Subtraction Models

Overview

In this first lesson of the unit, students explore subtraction using difference models with counters and small groups of objects, focusing on what “remains” after taking away.

Learning intentions

• WALT understand subtraction as “take away” and the meaning of the difference (how many are left).
• WALT use counters to model subtraction and show what remains.
• WALT record subtraction using simple number sentences with support.

Success criteria

• I can use counters to show a subtraction problem and count how many remain.
• I can match the action (take away) to the difference model (left-over counters).
• I can tell a subtraction story using “there were… and then… so now there are…”.
• I can write or copy a subtraction number sentence with a number sentence template (with teacher support if needed).

Curriculum links

• Number and place value: building meaning of whole numbers through counting and representing quantities.
• Addition and subtraction understanding: representing and solving simple subtraction with concrete materials and pictorial models.
• Mathematical communication: using words, objects, and simple symbols to explain thinking.
• Reasoning: explaining how the model shows the result.

Lesson structure (30 minutes)

1. 3 min | Hook & recall

• Teacher shows a small set of counters (e.g., 8) and asks: “How many do we have now?” Then performs a take-away action (remove 3) while students count aloud.
• Prompt: “What changed? What is the difference? How many are left?”

2. 7 min | Teacher model: difference model

• On a large mat (or board), teacher places counters to make a “starting group”, then physically removes some and places the removed counters aside.
• Teacher models language: “We had 8. We took away 3. We are left with 5.”
• Students repeat the counting and the sentence frame: “There were __. We took away __. Now there are __.”

3. 10 min | Guided practice in pairs (counters)

• Give each pair a subtraction card with two numbers (within 0–10 for most students; 0–20 for those ready).
• Students build the model: make the starting group with counters, take away the required amount, then count what remains.
• Teacher circulates using quick checks: “Show me the take-away part. Where do the left-over counters live?”

4. 5 min | Class share & align language

• 3–4 groups share their models. Teacher ensures correct use of “left/remaining”.
• Teacher emphasises difference model meaning: the final quantity is the remainder after removal.

5. 3 min | Quick independent check

• Each student completes one template: a box with “There were __”, “Take away __”, “Now there are __”.
• For students who need support, they choose from number cards or point to the correct count of remaining counters placed beside the template.

6. 2 min | Exit ticket & reflection

• Students answer orally or with a tiny whiteboard: “If we have 9 and take away 2, how many remain?”
• Teacher collects a few to confirm accuracy and number sense before the next lesson.

Resources

• Counter sets (including small ones for fine-motor support), plus a teacher demonstration mat
• Subtraction cards (start with 0–10; include examples like 7−2, 9−3, 6−1, later 10−4)
• Student recording templates: “There were __ / Take away __ / Now there are __”
• Number cards for choosing answers (support for EALD and students who need scaffolds)
• Visual “take away” icons (hand/arrow) and “left over” icons (remaining counters)
• Mini whiteboards and markers (or wipe-off boards) for quick check
• Pair work supplies: trays to keep counters organised
• Timer/visual agenda on the board

Assessment

• Observation during pair work: correct building of starting group, correct removal, and accurate counting of remaining counters.
• Template check: students’ ability to record the remainder using words/numbers with appropriate support.
• Exit question: quick calculation of one subtraction where the model matches the answer.

Differentiation

• EALD support: provide a picture word bank (“there were”, “take away”, “now there are”), plus visible icons for take away and left over; use sentence frames and choral repetition.
• Neurodivergent support: structured step-by-step routines (1) build, (2) take away, (3) count left, (4) say the sentence; reduce visual clutter on mats; offer sensory breaks by using a structured standing counter area if needed.
• Targeted support: for students still developing counting accuracy, use smaller starting numbers (up to 10) and limit take-away amounts (e.g., 1–4 removed), with teacher check-ins.
• Extension for advanced learners: create their own subtraction problem using counters (e.g., choose a starting number and a take-away number), then explain how the model shows the remainder; challenge them to make two different subtraction facts that have the same answer (e.g., 8−3 and 9−4 both leave 5 if within range).

Extension (optional)

• Advanced learners write an “I made…” card: “I started with __. I took away __. I left with __.” and show their counter model to a partner.