Mathematics · Year 1 · Additive Reasoning · Autumn Term

Subtracting by Counting Back (from 20)

Extending counting back strategies to solve subtraction problems from numbers up to 20.

• National Curriculum Attainment Targets
• KS1: Mathematics - Addition and Subtraction

About This Topic

Subtracting by counting back from numbers up to 20 strengthens Year 1 students' subtraction fluency within the Additive Reasoning unit. Children practise counting backwards accurately to solve take-away problems, such as 12 take away 5 equals 7, using fingers, number lines, or bead strings. This builds on prior counting skills and helps distinguish when counting back works best compared to counting on for addition.

Links to KS1 standards emphasise reasoning: students compare strategies across problem types, create subtraction scenarios suited to counting back, and explain why precision matters to avoid errors. Regular practice develops number sense up to 20, supports mental arithmetic foundations, and prepares for crossing the tens boundary in later years.

Active learning benefits this topic greatly. Manipulatives and movement activities turn abstract counting into concrete experiences, helping children visualise steps and self-correct miscounts. Collaborative games provide peer feedback, while varied contexts keep engagement high and reinforce justification skills through discussion.

Key Questions

1. Compare counting on with counting back for different types of problems.
2. Construct a subtraction problem that is best solved by counting back.
3. Justify the importance of knowing how to count back accurately.

Learning Objectives

• Calculate the result of subtracting up to 20 by accurately counting backwards.
• Compare the efficiency of counting back versus counting on for specific subtraction problems within 20.
• Construct a word problem where counting back is the most appropriate strategy for subtraction within 20.
• Justify the importance of precise counting back for accurate subtraction outcomes.

Before You Start

Counting to 20

Why: Students need to be able to count forwards and backwards accurately up to 20 to use this subtraction strategy.

Number Recognition up to 20

Why: Students must be able to identify and understand the value of numbers up to 20 to use them as starting points for counting back.

Introduction to Subtraction

Why: Students should have a basic understanding of the concept of 'taking away' before applying specific strategies like counting back.

Key Vocabulary

Counting Back	A strategy for subtraction where you start at the first number and count down a specific number of steps. For example, to solve 15 - 4, you start at 15 and count back four times: 14, 13, 12, 11.
Subtraction	The process of taking away a quantity from another quantity. It is the inverse operation of addition and can be represented by the minus sign (-).
Number Line	A visual representation of numbers in order, used to help with counting and calculations. For subtraction, you move left along the number line.
Take Away	A phrase used to describe subtraction, indicating that a part is removed from a whole. For example, '10 take away 3'.

Watch Out for These Misconceptions

Common Misconception

Counting back works the same as counting on.

What to Teach Instead

Counting back starts from the larger number and decreases, while counting on starts small and increases. Pairs role-playing both strategies on shared number lines clarify the difference. Peer teaching during relays reinforces correct direction through immediate feedback.

Common Misconception

Always start counting back from 10, even for teens.

What to Teach Instead

Students must practise from any number up to 20. Targeted games with teen starts, like bead slides from 18, build confidence. Small group discussions help justify strategy choice for different starting points.

Common Misconception

Skip numbers or lose track when counting back more than 5.

What to Teach Instead

Rhythmic choral counting in whole class and tactile tools like fingers prevent skips. Active verification in pairs, such as hopping and landing checks, corrects pacing and boosts accuracy.

Active Learning Ideas

Number Line Hops: Backwards Relay

Mark a giant number line on the floor from 0 to 20. In pairs, students start at a called number like 14 and hop back the required amount, such as 3 steps for 14-3. Partners verify the landing spot and record the answer. Switch roles after five problems.

25 min·Pairs

Bead String Slides: Subtraction Stations

Provide bead strings to small groups. Call out problems like 17-6; students slide beads back from the start number, counting aloud. Groups check answers with a partner before rotating to draw the process on mini whiteboards.

35 min·Small Groups

Toy Take-Away Dramas: Story Pairs

Pairs use 20 counters or toys to act out teacher-provided stories, like 'Start with 15 apples, eat 4'. One child sets up and counts back while the partner narrates and confirms. Pairs then invent and solve their own story.

30 min·Pairs

Counting Back Bingo: Whole Class

Distribute bingo cards with numbers 0-20. Call subtractions like 10-3=7; students mark the answer if on their card and count back aloud to confirm. First full line wins a group cheer.

20 min·Whole Class

Real-World Connections

• A baker decorating a cake might count back the number of sprinkles they have left to add. If they started with 15 sprinkles and have already placed 6, they count back 6 from 15 to know they have 9 left.
• A child playing a board game might need to move their piece back a certain number of spaces. If they are on square 18 and told to move back 5 spaces, they count back 5 from 18 to land on square 13.

Assessment Ideas

Quick Check

Present students with a set of subtraction problems (e.g., 17 - 5, 13 - 3, 19 - 7). Ask them to solve each using counting back and show their work on a mini-whiteboard or paper, circling their final answer.

Discussion Prompt

Pose the question: 'When is it best to count back to solve a subtraction problem, and when might counting on be easier?' Encourage students to give examples and explain their reasoning, referencing problems they have solved.

Exit Ticket

Give each student a card with a subtraction problem (e.g., 14 - 6). Ask them to write the answer and then one sentence explaining how they used counting back to find it. Collect these to gauge individual understanding of the strategy.

Frequently Asked Questions

How do I introduce subtracting by counting back in Year 1?

Start with concrete take-away using toys or counters up to 10, modelling finger counting back aloud. Progress to number lines for 11-20, comparing with counting on. Daily 10-minute routines build automaticity. Link to real contexts like sharing sweets to make relevant, ensuring all students verbalise steps for reasoning.

What manipulatives work best for counting back to 20?

Bead strings or abacuses allow sliding for visual feedback. Giant floor number lines support kinesthetic hopping. Ten frames with counters help decompose teens. Rotate these in stations to suit preferences, always pairing with verbal counting to connect action to numbers.

How can active learning help students master subtracting by counting back?

Active methods like number line relays and bead slides make counting visible and multisensory, reducing mental slips. Movement engages kinesthetic learners, while pair checks provide instant peer correction. Games in varied groupings build fluency and justification through talk, turning practice into play and deepening understanding beyond rote memorisation.

What are common errors in counting back subtraction and fixes?

Errors include reversing direction or skipping numbers. Address with explicit modelling, then guided pair practice on visuals. Use error analysis discussions: share wrong paths and correct collectively. Progress monitoring via quick quizzes ensures mastery before advancing.