Efficient Subtraction — Inventory

Progression 2 (Years 3–4) Number | Using add-on/count-back and decomposition for subtraction to 1 000 with zoo inventory.

Duration: 60 mins Strand: Number Context: Feed/gear inventories; restoration materials Representations: Open number line, place value subtraction, compensation

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

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 favors 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).

Back to Number Sense Journey (Progression 2)