Best for
Students who can add and subtract two-digit numbers and are building confident understanding of three-digit numbers, equal groups, and multiplication as an operation.
Pāngarau / Mathematics · Years 3–5 · Place Value & Multiplication
Numeracy Phase 2 — Core Strategies
Place value to 1000, tidy-number addition and subtraction, equal groups and arrays. Core practice for Phase 2 numeracy progressions. All examples are set in the Hamilton Zoo — a real Aotearoa conservation site where maths is part of everyday keeper work.
Free core resource, premium adaptation path
This handout provides the full Phase 2 strategy sequence, scaffolded examples, and write-on practice space. Te Wānanga becomes useful when you want the same content rebuilt for a different readiness band, a bilingual classroom, or a different local context.
- Generate supported versions using smaller or larger number ranges.
- Swap in your local contexts — school gardens, marae, sports events — without losing the maths.
- Save adapted copies in My Kete and refine them in Creation Studio.
Kaiako planning snapshot
- Use length: 45–60 minutes or split across two sessions.
- Grouping: Whole-class modelling, then pairs for strategy sections, independent for practice problems.
- Prep: Print one handout per student. Provide number lines (0–1000), base-10 blocks or drawings, and counters.
- Teaching move: "What tidy number is closest?" before showing the adjust step — let students estimate first.
- Differentiation: Allow use of materials throughout. Challenge early finishers to create their own Zoo problem.
Resources already provided
- Printed handout (one per student)
- Pencils or pens for write-on spaces
- Place-value chart (this page)
- Tidy-number number line scaffold
- Array drawing scaffold
- Eight mixed practice problems with Zoo contexts
- Learning intentions and success criteria
- Mātauranga Māori curriculum alignment notes
If the lesson covers place value partitioning, tidy numbers, add-on subtraction, or arrays, everything you need is on this page. No additional preparation required.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning to partition and rename 3-digit numbers using place value.
- We are learning to apply tidy-number strategies to add and subtract efficiently.
- We are learning to represent multiplication as arrays and repeated addition.
Paearu Angitu / Success Criteria
- I can break a 3-digit number into hundreds, tens, and ones.
- I can use a number line to solve tidy-number problems.
- I can draw an array and write the matching equation.
Strategy 1: Place Value to 1000
Hamilton Zoo context: The keeper team prepares food for all the animals every Monday. This week they have prepared 347 kg of food in total.
How it works
Each digit sits in a column — hundreds, tens, ones. Its position tells you its value.
347 = 300 + 40 + 7
(3 hundreds, 4 tens, 7 ones)
Place value chart — complete the empty rows:
| Number | Hundreds (rau) | Tens (tekau) | Ones (tahi) | Expanded form |
|---|---|---|---|---|
| 347 | 3 | 4 | 7 | 300 + 40 + 7 |
| 582 | ||||
| 216 | ||||
| 9 | 0 | 4 | ||
| 700 + 60 + 3 |
Te reo Māori numbers: tahi (1), tekau (10), rau (100), mano (1 000). Notice how these names reflect the grouped structure — just like our columns.
Strategy 2: Tidy Number Addition
Hamilton Zoo context: The zoo receives two deliveries of hay each week. Monday's delivery is 248 kg and Wednesday's is 153 kg. How much hay arrives in total?
How it works — three steps
- Round one number to the nearest 10 or 100.
- Add the rounded number.
- Adjust by the amount you rounded.
Example: 248 + 153
Round 248 up to 250 (added 2 extra).
250 + 153 = 403.
Adjust back: 403 − 2 = 401.
Number line — show the jumps:
248
+2
250
+153
403
−2
401
Now you try — show your number line below:
| Problem | Tidy number I will use | Adjust by | Answer |
|---|---|---|---|
| 364 + 227 | |||
| 197 + 486 |
Strategy 3: Efficient Subtraction
Hamilton Zoo context: At the start of the week there are 512 kg of keeper supplies in the storeroom. By Friday, 348 kg have been used. How much is left?
Add-on strategy (counting up)
Instead of taking away, count up from the smaller number to the larger number. Add the jumps together to find the difference.
Example: 512 − 348
348 → 350 (jump of +2)
350 → 400 (jump of +50)
400 → 512 (jump of +112)
Total: 2 + 50 + 112 = 164
Counting back (for small differences)
Use this when the two numbers are close together. Example: 403 − 397 — count back 6 to get 6.
