundwork for tenths and equivalent fractions in later years. It also connects to geometry through recognising 2D shapes and their properties, fostering precise language like 'equal parts' and 'quarter'.

Active learning shines here because young children grasp equality through manipulation. When they fold, cut, or share shapes hands-on, they see and feel why unequal parts do not make quarters. Collaborative tasks build confidence in articulating ideas, making abstract equality concrete and memorable.

Key Questions

1. Explain the difference between a half and a quarter of a shape.
2. Construct a way to show a quarter of a circle.
3. Analyze why all four parts must be equal to be called quarters.

Learning Objectives

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

Before You Start

Introduction to Halves

Why: Students need to understand the concept of dividing a whole into two equal parts before learning about dividing into four equal parts.

Recognising 2D Shapes

Why: Identifying shapes like circles, squares, and rectangles is necessary to partition them into equal 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.

Watch Out for These Misconceptions

Common Misconception

Any four parts of a shape count as quarters.

What to Teach Instead

Students often divide shapes unevenly and call them quarters. Hands-on folding and overlaying reveals size differences immediately. Pair discussions prompt them to refine partitions until parts match perfectly.

Common Misconception

Only straight-edged shapes like rectangles have quarters.

What to Teach Instead

Children may avoid circles or triangles, thinking quarters need straight lines. Manipulating curved playdough or folding paper shows quarters work on any shape. Group trials build flexibility in visualisation.

Common Misconception

A quarter is always the smallest part possible.

What to Teach Instead

Some confuse quarters with smaller divisions like eighths. Comparing to halves via cutting activities clarifies relative size. Collaborative sharing reinforces that quarters mean exactly four equal parts.

Active Learning Ideas

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.

35 min·Small Groups

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.

25 min·Pairs

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.

30 min·Whole Class

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.

20 min·Individual

Real-World Connections

• When sharing a pizza or a cake with three friends, each person receives a quarter of the whole, provided it is cut into four equal slices.
• Bakers often divide cakes and pies into quarters for serving, ensuring each customer receives a fair portion.

Assessment Ideas

Exit Ticket

Give each student a card with a shape drawn on it. Some shapes should be divided into four equal quarters, others into unequal parts or fewer/more than four parts. Ask students to circle the shapes that show quarters and write one sentence explaining their choice.

Discussion Prompt

Show students two shapes: one divided into four equal quarters and another divided into four unequal parts. Ask: 'Which shape is divided into quarters? How do you know? What is the difference between these two shapes?'

Quick Check

Provide students with paper circles. Ask them to fold their circle to show one quarter. Observe their folding technique and ask them to explain how they know they have made a quarter.

Frequently Asked Questions

How do I introduce quarters of shapes in Year 1?

Start with familiar shapes like circles from clocks or pies. Model folding a paper circle into halves first, then quarters, emphasising equal parts. Use real objects like quartered oranges for sensory reinforcement. Progress to students constructing their own divisions and justifying equality with peers.

What activities best teach equal quarters?

Hands-on tasks like playdough partitioning or paper folding work well. Students adjust parts until they stack perfectly, building intuition for equality. Follow with drawing or cutting challenges to transfer skills across shapes, always circling back to the key question of equal size and shape.

How can active learning help students understand quarters?

Active methods like manipulating shapes make equality tangible for kinesthetic learners. Folding, cutting, and sharing in pairs or groups lets students test ideas, correct errors through trial, and explain reasoning. This beats worksheets, as physical feedback cements why unequal parts fail, boosting retention and confidence in fraction talk.

How does this link to the wider Year 1 maths curriculum?

Quarters extend halving from earlier terms, feeding into number partitioning and data units. It supports geometry by naming 2D shapes and measures through fair sharing. These skills prepare for multiplication arrays in Year 2, while group activities align with problem-solving in the National Curriculum.