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

Sharing Equally

Dividing a set of objects into equal groups to solve simple division problems.

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

About This Topic

Sharing equally introduces Year 1 students to division by partitioning sets of objects into equal groups, a core part of the UK National Curriculum's KS1 Multiplication and Division standards. Children practise dividing up to 20 items into 2, 5, or 10 shares using concrete manipulatives like counters, blocks, or sweets. They answer key questions by explaining fair share methods, creating scenarios such as dividing 10 biscuits among 5 friends, and distinguishing sharing, which fixes group size, from grouping, which fixes objects per group.

This topic builds multiplicative thinking within the summer unit on Multiplicative Thinking and Data. Students develop partitioning fluency, recognise even numbers for equal shares, and connect division to real-life fairness. Comparing sharing and grouping sharpens language for maths discussions, laying groundwork for arrays and multiplication tables.

Active learning excels for sharing equally because children physically sort and redistribute objects, grasping equality through touch and sight. Collaborative tasks spark peer explanations of strategies, while role-play scenarios make abstract fairness concrete and relevant to daily life.

Key Questions

1. Explain how to ensure everyone gets a fair share.
2. Construct a scenario where sharing equally is important.
3. Compare sharing with grouping and identify their differences.

Learning Objectives

• Demonstrate how to share a set of up to 20 objects equally among 2, 5, or 10 groups.
• Compare the process of sharing equally with grouping, identifying the key difference in what is fixed.
• Construct a simple word problem that requires sharing equally to find a solution.
• Explain the concept of a 'fair share' using concrete examples.

Before You Start

Counting and Cardinality

Why: Students need to be able to count a set of objects accurately to begin sharing them.

Number Recognition

Why: Understanding the value of numbers is essential for determining how many objects are in each share.

Key Vocabulary

Share Equally	To divide a collection of items into groups where each group has the same number of items.
Fair Share	When every person or group receives the same amount of something, ensuring no one has more or less than others.
Group	A collection of items that are put together, often with the same number of items in each group when sharing.
Divide	To split a whole into equal parts or groups.

Watch Out for These Misconceptions

Common Misconception

Sharing equally means handing out one item at a time alternately.

What to Teach Instead

This one-to-one method works only for specific cases and ignores group totals. Hands-on sorting with manipulatives shows children must check final group sizes match. Peer teaching during pair checks corrects this quickly.

Common Misconception

Sharing and grouping are identical processes.

What to Teach Instead

Sharing divides into equal amounts per person with fixed group number, while grouping makes equal sets with fixed items per set. Role-play activities highlight differences as children test both with same objects. Group discussions refine their comparisons.

Common Misconception

A remainder means sharing equally is impossible.

What to Teach Instead

Remainders occur with uneven divisions, but focus first on even totals. Manipulative exploration reveals patterns in divisible numbers. Collaborative problem-solving encourages inventing fair adjustments, like setting extras aside.

Active Learning Ideas

Pairs: Counter Share Challenge

Pairs receive 12 counters and divide them into 2, 3, or 4 equal groups. They record each division with drawings and discuss why some numbers work better. Partners check each other's work for fairness.

20 min·Pairs

Small Groups: Role-Play Picnic

Groups of 4 role-play a picnic with 16 pretend sandwiches to share equally. They try different group sizes, note remainders, and agree on fair methods. Present one solution to the class.

30 min·Small Groups

Whole Class: Floor Mat Division

Use a large floor mat marked with sharing circles. The class shares 20 teddies into equal groups around the mat, with volunteers demonstrating steps. Everyone predicts and verifies equality.

40 min·Whole Class

Individual: Draw Fair Shares

Each child draws 10 apples and shares them into 2 or 5 groups, labelling amounts. They create a word problem for their drawing and swap with a neighbour to solve.

15 min·Individual

Real-World Connections

• Party planners often need to share party favors equally among guests. For example, if there are 12 party bags and 6 children, each child should receive 2 bags to ensure a fair share.
• Families share food during meals. If a pizza has 8 slices and 4 people are eating, each person gets 2 slices so everyone has an equal amount.

Assessment Ideas

Exit Ticket

Provide students with 10 counters and ask them to show how to share them equally between 2 dolls. On the back, ask them to draw a picture of their sharing and write one sentence about why it is fair.

Quick Check

Hold up a set of 6 cubes. Ask: 'If I want to share these equally among 3 friends, how many cubes does each friend get?' Observe student responses and listen for their reasoning.

Discussion Prompt

Present a scenario: 'Sarah has 15 stickers and wants to give them to her 3 friends. How can she make sure each friend gets the same number of stickers?' Facilitate a class discussion where students explain their strategies for sharing.

Frequently Asked Questions

How to teach sharing equally in Year 1 maths?

Start with concrete objects like 10 cubes divided into 2 groups of 5. Use real-life contexts, such as sharing fruit at snack time, to model steps: count total, decide groups, partition evenly, verify. Progress to drawings and numerals. Regular practice with varied totals builds confidence and fluency in under 20.

What manipulatives work best for sharing equally?

Counters, linking cubes, buttons, or sweets provide tactile feedback for partitioning. Numicon shapes show number compositions visually, aiding equal group recognition. Everyday items like straws or pencils connect to life. Rotate materials weekly to maintain engagement and reveal multiple partitioning views.

How does active learning help with sharing equally?

Active learning engages Year 1 children through hands-on manipulation, making division tangible rather than abstract. Sorting objects into groups fosters trial-and-error discovery of equality, while pair talks build justification skills. Role-plays link maths to social fairness, boosting retention. Whole-class demos model verification, ensuring all grasp concepts collaboratively.

Real-life examples for sharing equally lessons?

Divide class snacks like 12 grapes among 4 friends or 15 raisins into 3 bowls. Playground scenarios, such as sharing 10 balls into 2 teams, emphasise fairness. Home links include dividing toys or cookies. These contexts answer key questions on importance and methods, deepening relevance.