Mathematics · Year 2 · Groups, Arrays, and Sharing · Spring Term

Division by 2, 5, and 10

Recalling and using division facts for the 2, 5, and 10 times tables.

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

About This Topic

In Year 2 mathematics, division by 2, 5, and 10 centres on recalling facts from the 2, 5, and 10 times tables. Pupils practise dividing multiples, such as 14 ÷ 2 = 7, 35 ÷ 5 = 7, and 80 ÷ 10 = 8, with speed and confidence. They explain how division reverses multiplication, like 6 × 5 = 30 so 30 ÷ 5 = 6, predict quotients for familiar dividends, and create problems such as sharing 20 marbles among 10 children.

This topic supports KS1 National Curriculum goals in multiplication and division by building fluency and reasoning. Pupils spot patterns, including how division by 10 moves digits one place to the left on the place value chart. Visual tools like arrays show division as grouping or sharing equally, connecting to unit fractions and preparing for multi-step problems in later years.

Active learning suits this topic perfectly since manipulatives turn rote facts into meaningful actions. When pupils group counters or play sharing games, they experience the inverse relationship firsthand. Collaborative challenges boost recall through repetition and discussion, making lessons engaging and effective for all learners.

Key Questions

1. Explain how division is the inverse of multiplication.
2. Predict the quotient when dividing by 2, 5, or 10.
3. Construct a real-world problem that requires division by 5 to solve.

Learning Objectives

• Calculate the quotient when dividing numbers by 2, 5, and 10 using multiplication facts.
• Explain the relationship between multiplication and division as inverse operations using examples.
• Construct a word problem that requires division by 5 to find the solution.
• Identify the dividend, divisor, and quotient in a given division equation.

Before You Start

Multiplication Facts for 2, 5, and 10

Why: Students need to know these multiplication facts to confidently recall the related division facts.

Grouping and Sharing

Why: Understanding the concepts of making equal groups and sharing items equally provides a concrete foundation for division.

Key Vocabulary

Division	The process of splitting a number into equal parts or groups. It is the inverse operation of multiplication.
Quotient	The answer obtained when one number is divided by another. For example, in 20 ÷ 5 = 4, the quotient is 4.
Dividend	The number that is being divided in a division problem. In 20 ÷ 5 = 4, the dividend is 20.
Divisor	The number by which the dividend is divided. In 20 ÷ 5 = 4, the divisor is 5.
Inverse Operation	Operations that undo each other. Multiplication and division are inverse operations.

Watch Out for These Misconceptions

Common Misconception

Division by 10 adds a zero to make the number bigger.

What to Teach Instead

Division by 10 actually makes numbers smaller, as 40 ÷ 10 = 4. Base-10 blocks let pupils remove groups of 10 visually, clarifying place value shifts. Group explorations reveal the pattern across numbers.

Common Misconception

20 ÷ 5 = 100 because you multiply instead.

What to Teach Instead

Pupils confuse operations by reversing them. Arrays with 20 dots partitioned into 5 groups show 4 per group clearly. Pair discussions reinforce the inverse link through shared examples.

Common Misconception

You divide only by sharing objects, not grouping them.

What to Teach Instead

Both sharing and grouping represent division equally. Hands-on trials with counters in equal groups of 2 or 5 highlight both models. Small group rotations build flexible thinking.

Active Learning Ideas

Pairs: Counter Sharing

Provide pairs with 20 to 60 counters and division cards (÷2, ÷5, ÷10). Pupils share into equal groups, record quotients, and explain using multiplication. Pairs then swap cards to check.

25 min·Pairs

Small Groups: Array Builders

Groups receive interlocking cubes or drawings to make arrays for multiples of 2, 5, 10. They divide arrays and label facts. Rotate roles: builder, recorder, checker.

30 min·Small Groups

Whole Class: Fact Family Chains

Display a multiplication fact like 4 × 5 = 20. Class calls out divisions: 20 ÷ 5 = 4, 20 ÷ 4 = 5. Chain to next fact, using fingers or whiteboards to track.

20 min·Whole Class

Individual: Story Problems

Pupils draw pictures and write one ÷2, ÷5, ÷10 problem from daily life, like halving a pizza. Swap with a partner to solve and verify with drawings.

15 min·Individual

Real-World Connections

• A baker needs to divide 50 cookies equally into bags of 5 for a customer. They use division to calculate that each bag will contain 10 cookies (50 ÷ 5 = 10).
• A teacher has 20 pencils to share equally among 10 students. They use division to determine that each student will receive 2 pencils (20 ÷ 10 = 2).

Assessment Ideas

Exit Ticket

Give each student a card with a division problem (e.g., 30 ÷ 10 = ?). Ask them to write the answer and then write the related multiplication fact that proves their answer.

Quick Check

Ask students to hold up fingers to show the answer to rapid-fire division questions (e.g., 'What is 12 divided by 2?'). Then, ask a few students to explain their answer using the inverse multiplication fact.

Discussion Prompt

Pose the question: 'Imagine you have 25 sweets and want to share them equally among 5 friends. How many sweets does each friend get? How do you know?' Encourage students to explain their reasoning using division and multiplication.

Frequently Asked Questions

How do you explain division as the inverse of multiplication in Year 2?

Start with known multiplication facts, like 3 × 10 = 30, then ask what undoes it to get back to 3: 30 ÷ 10 = 3. Use part-whole models or number lines to show the connection. Practice with fact families on cards, flipping between × and ÷. This repeated linking builds automatic recall in 4-6 weeks of daily practice.

What are effective ways to practise division facts by 2, 5, and 10?

Combine daily chants, flash cards, and timed games for fluency. Link to times tables through songs or rhymes. Weekly quizzes track progress, with manipulatives for support. Real-world tasks, like dividing class snacks, apply facts contextually and motivate pupils.

How can active learning help students master division by 2, 5, and 10?

Active methods like sharing counters or building arrays make facts concrete, helping pupils see why 25 ÷ 5 = 5. Games in pairs or groups add fun and peer support, improving recall by 30-50% over worksheets. Movement in relays reinforces patterns kinesthetically, while creating problems builds ownership and deeper reasoning.

What real-world problems use division by 5?

Examples include sharing 15 pencils among 5 pupils (3 each), calculating 25p ÷ 5p coins (5 coins), or dividing 20 minutes into 5 equal play breaks (4 minutes). Pupils invent scenarios like halving pizzas into fifths. These connect maths to life, enhancing problem-solving and engagement.