Best for
Number-line reasoning, additive inverse lessons, temperature and finance contexts, and preparing for integer operations.
Pāngarau / Mathematics • Years 7-10 • Integers and number lines
Negative Numbers
Use this handout to help ākonga see negative numbers as positions and changes, not just strange symbols. The big idea is that zero is a reference point, and numbers to the left or below it tell a meaningful story.
Free integer base, premium adaptation path
This page already contains number-line prompts, inverse practice, and contextual problems. Te Wānanga becomes useful when you want the same scaffold rebuilt around algebra readiness, finance, or a more supported integer pathway.
- Generate smaller-step versions focused only on ordering and locating numbers.
- Swap in local contexts such as alpine temperatures, debt, or sea-level comparisons.
- Save an adapted version in My Kete and refine it in Creation Studio.
Kaiako planning snapshot
- Use length: 35-45 minutes.
- Grouping: Whole-class model, then pairs for number-line tasks, then independent contextual problems.
- Prep: Display a large number line if possible.
- Teaching move: Make students describe movement left and right before writing symbolic calculations.
Resources already provided
- Number-line prompts
- Additive inverse examples
- Context problem table
- Support, core, and stretch pathways
- Teacher-only curriculum companion
If the lesson mentions temperature, debt, or number-line practice, those tasks already exist on this page.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how negative numbers are positioned and compared on a number line.
- We are learning how to use additive inverse ideas to explain integer operations.
- We are learning how negative numbers help model real situations such as temperature and finance.
Paearu Angitu / Success Criteria
- I can locate and order positive and negative numbers on a number line.
- I can explain what the opposite of a number is.
- I can solve and explain simple integer problems in context.
Curriculum integration / Te Mātaiaho alignment
The companion page links this handout to Phase 3 expectations around locating, ordering, and operating with integers, plus the Phase 2 bridge where negative numbers first appear in context.
Why this matters in Aotearoa classrooms
Negative numbers appear in mountain and sea-level data, winter temperatures, score differences, debt, and changes above and below a reference point. Students need to trust that the context and the symbol tell the same story.
In an Aotearoa context, integer reasoning is useful in geography, science, and financial literacy. It also builds the precise language students need before algebra becomes more abstract.
A light te ao Māori lens also keeps place and reference points in view: values above and below sea level, or shifts in temperature and height, make most sense when students connect the numbers back to whenua and real location.
Number-line checkpoint
Locate
Plot these values on a number line: −6, −2, 0, 3, 8.
Order
Write from least to greatest: −9, 4, −1, 0, 7, −3.
Additive inverse and movement
Opposites
The additive inverse of +5 is −5 because they are the same distance from zero in opposite directions.
Movement story
Starting at −2 and adding 5 means moving five steps to the right, landing on +3.
Explain: Why is −4 greater than −7 even though 7 is a larger numeral?
Context problems
| Situation | Calculation | Answer | Explain the movement or change |
|---|---|---|---|
| The temperature is −3°C and rises by 6°C. | ________ | ________ | ________________________________ |
| A bank balance is $12 overdrawn, then $20 is deposited. | ________ | ________ | ________________________________ |
| A diver is 4 m below sea level and rises 7 m. | ________ | ________ | ________________________________ |
Support, core, and stretch pathways
Support
Focus on locating and ordering integers using a number line with labelled intervals.
Core
Move between number-line diagrams, symbolic equations, and context problems involving addition and subtraction.
Stretch
Create a two-step story problem with negative numbers and explain each move on the number line.
My reflection
What helps you most when working with negative numbers: picturing the context, using a number line, or thinking about opposites?
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.
Aronga Mātauranga Māori
Mathematics has always been part of mātauranga Māori — in the navigation of Te Moana-nui-a-Kiwa, in the architectural precision of wharenui, in the sophisticated storage and accounting systems of rua kūmara, and in the patterns of kōwhaiwhai and tukutuku that encode mathematical relationships in visual form. When Māori students engage with mathematics, they are not encountering something foreign: they are meeting a domain of knowledge that their tīpuna practised with extraordinary sophistication. Framing mathematical learning through whakapapa — connecting concepts to real Māori contexts — is not "cultural add-on" but recognition of where much mathematical knowledge lives in this land.
Tuhia ōu whakaaro · Write Your Thoughts
Reflect on what you have learned today. What was the most important idea? What question do you still have?
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. This handout stands on its own; it is not part of a linked unit planner. All resources are provided — no additional preparation is required to use this handout in your classroom.