Mathematics · Year 2 · Parts of the Whole · Spring Term

Halves and Quarters of Shapes

Identifying and shading halves and quarters of 2D shapes.

• National Curriculum Attainment Targets
• KS1: Mathematics - Fractions

About This Topic

Fraction families involve recognizing, naming, and writing unit fractions (like 1/3 and 1/4) and non-unit fractions (like 2/4 or 3/4). In Year 2, the National Curriculum focuses on halves, quarters, and thirds. Students learn that the denominator (bottom number) tells us how many equal parts the whole is divided into, while the numerator (top number) tells us how many of those parts we are looking at.

This topic also explores the relationship between different fractions, such as the fact that 2/4 is the same as 1/2. Understanding these connections helps students build a mental map of how numbers can be broken down. Students grasp this concept faster through structured discussion and peer explanation, where they 'build' fractions using sets of objects and describe them to their classmates.

Key Questions

1. Explain how to divide a shape into two equal halves.
2. Compare the size of a half to the size of a quarter of the same shape.
3. Design different ways to show a quarter of a rectangle.

Learning Objectives

• Identify and shade one half of a given 2D shape.
• Identify and shade one quarter of a given 2D shape.
• Compare the size of a half to the size of a quarter of the same shape.
• Design and draw at least two different ways to divide a rectangle into quarters.
• Explain why a shape must be divided into equal parts to show halves or quarters.

Before You Start

Recognizing 2D Shapes

Why: Students need to be able to identify basic 2D shapes like circles, squares, and rectangles before they can divide them.

Counting and Comparing Numbers

Why: Understanding the concept of 'two' and 'four' is fundamental to grasping halves and quarters.

Key Vocabulary

Half	One of two equal parts that a whole is divided into. It is represented as 1/2.
Quarter	One of four equal parts that a whole is divided into. It is represented as 1/4.
Equal parts	Sections of a whole that are exactly the same size.
Whole	The entire shape or object before it is divided into parts.

Watch Out for These Misconceptions

Common Misconception

Thinking 1/4 is bigger than 1/2 because 4 is bigger than 2.

What to Teach Instead

This is the most common fraction error. Use 'The Denominator Mystery' to show that more shares mean smaller pieces. Physically sharing a pizza between 2 vs. 4 people makes this instantly clear.

Common Misconception

Only recognizing fractions of shapes, not of sets.

What to Teach Instead

Students might know half a circle but not half of 6 apples. Use 'Fraction Builders' with physical objects like counters to show that the same rules of 'equal groups' apply to quantities.

Active Learning Ideas

Stations Rotation: Fraction Builders

Station 1: Use colored beads to make a fraction of a set (e.g., 1/3 are red). Station 2: Shade fractions of shapes. Station 3: Write fraction 'labels' for pre-made models. Groups rotate and check the previous group's work.

45 min·Small Groups

Gallery Walk: The Fraction Museum

Students create 'exhibits' showing a fraction in three ways: as a shape, as a set of objects, and as a number. The class walks around to find all the 'quarters' or 'thirds'.

30 min·Individual

Think-Pair-Share: The Denominator Mystery

Show a 1/2 and a 1/4. Ask students: 'Which number is bigger, 2 or 4? Which fraction is bigger?' Pairs discuss why the larger number on the bottom actually means a smaller piece.

15 min·Pairs

Real-World Connections

• When sharing a pizza, children learn to cut it into equal halves or quarters so everyone gets a fair share. This helps them understand the practical need for equal division.
• Bakers use fractions when measuring ingredients for recipes, like needing half a cup of flour or a quarter teaspoon of salt. Precise measurements ensure the recipe turns out correctly.

Assessment Ideas

Exit Ticket

Give each student a paper circle. Ask them to draw lines to show one half, then draw lines on a new circle to show one quarter. Collect and check if the parts are equal.

Quick Check

Display a rectangle divided into four unequal parts. Ask: 'Are these quarters? Why or why not?' Then display a rectangle divided into four equal parts and ask: 'What fraction does one part show?'

Discussion Prompt

Hold up a square. Ask: 'How can we divide this square into two equal halves?' Then ask: 'If I cut this square in half, and then cut one of those halves in half again, what fraction would the smallest pieces be? How does this compare to the first half?'

Frequently Asked Questions

What is a unit fraction?

A unit fraction is a fraction where the top number (numerator) is 1, such as 1/2, 1/3, or 1/4. It represents one single part of the whole.

How can active learning help students understand fraction families?

Active learning, such as the 'Fraction Museum,' encourages students to see fractions in multiple contexts. By building fractions with physical objects and then labeling them, they connect the abstract symbol (1/3) to a concrete reality. Peer discussion about why 1/4 is smaller than 1/2 helps them confront and correct the common misconception that 'bigger denominator equals bigger fraction'.

Why do we learn about thirds in Year 2?

Thirds are the first time students encounter a fraction that doesn't involve halving. It forces them to think about dividing by three and helps them understand that any number can be a denominator.

How do I explain the top and bottom numbers?

Call the bottom number the 'namer' (it tells us the name of the piece, like a quarter) and the top number the 'counter' (it tells us how many pieces we have).