Arrays & Equal Groups — Viewing Seats
Progression 2 (Years 3–4) Number | Connecting repeated addition to multiplication with zoo seating and conservation plots.
Learning Intentions & Success Criteria
Te Mātaiaho: use place value to operate with whole numbers to 1 000
NZC L2–3: early multiplication (arrays, groups)
Key idea: equal groups build multiplication
Ākonga are learning to:
- Represent equal groups as arrays.
- Write repeated addition and multiplication equations for arrays.
- Describe rows/columns using factors.
Success looks like:
- I can draw an array from a context and label rows/columns.
- I can write both 4×6 and 6×4 with matching addition.
- I can explain which factor is rows vs. columns.
Teacher prompts
- “How many rows? How many in each row?”
- “Show the repeated addition.”
- “What changes when we rotate the array?”
Kupu / Vocabulary
- array / whakarārangi
- row / rārangi
- column / pou
- factor / tauwehe
- repeated addition / tāpiri ā-porowhiu
- commutative / tauutu
Materials
- Array grids; counters; context photos (zoo seating, trap grids).
- A5 Handout: Progression 2 core (arrays) or generator “Multiplication facts 2–10.”
Lesson Flow
Hook (5 mins)
- Show seating photo (4 rows, 6 per row); ask total and how you know.
Teach/Model (12 mins)
- Build 4×6 array; label rows/columns; write 6+6+6+6 and 4×6.
- Rotate to 6×4; discuss same total, switched factors (commutativity).
Guided Practice (15 mins)
- Station A: Match photo to array drawing and equation.
- Station B: Build arrays from word cards (rows/columns given).
- Station C: Trap grid/planting grid; write both addition and multiplication.
Independent/Extension (10–12 mins)
- Draw two original arrays (choose factors 2–10); label and write equations.
- Extension: find arrays with same total but different factors (factor pairs).
- Support: limit to arrays up to 5×5; provide templates.
Exit Check (5 mins)
- Draw 3×7; write repeated addition and multiplication equations.
Place-based options
- Hamilton Zoo viewing deck rows; Tiritiri trap grids; Zealandia planting rows.
Stress the language of rows/columns; link repeated addition to multiplication; highlight commutativity without overloading notation.
Differentiation & Support
Scaffolds
- Start with small arrays (up to 4×4).
- Use color to highlight rows and columns.
- Provide templates with grid outlines.
Extensions
- Find factor pairs for a given total (e.g., 24).
- Link arrays to area (length × width) with units.
- Create an array word problem and solve two ways.
Common Misconceptions
- Confusing rows and columns. Remedy: label with arrows and count aloud.
- Writing multiplication without matching the array. Remedy: trace the rows/columns.
- Assuming only one equation is correct. Remedy: show rotation.
Assessment & Evidence
- Exit drawing correctness; factor/row/column labeling.
- Station notes: are learners mixing rows/columns? Using addition only?
Whānau Connection
- Send home an “array hunt”: egg cartons, tiles, windows.
- Invite whānau to share a real-life array (garden rows, shelves).
Handout Link
Use Progression 2 core handout (arrays) or generator “Multiplication facts (2–10).” Encourage both addition and multiplication notation.