Your turn — choose the best strategy and show your working:
| Problem | Strategy I chose | Working | Answer |
|---|---|---|---|
| 625 − 387 | |||
| 502 − 498 |
Strategy 4: Arrays & Equal Groups
Hamilton Zoo context: The amphitheatre at Hamilton Zoo has rows of viewing seats. There are 6 rows with 7 seats in each row.
How it works
An array arranges objects in equal rows and columns. We can write the total as:
- Repeated addition: 7 + 7 + 7 + 7 + 7 + 7 = 42
- Multiplication: 6 × 7 = 42
- Or turned around: 7 × 6 = 42 (same answer — commutative property)
Example array — 4 rows of 5 seats (shade or draw dots to complete):
Repeated addition: _____ + _____ + _____ + _____ = _____
Multiplication equation: _____ × _____ = _____
Now draw your own array for the Zoo amphitheatre (6 rows × 7 seats):
Draw your array here — use dots, crosses, or small circles.
Repeated addition: _________________________________________
Multiplication equation: _____ × _____ = _____
Practice Problems — Hamilton Zoo
Show your working for each question. Circle which strategy you used.
-
Giraffes: The Zoo records that each giraffe eats about 34 kg of leaves per day.
There are 4 giraffes. How many kilograms of leaves are needed each day?
Strategy: repeated addition / array / other
Working: Answer: _______________ -
Kiwi: The kiwi enclosure has supplies worth 438 points on the keeper's inventory.
After restocking, the total is 625 points. How many points were added?
Strategy: add-on / tidy number / other
Working: Answer: _______________ -
Tuatara: The viewing platform has 8 rows of 6 seats. How many seats in total?
Array equation: _____ × _____ = _____ Repeated addition: ________________________ -
Kākāpō: The kākāpō conservation team weighs 547 g of supplementary food
on Monday and 389 g on Wednesday. What is the total?
Strategy: tidy number / counting on / other
Working: Answer: _______________ -
Place value challenge: Write 5 different ways to show the number 630.
(e.g. 600 + 30 + 0, or 63 tens, or …)
-
Inventory: There are 802 items in the zoo store. Keepers use 347 items
this week. How many remain?
Working: Answer: _______________ -
Seating arrays: The zoo opens a second amphitheatre. If there are 9 rows
and each row has 8 seats, write the multiplication equation and the repeated addition.
Multiplication: _______________ Repeated addition: _______________ -
Make your own: Write a Zoo problem using numbers between 100 and 999
that requires tidy-number addition. Swap with a partner to solve.
Curriculum integration / Te Mātaiaho alignment
These Phase 2 strategies align with the Pāngarau / Mathematics learning area of Te Mātaiaho. Place value to 1000, multiplicative thinking, and efficient calculation strategies are core progressions for Years 3–5. The Hamilton Zoo context connects to the Science and Social Sciences strands through conservation mathematics.
Hononga Marautanga · Curriculum Alignment
Pāngarau / Mathematics
Years 3–5: Understand place value of numbers to at least 1000; use a range of additive and multiplicative strategies with whole numbers; represent multiplication using arrays and repeated addition; explain and justify number reasoning.
Science — Conservation context
Level 2–3: Explore how mathematics supports conservation practice; gather and interpret numerical data about animal populations and food requirements; connect quantitative reasoning to environmental stewardship.
Aronga Mātauranga Māori
This resource sits within a kaupapa that recognises mātauranga Māori as a living knowledge system with its own frameworks, values, and ways of understanding the world. The Māori number system — with its structured progression from tahi to tekau (10) to rau (100) to mano (1 000) — makes the grouped, layered structure of place value visible in language. This is not coincidence; it reflects how knowledge itself is layered and built through whakapapa — each layer grounding the next. The concept of kaitiakitanga (guardianship) grounds our conservation contexts: the numbers in this handout are not abstract — they represent real food weights, real animal populations, and real keeper decisions at Hamilton Zoo and NZ conservation sites. Counting carefully is an act of whanaungatanga — of caring for relationships between people, animals, and the natural world. Students are invited to see themselves as kaitiaki of mathematical precision as well as of te taiao.
Tuhia ōu whakaaro · Write Your Thoughts
Which strategy did you find most useful today? What would you like to practise more?
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. The Strategy Passport and Challenge Extension are companion resources for this phase. All resources are provided — no additional preparation is required to use this handout in your classroom.