Efficient Subtraction — Inventory
Progression 2 (Years 3–4) Number | Using add-on/count-back and decomposition for subtraction to 1 000 with zoo inventory.
Learning Intentions & Success Criteria
Te Mātaiaho: use place value to operate with whole numbers to 1 000
NZC L2–3: subtraction with add-on and decomposition
Key idea: choose add-on for close numbers
Ākonga are learning to:
- Use add-on (finding the difference) for close numbers.
- Count-back and decompose when helpful.
- Check with inverse addition.
Success looks like:
- I can solve 402 − 368 with add-on steps to the nearest tidy number.
- I can show my hops and total difference.
- I can explain why I chose add-on vs. take-away.
Teacher prompts
- “Are the numbers close or far apart?”
- “Which tidy number will help you hop?”
- “How will you check using addition?”
Kupu / Vocabulary
- difference / rerekētanga
- add-on
- count-back
- decompose / wāwāhi
- rename / tapa anō
- inverse / huri whakararo
🧠 Subtraction Strategy Lab (8 mins)
Before — Estimate
Estimate the difference in 402 − 368. Are the numbers close enough for counting up to be useful?
During — Compare two representations
Complete an open-line add-on path from 368 to 400 to 402, then sketch a count-back route for the same calculation.
| Strategy | Hops or parts | Difference | Why it fits |
|---|---|---|---|
| Add on | … | … | … |
| Count back | … | … | … |
Kaiako moves
- Name subtraction as difference as well as take-away.
- Total the hop sizes on the add-on line; do not count the endpoints as hops.
After — Pair process
Decide with a partner which representation makes this small difference clearest and point to the evidence.
Immediate use
Use the close-or-far decision at Stations A and B, then verify one answer with inverse addition at Station C.
Support + stretch
- Support: Use a partly marked line with 368, 400, and 402 already labelled.
- Stretch: Choose among add-on, count-back, and decomposition for mixed close/far number pairs.
Materials
- Open number line templates; base-10 blocks for decomposition demos.
- Inventory cards (e.g., 742 items left, 389 used).
- A5 Handout: Progression 2 core (subtraction) or generator “Subtraction to 1 000.”
Lesson Flow
Hook (5 mins)
- Inventory card: 402 bags, 368 used. Ask: “Add-on or take-away?”
Teach/Model (12 mins)
- Model add-on: 368→370 (+2)→400 (+30)→402 (+2) = 34.
- Model decomposition for 521 − 278 using PV blocks; record aligned subtraction, then check with addition.
Guided Practice (15 mins)
- Station A: Add-on close numbers (within 50).
- Station B: Decompose for non-close; use blocks once, then record.
- Station C: Inverse check—solve subtraction, verify by adding the difference.
Independent/Extension (10–12 mins)
- Four problems; label strategy used.
- Extension: choose best strategy for each; justify.
- Support: constrain to < 500 and close numbers; scaffold line.
Exit Check (5 mins)
- Prompt: 635 − 589; show add-on hops.
Place-based options
- Hamilton Zoo inventory (feed/gear); Otago Peninsula pest control logs; add-on for close tallies.
Push add-on for close numbers; reserve decomposition for larger gaps. Always check with inverse.
Differentiation & Support
Scaffolds
- Use add-on with differences under 50.
- Provide number line templates with marked tidy numbers.
- Use base-10 blocks for the first two examples.
Extensions
- Choose strategy for each problem and justify efficiency.
- Use add-on with three hops to tidy numbers.
- Create a subtraction story that favours add-on.
Common Misconceptions
- Skipping compensation hops in add-on. Remedy: label each hop.
- Renaming errors in subtraction. Remedy: use PV blocks to trade.
- Checking with addition incorrectly. Remedy: line up addends and sum to original.
Assessment & Evidence
- Exit hop accuracy; note if hops to tidy numbers are efficient.
- Misconceptions: subtracting ones from tens without renaming; skipping a hop.
Whānau Connection
- Send home a “difference finder” prompt (e.g., distances, scores, prices).
- Invite whānau to share a close-number example for class practice.
Handout Link
Use Progression 2 core handout (subtraction) or generator “Subtraction to 1 000,” 24–28 questions (mix close and non-close).
Curriculum alignment
- Number — Knowledge: - Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.
- Measurement — Knowledge: - Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.
- Statistics — Knowledge: - Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.
- Algebra — Knowledge: - Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.
- Geometry — Knowledge: - Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 1 (Years 0–3) · Statistics (Knowledge): “- Addition is putting parts together to find a total or whole. - Subtraction is separating a number into two or more parts or finding the difference between two numbers.”
- NZC (2007) · Mathematics and Statistics · Level 3: “Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.”
📋 Kaiako Planning Snapshot
Teacher planning support for this resource — learning intentions, success criteria, and inclusive practice guidance are summarised below.
Inclusion Guidance
- ESOL / ELL learners: Pre-teach key vocabulary (numeracy, number, efficient) using visual word walls or bilingual glossaries before the lesson. Reduce language load with diagrams and visual models. Partner-share and think-pair-share strategies encouraged.
- Neurodiverse learners / ADHD: Break the lesson into clear segments with visual checkpoints. UDL principle: offer ākonga a choice in how they demonstrate understanding (verbal, written, visual/drawn). Provide anchor charts or reference cards for numeracy number p2 l3 concepts throughout.
- Dyslexia: Provide audio-text alternatives for written materials. Use high-contrast fonts and generous line spacing. Allow voice recording as an alternative to written responses where possible.