Subzero Expedition
Students staff a polar research station, logging temperature swings and elevation changes on the number line — where opposites cancel to zero, subtracting means adding the inverse, and distance is the absolute value of the difference.
Common Core standards covered
- 7.NS.A.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
- 7.NS.A.1.aDescribe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
- 7.NS.A.1.bUnderstand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
- 7.NS.A.1.cUnderstand subtraction of rational numbers as adding the additive inverse, p − q = p + (−q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
- 7.NS.A.1.dApply properties of operations as strategies to add and subtract rational numbers.
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Teacher-facing overview
Big idea: Add and subtract rational numbers on horizontal and vertical number lines, using additive inverses and absolute value to interpret real-world changes.
Student target: “I can add and subtract rational numbers by moving on a number line, rewrite any subtraction as adding the additive inverse, and find the distance between two values with absolute value.”
Success criteria: I can model p + q as a move of |q| in q's direction, starting at p. · I can name and use zero pairs — opposite quantities that combine to 0. · I can rewrite p − q as p + (−q) and explain why they land the same place. · I can find the distance between two rationals as the absolute value of their difference.
Essential question
At a station where everything is measured against zero — freezing, sea level, an even account — what does it MEAN to add a negative or subtract a drop?
Learning target: I can add and subtract rational numbers by moving on a number line, rewrite any subtraction as adding the additive inverse, and find the distance between two values with absolute value.
Success criteria
- I can model p + q as a move of |q| in q's direction, starting at p.
- I can name and use zero pairs — opposite quantities that combine to 0.
- I can rewrite p − q as p + (−q) and explain why they land the same place.
- I can find the distance between two rationals as the absolute value of their difference.
Why this matters
7.NS.A.1 is the year's foundation: every later unit — solving px + q = r, signed rates, coordinate work — assumes students can move both directions on the number line without counting on fingers. The expedition makes each sub-part physical: zero pairs are climb-and-descend days (a), adding is moving (b), subtracting a drop is adding a rise (c), and rearranging a day's changes to pair opposites first is the properties strategy (d). Grade 8's number system work builds directly on this fluency.
Students should already be able to
- Locating positive and negative numbers, including fractions, on a number line.
- Absolute value as distance from zero.
- Adding and subtracting fractions and decimals (positive cases).
Vocabulary to define explicitly
- Additive inverse (opposite)
The number the same distance from 0 on the other side; a number plus its opposite makes 0.
Example: +500 m of climbing and −500 m of descending: the team sleeps at the elevation it woke at.
Not an example: −8 and 8.5 are not opposites — opposites match in distance from zero exactly.
🔒 3 more terms with examples and non-examples — Adding on the number line, Subtraction as adding the inverse, Distance as absolute value — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- Warm-up move descriptions (direction and size).
- Ledger equations during crew work — the rewrite line especially.
- The drone/ice-cave distance discussion.
Summative — the graded evidence: The exit ticket (two moves, one rewrite, one distance), scored with the four-criterion rubric.
The task students work on
Aurora Research Station tracks everything against zero: temperature against freezing, elevation against sea level, the supply account against an even balance. Your crew keeps today's ledger. Dawn temperature: −8°C. A warm front adds 15 degrees; an evening storm takes 12; overnight, a forecast 9-degree drop FAILS to arrive and must be subtracted back out of the projection. Meanwhile the survey team compares the drone (120 m) with the ice cave (−45 m), and the supply run logs a +500 m climb followed by a −500 m descent. Every line of the ledger becomes an equation on the number line.
Station ledger — one equation per event.
| Event | Start | Change | Equation | Result |
|---|---|---|---|---|
| Warm front | −8°C | +15 | ||
| Evening storm | −12 | |||
| Canceled 9° drop | remove a −9 | |||
| Supply run | camp | +500 then −500 | ||
| Drone vs ice cave | 120 m and −45 m | distance? |
Anticipated student strategies
Movement first because every rule is a summary of it; zero pairs second as the structural shortcut; bare rules last, re-grounded in the line they came from.
- Number-line hops. The student draws each change as an arrow: start at −8, arrow 15 right lands at 7; arrow 12 left lands at −5.
The anchor representation — share first. Insist arrows carry their length written on them; that's |q| doing its job.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Draw the vertical thermometer line. Start at −8, move UP 15: cross zero at the eighth step, seven more to 7°C. Write it: −8 + 15 = 7. Name the anatomy: start, move of |15| in the positive direction, landing point.
Listen for: Zero is just a landmark on the way; the move is 15 either way. (Distance from −8 to 0 is 8, then 7 more.)
Board the rewrite rule p − q = p + (−q) with three quick instances: 3 − 8 = 3 + (−8) = −5; −5 − (−9) = 4; 10 − (−2) = 12. Then the supply run: +500 then −500 nets zero — a zero pair, and the reason 'a number plus its opposite is 0' is a station fact, not a slogan.
- Every subtraction becomes an addition — after that, one skill covers everything.
- Zero pairs vanish first when a ledger has many changes.
Listen for: Removing a 9-step-down is the same change as taking 9 steps up — both undo the same thing. On the line, both arrows are identical.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “Subtracting always makes the answer smaller.” −5 − (−9) = 4. Subtracting a NEGATIVE adds its positive opposite — the projection warmed. The rewrite makes the sign of the move visible before you commit.
- “−8 + 15: the bigger number wins, so just say 15 − 8 = 7 and move on.” — the teacher response is in the full lesson.
- “Distance between 120 and −45 is 120 − 45 = 75.” — the teacher response is in the full lesson.
- “p − q and q − p are the same thing.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 5 independent.
- I doLog the station's day as equations: dawn −8°C, warm front +15, storm −12, then the canceled 9° drop removed from the projection.
🔒 6 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- The temperature is −6°C and rises 10 degrees. Equation and result?
🔒 3 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Model temperature changes as number-line moves. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Log the station's day: adds, drops, and zero pairs. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Rewrite every subtraction as adding the inverse. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Find distances with absolute value. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Vertical number lines for temperature and elevation keep the metaphor physical; integers first, then halves and quarters. Extend with fraction and decimal changes, or let teams design their own expedition day.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One completed expedition ledger with every change written as an equation and one distance found via absolute value.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.