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

Multiplication by 2, 5, and 10

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

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

About This Topic

Doubling and halving are the first steps toward understanding the relationship between multiplication and division. In Year 2, students learn that doubling is the same as multiplying by 2, and halving is the same as dividing by 2. This concept is closely linked to the 2 times table and is a vital mental maths strategy. The National Curriculum expects students to recall doubles and halves of numbers up to 20 and use them to solve problems.

This topic also bridges into fractions, as halving a quantity is the same as finding one half (1/2). By exploring these concepts together, students develop a more holistic understanding of number. Students grasp this concept faster through structured discussion and peer explanation, particularly when using mirrors or folding shapes to visualize the 'symmetry' of doubling and halving.

Key Questions

1. Predict the product of any number multiplied by 2, 5, or 10.
2. Explain the patterns observed in the 2, 5, and 10 times tables.
3. Design a strategy to quickly recall multiplication facts for 2, 5, and 10.

Learning Objectives

• Calculate the product of any whole number up to 10 multiplied by 2, 5, or 10.
• Identify and explain the patterns in the 2, 5, and 10 times tables, such as the even numbers for the 2 times table or the ending digits for the 5 and 10 times tables.
• Design a personal strategy for rapidly recalling multiplication facts for the 2, 5, and 10 times tables.
• Compare the results of multiplying by 2, 5, and 10 to predict outcomes for given numbers.

Before You Start

Addition and Subtraction Facts to 20

Why: Students need a solid foundation in addition to understand multiplication as repeated addition.

Counting in 2s, 5s, and 10s

Why: This builds the foundational skip counting skill necessary for understanding the structure of these multiplication tables.

Key Vocabulary

multiplication	An operation that represents repeated addition. For example, 3 multiplied by 2 is the same as 2 added together 3 times.
times table	A list of the results of multiplying a particular number by a sequence of whole numbers, typically from 1 to 10 or 12.
product	The result of multiplying two or more numbers together.
doubling	Multiplying a number by 2, which is the same as adding the number to itself.

Watch Out for These Misconceptions

Common Misconception

Thinking that halving means splitting into any two parts.

What to Teach Instead

Students might split 10 into 7 and 3. Use physical folding or 'The Mirror Game' to show that halves must be identical. If the two sides don't match, it isn't a half.

Common Misconception

Confusing 'double' with 'add two'.

What to Teach Instead

This is common when students mishear instructions. Use visual cues, doubling always involves two groups of the *same* size, not just adding two more items. Peer teaching where one student 'proves' the double with blocks helps.

Active Learning Ideas

Simulation Game: The Mirror Game

One student acts as the 'original' and holds up a number of fingers or blocks. The 'mirror' student must match them exactly. Together, they count the total to find the double.

15 min·Pairs

Stations Rotation: Halving Headquarters

Station 1: Halving playdough shapes. Station 2: Halving sets of counters. Station 3: Using a 'halving machine' (a box with two exits) to split numbers. Students record their results at each stop.

40 min·Small Groups

Think-Pair-Share: Double the Double

Ask students: 'If we know double 2 is 4, how can we find double 4?' Pairs discuss the pattern and try to apply it to other numbers like 3 and 5.

15 min·Pairs

Real-World Connections

• Cashiers in a supermarket use multiplication by 10 when calculating the cost of multiple items that are priced at £10 each, quickly totaling the bill.
• A baker might multiply by 2 to determine how many cookies are in two batches if each batch contains 12 cookies, helping them manage inventory.
• When planning a party, organizers might multiply the number of guests by 5 to estimate the total number of party favors needed if each guest receives 5 items.

Assessment Ideas

Exit Ticket

Give each student a card with a multiplication problem, such as '4 x 5 = ?' or '7 x 2 = ?'. Ask them to write the answer and then one sentence explaining a pattern they used or saw in the 5 or 2 times table to help them solve it.

Quick Check

Call out numbers and ask students to respond with the product when multiplied by 10. For example, say 'six' and students respond with 'sixty'. Repeat for 2 and 5, varying the order to check recall speed.

Discussion Prompt

Pose the question: 'If you know 3 x 10 = 30, how can you quickly figure out 4 x 10?' Facilitate a discussion where students share strategies, comparing adding 10 to the previous product versus recalling the fact directly.

Frequently Asked Questions

How do doubling and halving relate to the 2 times table?

Doubling a number is the same as 'number x 2'. Halving a number is the same as 'number ÷ 2'. They are the inverse of each other.

How can active learning help students understand doubling and halving?

Active learning strategies like 'The Mirror Game' provide a powerful visual and physical metaphor for doubling. When students see the 'other half' reflected, they understand that doubling is about replication. Similarly, station rotations with playdough or counters allow them to physically test if a number can be split equally, making the concept of 'even' and 'odd' much clearer.

Why can't we halve odd numbers easily?

Because there will always be one 'left over' that cannot be split into a whole number. This is a great way to introduce the idea of remainders or fractions.

What is the best way to learn doubles to 20?

Use 'near doubles' as a strategy. If a child knows 5+5=10, they can work out 5+6 by adding one more. Physical games and songs also help with rapid recall.