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

Halving Even Numbers to 20

Extending halving skills to even numbers up to 20 using concrete materials.

• National Curriculum Attainment Targets
• KS1: Mathematics - Multiplication and Division
• KS1: Mathematics - Fractions

About This Topic

Halving even numbers up to 20 builds directly on Year 1 students' experience with halving to 10. Children use concrete materials such as counters, linking cubes, or beads to partition even totals into two equal whole-number groups. They compare strategies for smaller numbers with those for teens, construct reliable methods to halve 16, and explain why only even numbers yield equal wholes. This work aligns with KS1 standards in Multiplication and Division while introducing Fractions through halves.

Within the Multiplicative Thinking unit, halving develops partitioning fluency, doubles facts, and early reasoning about operations. Students practise mathematical talk by justifying methods and spotting patterns, such as 10 halved is 5 while 20 halved is 10. These skills prepare for grouping in multiplication and support data handling by equalising sets.

Active learning suits this topic perfectly. Hands-on sharing with manipulatives reveals the even-odd distinction visually, while pair discussions encourage strategy sharing and error correction. Children gain confidence as they physically verify halves, making abstract ideas concrete and memorable.

Key Questions

1. Compare halving numbers to 10 with halving numbers to 20.
2. Construct a method to halve the number 16.
3. Justify why only even numbers can be halved into two equal whole numbers.

Learning Objectives

• Calculate the half of any even number up to 20 using concrete manipulatives.
• Compare the process of halving numbers to 10 with halving numbers to 20.
• Construct a step-by-step method to find half of the number 16.
• Explain why only even numbers can be divided into two equal whole number groups.

Before You Start

Halving Numbers to 10

Why: Students need prior experience with halving smaller numbers to build confidence and understanding for larger numbers.

Identifying Even and Odd Numbers

Why: Understanding the concept of even numbers is fundamental to knowing which numbers can be halved into equal whole number groups.

Key Vocabulary

Halving	Splitting a whole into two equal parts. For example, halving 10 means making two groups with 5 in each.
Even Number	A whole number that can be divided exactly by 2, meaning it can be shared into two equal groups with none left over.
Whole Number	A number that is not a fraction or decimal, such as 0, 1, 2, 3, and so on.
Concrete Materials	Physical objects like counters, blocks, or toys that children can touch and move to help them understand mathematical ideas.

Watch Out for These Misconceptions

Common Misconception

Any number can be halved into two equal whole numbers.

What to Teach Instead

Only even numbers divide evenly by 2 into wholes; odds leave a remainder. Pair work with counters shows the leftover one clearly, prompting discussions that build the justification rule through shared evidence.

Common Misconception

Halving 16 always means counting by 2s from 1.

What to Teach Instead

Children may skip partitioning and rote-count, missing the equal-groups concept. Group tower-building forces physical splits, helping them construct and compare reliable methods while reasoning about doubles links.

Common Misconception

Numbers over 10 cannot be halved the same way as to 10.

What to Teach Instead

Strategies scale up with practice. Manipulative stations let small groups test and compare, revealing patterns like double the half, which cements transferable skills through collaboration.

Active Learning Ideas

Pairs: Counter Sharing Challenge

Give pairs bags of 12, 16, or 20 counters. They share into two bowls equally, draw the halves, and label with numbers. Pairs then explain their method for 16 to the class. Extend by inventing a story for the counters.

25 min·Pairs

Small Groups: Cube Tower Halving

Groups build towers with even cubes up to 20, then snap or separate into two equal towers. Record the original and halves on charts. Compare towers to 10 with those to 20, noting doubled sizes.

30 min·Small Groups

Whole Class: Even Number Line-Up

Students hold numeral cards 10-20. Call even numbers; holders pair up and halve by sharing counters between them. Class discusses why odds stay out and justifies the rule.

20 min·Whole Class

Individual: Bead String Split

Each child threads even beads up to 20 on strings, folds to find halves, and records pairs. They mark even vs odd attempts to see patterns.

15 min·Individual

Real-World Connections

• Sharing sweets equally between two friends: If you have 12 sweets and want to share them equally with one friend, you need to find half of 12 to know how many each person gets.
• Dividing resources in a classroom: A teacher might need to divide 18 pencils equally between two tables for an art project, requiring the calculation of half of 18.

Assessment Ideas

Quick Check

Give each student 16 counters. Ask them to physically divide the counters into two equal groups and record how many are in each group. Then, ask them to write the number sentence: 16 divided by 2 equals 8.

Discussion Prompt

Present students with the numbers 15 and 14. Ask: 'Which of these numbers can we share into two perfectly equal whole number groups? How do you know?' Encourage them to use the terms 'even' and 'odd' in their explanations.

Exit Ticket

On a small card, write the number 18. Ask students to draw a picture showing how they would halve this number using objects, and then write the answer to 'What is half of 18?'

Frequently Asked Questions

How do I teach halving even numbers to 20 in Year 1?

Start with concrete manipulatives like counters for sharing into equal groups. Guide comparisons between halving to 10 and 20, focus on constructing a method for 16 using cubes, and use talk partners to justify even-only rules. Progress to drawings and number sentences, linking to doubles for reinforcement. This sequence builds fluency per KS1 standards.

Why focus on even numbers when halving in Year 1?

Even numbers ensure equal whole halves, aligning with KS1 Multiplication and Division goals. It introduces partitioning without fractions yet, while justifying the even rule develops reasoning. Concrete sharing activities make the concept accessible, preparing for multiplication facts and data equalising.

What manipulatives work best for halving even numbers?

Counters, linking cubes, beads, or straws allow tactile splitting into equal groups. For 16 specifically, two-colour counters visualise halves. Rotate materials across lessons to vary engagement, always pairing with recording to connect action to numerals and support progression to abstract work.

How does active learning help with halving even numbers?

Active approaches like pair sharing and group partitioning make halving visible and interactive, helping students discover even-odd rules through trial. Collaborative justification builds reasoning and corrects errors on the spot, while hands-on repetition boosts retention over worksheets. Year 1 children internalise concepts faster when physically verifying equals, gaining confidence for multiplicative thinking.