Area Models — Map Overlays
Progression 2 (Years 3–4) Number | Using area/box models for multi-digit addition and early multiplication in map/grid contexts.
Learning Intentions & Success Criteria
Te Mātaiaho: use place value to operate with whole numbers to 1 000
NZC L2–3: partition for addition and early multiplication
Key idea: break, then recombine
Ākonga are learning to:
- Partition numbers into hundreds/tens/ones for partial sums.
- Use box/area models to organise calculations.
- Explain how partial parts combine to a total.
Success looks like:
- I can draw a box model and place each partial sum/product correctly.
- I can recombine partials accurately.
- I can connect the model to a written algorithm.
Teacher prompts
- “What are the parts in each place value?”
- “Where does this partial belong?”
- “How do the parts recombine?”
Kupu / Vocabulary
- partition / wāwāhi
- partial sum
- area model / tauira horahanga
- box model
- recombine / whakahono
- algorithm / tikanga tātai
🧩 Box-Model Launch (8 mins)
Before — Estimate
Estimate 243 + 156. Which hundreds, tens, and ones parts should appear in a box organiser?
During — Build and annotate
As the kaiako models 243 + 156 with place-value cards, place each partial in the matching box region before recombining.
| Place-value part | First number | Second number | Partial sum |
|---|---|---|---|
| Hundreds | … | … | … |
| Tens | … | … | … |
| Ones | … | … | … |
Kaiako moves
- Align every partial with its place value and keep the estimate visible before recombining.
- Call this an addition box organiser; reserve “area model” for a product represented through area.
After — Pair process
Match each written partial to its box region with a partner, then check that the recombined total is close to the estimate.
Immediate use
Complete the first addition box at Station A before moving to a small-product box only when ready.
Support + stretch
- Support: Use a pre-partitioned hundreds/tens/ones template and addition only.
- Stretch: Explain how a friendly multiplication box uses the same break-and-recombine idea through distributivity.
Materials
- Grid paper; box model templates.
- Context cards: two zones sizes (e.g., 276 + 158 visitors) and small products (e.g., 24 × 6 for seats).
- A5 Handout: Progression 2 core (addition/area) or generator “Addition to 1 000.”
Lesson Flow
Hook (5 mins)
- Two map zones visitor counts; overlay to find combined total.
Teach/Model (12 mins)
- Model box for 276 + 158: split to hundreds/tens/ones; add partials; recombine.
- Model small product 24 × 6 as (20 × 6) + (4 × 6).
Guided Practice (15 mins)
- Station A: Addition box models (three sets).
- Station B: Small products with box (facts-based).
- Station C: Reasonableness check with rounded estimates.
Independent/Extension (10–12 mins)
- Two addition boxes and one small product box.
- Extension: 2-digit × 2-digit with friendly numbers (e.g., 32 × 14) if ready.
- Support: keep to addition only; scaffolded template.
Exit Check (5 mins)
- Box model for 187 + 236; write final total.
Place-based options
- Hamilton Zoo/Zealandia map overlays: combine two enclosure counts.
Keep partials organised; emphasise structure as a bridge to algorithms without rushing to standard form.
Differentiation & Support
Scaffolds
- Use templates with labelled rows/columns.
- Start with two-digit addition only.
- Use colour to match partials to place values.
Extensions
- Introduce 2-digit by 2-digit products with friendly numbers.
- Compare box model to standard algorithm and explain similarities.
- Check using estimation before final answer.
Common Misconceptions
- Placing partials in the wrong box. Remedy: label rows/columns first.
- Dropping a place value when recombining. Remedy: line up hundreds/tens/ones.
- Confusing sum vs. product. Remedy: name the operation for each example.
Assessment & Evidence
- Exit box accuracy; correct placement of place-value partials.
- Look for dropped place value when recombining.
Whānau Connection
- Share a simple box model for a household total (e.g., visitors, items).
- Invite whānau to suggest two numbers to combine with a box model.
Handout Link
Use Progression 2 core handout (addition/area) or generator “Addition to 1 000,” 24–28 items. Include one small-product box if appropriate.
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) · Geometry (Knowledge): “- Counting can be organised in groups (e.g. ten ones can be renamed as one 10). - The same value can be represented with different groupings (e.g. 12 is six pairs or 12 ones or one 10s and two ones).”
- 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, area) 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 l6 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.