Numeracy Fundamentals: Number Sense Journey

🎯 Three Progressions for Number Fluency

Learners count native birds, design feeding runs, and budget for enclosures at Hamilton Zoo and conservation sites including Tiritiri Matangi, Zealandia, Sanctuary Mountain Maungatautari, and Otago Peninsula .

        1️⃣
       
        Years 1-2: Counting to 20
       
        2️⃣
       
        Years 3-4: Place Value to 1000
       
        3️⃣
       
        Years 5-6: Fractions & Decimals
       
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        Built-in Handout Generator!

📚 Progression 1: Number Foundations (Years 1-2)

Counting to structured strategies. Big idea: Numbers name quantities, can be composed/decomposed, and support additive thinking to 20.

Counting Collections — Aviary & Wētā Survey

Subitising flashes, build bird groupings to 20, tens frames as "bird perches".

Number Line Walks — Zoo Paths

Outdoor chalk lines as zoo pathways, jump counts forward/back to reach enclosures.

Make-10 Treat Packs

Ten-frame games, rainbow facts, equation matching to pack treats for lemurs.

Doubles & Near Doubles

Domino doubles, penguin pair cards, near doubles on kākā feeding posts.

Part-Part-Whole Crates

Connecting cubes as crates, partition 12 fish, discuss efficient splits.

Keeper Story Problems

Feeding route and native bird counts, act out add-to/take-from problems.

Strategy Congress

Choose and defend counting-on vs make-10 when topping up habitats.

Fluency Circuit & Mini Check

Games: cover-up tens frame, ladder races, quick image animal cards.

📚 Progression 2: Multiplicative Foundations (Years 3-4)

Place value to 1000 underpins efficient strategies for addition, subtraction, and early multiplication/division.

Place Value Towers — Giraffe Feed

Base-10 blocks, build 3-digit feed counts, expand and rename.

Tidy Number Addition — Manifests

Number lines and tidy numbers for delivery totals.

Efficient Subtraction — Inventory

Add-on and counting-back with open number lines.

Arrays & Equal Groups — Viewing Seats

Build arrays, record as repeated addition and multiplication.

Fact Families — Keeper Kits

×/÷ fact families for 2, 5, 10, then 3, 4 to pack keeper kits.

Area Models — Map Overlays

Partition by place value, record partial sums on map grids.

Multiplicative Strategies — Fencing

Doubling/halving, "make a tidy group" for fence panel estimates.

Mixed Problems — Shift Handover

Choose and justify operation, peer feedback for shift handover.

Progression 1 — Addition/Subtraction to 20

Operation focus

Number range

Questions

Progression 2 — Place Value & Multiplication to 1000

Operation focus

Number range

Questions

📄 Resources / Ngā Rauemi

📝 Handouts

🎬 Videos & PLD

🦜 Context Sites

🌿 Te Ao Māori Integration

Tau Number

Tatau Count

Tāpiri Add

Tango Subtract

Whakarea Multiply

Whakawehe Divide

📋 Curriculum Alignment

Te Mātaiaho: Number — Quantify, order, compare; use place value to operate

NZC Mathematics — Number & Algebra L1-4:

Number knowledge and additive strategies to 20
Place value to 1000, tidy number strategies
Basic multiplication/division facts
Multiplicative strategies, fraction/decimal equivalence

Whakataukī: Mā te huruhuru ka rere te manu — With structure, ideas fly

Kaiako Planning Snapshot

Ngā Whāinga Akoranga — Learning Intentions

Develop number sense through counting, grouping, and place value understanding across the early learning journey (Phases 1–3).
Recognise and use patterns in number systems, including traditional Māori counting systems, to build multiplicative thinking.
Communicate mathematical reasoning using correct vocabulary and te reo Māori number language.

Paearu Angitu — Success Criteria

I can count forwards and backwards confidently, grouping objects and explaining my reasoning.
I can use place value understanding to add, subtract, multiply, and divide with increasing complexity.
I can identify patterns in number sequences and explain the rule in words or symbols.

Teacher Planning Snapshot

Year level: Y0–Y3 (adaptable across early learning journey) | Duration: Ongoing progressive unit
Curriculum alignment: Te Mataiaho Mathematics and Statistics — Phases 1–3 — Number and Algebra; counting, place value, multiplicative strategies, fraction and decimal foundations. Connects to te reo Māori through traditional counting language.
Mātauranga Māori: Traditional Māori counting systems (kotahi, rua, toru...) and grouping practices encode mathematical structure rooted in whakapapa and relational knowledge. Contextualised pāngarau through mahi-a-ringa (hangi fractions, kūmara storage, tukutuku counting patterns) connects mātauranga Māori as a living mathematical framework. Whanaungatanga supports collaborative counting games; kaitiakitanga frames resource-sharing problems with ethical dimension.
Entry support: Concrete materials first (beans, pebbles, sticks) before symbols. Use te reo Māori number words alongside English. Physical grouping and sorting before written recording.
On-level: Follow the progressive phase sequence — counting strategies, then additive, then multiplicative. Use number lines, hundreds boards, and place value charts as bridge representations.
Extension: Introduce fraction and decimal equivalence. Explore Māori traditional counting bases and compare with base-10 system. Students investigate number patterns in tukutuku grid structures.

Inclusion and Accessibility

ESOL / ELL: Te reo Māori number names are taught alongside English — dual language approach benefits all learners. Visual number lines and concrete manipulatives reduce language demand.
Accessibility: All counting activities adaptable with physical manipulatives. Large-format number charts available. Oral response accepted alongside written recording.
Neurodiverse learners: Consistent routine for number warm-ups reduces cognitive load. Concrete-pictorial-abstract sequence supports processing. Choice in recording format (verbal, drawn, written).

Pedagogical Foundations | Ngā Tūāpou Akoranga

Number sense is not counting — it is an intuitive understanding of quantity, relationship, and pattern that underpins all later mathematical learning. Three researchers explain why pāngarau at Y0‑3 requires more than rote practice.

Cognitive Development

Jean Piaget

Piaget’s conservation tasks — does the child understand that six blocks rearranged is still six blocks? — are the diagnostic heart of early number sense. Children at Y0‑3 are actively developing conservation across number, length, and quantity. This unit’s hands-on, concrete manipulation activities are not pre-mathematical; they are the cognitive work through which conservation — the foundation of arithmetic — is built.

Social Constructivism

Lev Vygotsky

Counting, before it is internalised as a mental operation, is a social activity done aloud with others — a teacher, a peer, a parent. Vygotsky’s insight that mathematical concepts are first interpersonal then intrapersonal explains why shared counting, subitising games, and partner-talk are not supplementary to number learning; they are the developmental pathway through which numbers become mental objects the child can act on independently.

Kaupapa Māori

Graham Smith

“Pāngarau Tuatahi” — first mathematics — signals that this unit belongs to a Māori mathematical tradition, not Western arithmetic with a te reo title. Smith’s framework validates mātauranga Māori mathematical concepts — tāhuna (measurement), tatau (counting), tauira (pattern) — as epistemologically rigorous. Naming the mathematics in te reo is not translation; it is situating number sense within a living intellectual tradition.

→ Explore all theorists at Te Whare Ako — Teaching Theory