About this standard

Planning in mathematics is a craft. It involves sequencing content logically, anticipating misconceptions, building in time for consolidation, and creating opportunities for mathematical discourse. Standard 4 asks us to plan deliberately and implement with responsiveness — designing with intent, then reading the room and adapting.

Key indicators
Design and deliver coherent, curriculum-aligned learning sequences with clear learning intentions
Use a range of teaching strategies appropriate to the learning context and the needs of ākonga
Respond flexibly to emerging learning needs within lessons — adapting pace, depth, or approach
Integrate te ao Māori perspectives and meaningful contexts into mathematics planning
Evidence & Artifacts
Interactive Lesson · 18 Slides V = πr²h · V = ⅓Ah

Volume: Cylinders, Pyramids & Compound Shapes

Year 10 Measurement 18 slides Structured sequence Exit ticket

This lesson demonstrates planning across a full 60-minute structure: whakatauki → prior knowledge bridge → conceptual development → guided practice → common mistakes → independent differentiated work → exit ticket. The sequence is deliberate at every stage and maps to the NZ Curriculum level 5 Measurement strand.

Also evidences: Std 1 — Te Tiriti Std 2 — Content Knowledge Std 5 — Safe Environments Std 6 — Assessment
Lesson Structure — 60 min
0–3 min
Whakatauki & Mihi
Open with mihi, then present the whakatauki "Tē tōia, tē haumatia" with discussion of how it connects to volume problem-solving strategy.
Slide 1
3–10 min
Prior Knowledge Bridge
Revisit prism formula V = A × l. Establish the cylinder as a circular prism. Build from what learners already know to reduce cognitive load at the new concept.
Slides 2–4
10–25 min
Conceptual Development
Animated introduction of V = πr²h with step-by-step derivation. Transition to pyramids — using the ⅓ relationship animated visually. Students predict the formula before it is revealed.
Slides 5–9
25–35 min
Guided Worked Examples
Step-by-step worked examples with reveal animation — students attempt each step before the answer appears. Compound shapes introduced with a decomposition strategy.
Slides 10–12
35–38 min
Common Mistakes
Explicit slide showing the most frequent error (using diameter instead of radius). Students identify the mistake before the correction is shown. Normalises error as part of learning.
Slide 13
38–55 min
Independent Practice — Chilli Levels
Differentiated by challenge (Medium / Spicy / Extra Hot). Learners self-select their starting level. Teacher circulates — targeted support to Medium learners, extension nudges to those on Extra Hot.
Slides 14–15 → Emporium
55–60 min
Exit Ticket
Two questions assessing both cylinder and pyramid. Shown on screen — students write on paper or mini-whiteboard. Collected and used to plan the next lesson's opening.
Slides 16–17
Formal observation — 25 June 2026
9NUM · Professional Growth Cycle Observation · Kaitautoko: Kevin Hoy

A structured peer observation combining the Hikairo Schema with Rolleston College's "Teaching Qualities" framework, rated across three domains — Cultural Responsiveness, Explicit Teaching, and Active Learning. Explicit Teaching was the agreed focus for this visit.

Cultural Responsiveness 3× A 1× B
Huataki (beginnings), Ihi (high expectations) and supportive language all rated A — greeted learners individually, set clear expectations, and used consistent positive reinforcement ("nearly there," "great question"). Whanaungatanga rated B: names and questioning were strong, but the observer noted more time at the front of the room than moving to learner level in the first 13 minutes.
Explicit Teaching — lesson focus 2× A 1× A− 2× B
Learning intentions displayed and delivered with an assertive, confident tone (A). Checking for understanding (A−) used random calling, hands-up, and re-questioning so learners could see where reasoning went wrong. Independent practice (A) was focused and self-motivated. Two developing areas: daily review didn't fully connect prior angle knowledge to the new quadrilateral content, and modelling stopped short of a fully shared worked example.
Active Learning 1× A 1× A− 1× B
Strong teacher–student interaction (A) and consistent feedback loops (A−) throughout. Rangatiratanga/agency rated B — the observer would like to see students coming up to the whiteboard or using think-pair-share, rather than Q&A routing back through the teacher each time.
Commend
  • Good solid relationships and boundaries in class
  • Humour used often to move students along
  • Connected checking your answers to other subjects
  • Incentives used to encourage learning (e.g. going outside)
  • Noise level good, lots of on-task behaviour
Recommend
  • Move around the room a bit more
  • Allow students to come to the whiteboard and show their answers
  • Try a starter team-puzzle activity, feeding back to the class
Also evidences: Std 1 — Te Tiriti Std 5 — Safe Environments Std 6 — Assessment Std 8 — Relationships
9NUM · Term 3 Check-in · 8:50–9:30am
Observer notes

Learners settled with 6 Do Now questions on the whiteboard. Names used, warm tone throughout. Answers reviewed collaboratively — teacher explains thinking, not just answers. Exercise books for note-taking; examples well-discussed with learners actively involved. Lesson moving at a good pace. Teacher roams and supports all learners.

