Mixed Problems — Shift Handover
Progression 2 (Years 3–4) Number | Applying place value, addition/subtraction, arrays, and basic facts in mixed zoo/conservation scenarios with a mini-check.
Learning Intentions & Success Criteria
Te Mātaiaho: use place value and multiplicative thinking
NZC L2–3: apply additive/multiplicative strategies
Key idea: choose, label, justify
Ākonga are learning to:
- Select and apply efficient strategies to mixed problems.
- Explain and tag strategies used.
- Check reasonableness with estimation.
Success looks like:
- I can match a problem to a fitting strategy and name it.
- I can show working clearly for someone taking over my shift.
- I can estimate and verify my answer.
Teacher prompts
- “Which strategy is most efficient here?”
- “How will you label your steps?”
- “What is your estimate first?”
Kupu / Vocabulary
- estimate / tata
- strategy / rautaki
- justify / whakamana
- reasonableness / tika o te whakaaro
- verify / manatoko
- label / tapanga
🧠 Shift-Handover Strategy Match (8 mins)
Before — Estimate and choose privately
For one place-value problem, one close-subtraction problem, and one array problem, write an estimate and choose the strategy you would try first.
During — Record your evidence
| Problem type | Estimate | Strategy choice | Evidence in the numbers or representation |
|---|---|---|---|
| Place value | … | … | … |
| Close subtraction | … | … | … |
| Array | … | … | … |
Kaiako moves
- Ask for evidence in the numbers or representation and withhold correctness until choices are justified.
- Keep the estimates visible as a later reasonableness check.
After — Pair process
Compare one different choice with a partner. Explain the evidence before changing either strategy tag.
Immediate use
Carry the strategy tags into the shift-handover task, then complete the mini-check independently.
Support + stretch
- Support: Provide an icon and worked example for each strategy family.
- Stretch: Solve one item two ways and evaluate which method is more efficient.
Materials
- Mixed problem set (add/sub/arrays/facts to 1 000).
- Strategy tags/icons; mini-check sheet (6 items).
- A5 Handout: Progression 2 core mixed or generator “Mixed (add/sub/×/÷).”
- Strategy passport (Progression 2).
Lesson Flow
Hook (5 mins)
- Keeper handover board with 4 tasks (add, subtract, array, fact); students pick which strategy to use.
Model (8 mins)
- Model tagging: “This is near-100 addition → tidy numbers.”
- Model array/fact: choose multiplication/array vs. repeated addition.
Stations (20 mins)
- Set A: Add/sub (tidy, add-on) problems.
- Set B: Arrays/fact families.
- Set C: Choice problems; tag strategy used.
Mini Check (10–12 mins)
- 6 items: PV compare, addition, subtraction, array total, fact family, choose-your-strategy word problem.
Reflection (5 mins)
- Strategy passport update (Progression 2 version forthcoming).
- Pair share: “I chose ___ because ___.”
Place-based options
- Shift board built from Hamilton Zoo / Waikato restoration scenarios; rotate weekly.
Emphasise strategic choice and communication for handover: clear working, labelled strategy, quick estimate.
Differentiation & Support
Scaffolds
- Offer a strategy menu for each problem set.
- Limit to add/sub only for some learners.
- Provide sentence frames for justification.
Extensions
- Require two strategies for one problem.
- Create a mixed problem set for peers.
- Use estimation to detect errors in a worked example.
Common Misconceptions
- Choosing a strategy that does not fit the numbers. Remedy: compare options first.
- Skipping estimation and trusting first answer. Remedy: require an estimate.
- Unclear working for handover. Remedy: label steps with strategy tags.
Assessment & Evidence
- Mini-check accuracy; note strategy matches.
- Station work: clarity of tagging and representation.
Whānau Connection
- Send home a “shift handover” problem for whānau to solve and label strategy.
- Invite whānau to share a mixed-number task from mahi or home.
Handout Link
Use Progression 2 core mixed handout or generator “Mixed (add/sub/×/÷),” 24–28 questions. Capture reflections in the Progression 2 passport.
Strategy Passport: printable A4 (fold to A5).
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 2 (Years 4–6) · Number (Knowledge): “- Multiplication, division, fractions, decimals, and percentages can be used to solve problems involving relative quantities and measures.”
- NZC (2007) · Mathematics and Statistics · Level 3: “Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.”