Observer note: could algebraic rules be written down explicitly, rather than inferred from examples only?

Low-level behaviour appropriately ignored. Wana learners without textbooks noted as a challenge for the independent work phase.

Learner voice
"Mr Gee knows me."
"The work is at the right level but sometimes too easy once I know what to do."
"The lessons sometimes move slow but mostly just right."
"Mr Gee makes the lessons fun and helps me when I need."
Also evidences
Std 1 — Te Tiriti Std 5 — Safe Environments Std 8 — Relationships
Planning for acceleration — Year 10 Extension Cohort
NCEA 1.4 Revision · 40 Slides · Year 10 Extension 2⁵ x⁻² ∛64 a^½ Index laws · negative & fractional indices · roots · exponential equations

Powers & Roots — NCEA 1.4 Revision Deck

Year 10 Extension NCEA 1.4 Mathematical Reasoning 40 slides 5 parts Entered NCEA 1.4 one year early

Planned for a Year 10 connected class extended and entered into NCEA 1.4 (Mathematical Reasoning) a full year early. The deck is sequenced across five deliberate parts — index laws, negative indices, fractional indices and roots, common-base simplifying, and solving exponential equations — opening with a hook and a roadmap slide so students always know where a given law sits in the bigger picture, and closing with quickfire checks and a graded exit ticket on every part. Every law gets its own explicit common-mistakes slide, since these ākonga were being pushed a full year ahead of the standard timeline and misconceptions needed to be caught immediately, not left to surface in the exam.

Also evidences: Std 2 — Content Knowledge Std 3 — Know the Learner Std 6 — Assessment
Planning — Tukutuku, Wharenui & Waka Hourua

Three further lessons follow the same deliberate planning structure as the volume lesson above — whakatauki opening, conceptual build, guided practice, and a Codebreaker extension task — while using tukutuku, wharenui, and waka hourua as the planned context throughout, rather than an add-on. Full lessons on Standard 1.

Further planning evidence, cross-referenced
NCEA Numeracy CAA Prep — a 7-module self-paced programme, planned around all three CAA outcomes with a deliberate onboarding sequence for at-risk ākonga. Full evidence on Standard 3 and Standard 6.
The Grading Algorithm — Statistical Enquiry — a 23-slide, three-part sequence planned around a real-world hook, the 2020 UK A-level algorithm scandal. Full lesson on Standard 2.
Extension Tools — AlgebraLand — 30+ lessons planned with four difficulty tiers and a Codebreaker task built into every topic, so high-achieving ākonga are never waiting. Full evidence on Standard 3 and Standard 6.
Reflections
Guiding questions
  • How do my lesson plans show intentional sequencing and progression?
  • What range of teaching approaches am I using and why?
  • How do I adjust my teaching when learners aren't progressing as expected?
  • What does a well-planned mathematics lesson look like for me?
Reflection — Term 1, 2026

Planning with purpose — what the lesson structure taught me

Building this lesson made me realise how much I used to under-plan the middle section of a lesson. I would plan the opening and the task, but not map out how I was going to move from concept introduction to independent practice — that transition was where learners would often get lost, and where I would lose the thread.

The structure I've settled on — whakatauki, prior knowledge, concept, guided example, common mistakes, independent work, exit ticket — is not rigid, but it gives every lesson a coherent arc. Having the common-mistakes slide as a named, deliberate phase was a significant change for me. Previously I would address errors reactively. Building it into the plan made error-discussion feel normal and expected rather than corrective, which changed the tone of those moments considerably.

The exit ticket is the element I am still developing in my planning. I have been using it to see broadly who understood and who didn't, but I am not yet consistently using that data to shape the following lesson's opening. That is my next target: a tighter feedback loop between end-of-lesson evidence and next-day planning.