Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Represent increases and decreases with signed changes.
- Add integers across zero.
- Distinguish the final reading from the net change.
Before you start
Order integers on a number line and add or subtract positive whole numbers.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A fictional outdoor thermometer reads −4°C at dawn. The temperature rises by 9°C, then falls by 7°C. What is the final reading?
Why this math matters
Negative numbers describe values below a chosen reference. A temperature and a temperature change play different roles: one names a position, while the other tells how far and in which direction to move.
Set up the model
A useful answer starts with clear assumptions:
- All readings and changes use degrees Celsius.
- The stated changes happen in sequence, with no other change between them.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Track temperature across zero
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional outdoor thermometer reads −4°C at dawn. The temperature rises by 9°C, then falls by 7°C. What is the final reading?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Write the changes with signs
start = −4°C; changes = +9°C and −7°C
A rise moves right on the number line, and a fall moves left. The sign describes direction relative to increasing temperature.
Follow the first move
−4 + 9 = 5°C
Four degrees of warming reach zero, leaving five more degrees of warming. The intermediate reading is positive.
Finish and compare
5 − 7 = −2°C; net change = 9 − 7 = +2°C
The final reading is two degrees below zero but two degrees warmer than the starting reading. Those statements describe different comparisons.
The result
The final reading is −2°C, after a net increase of 2°C.
A negative reading does not mean the latest change was negative overall. Always state the reference: below zero, below the previous reading, and below the starting reading are different claims.
Common mistakes to catch
- Dropping the initial negative sign changes the entire calculation.
- The distance from zero is an absolute value and does not preserve whether a temperature is above or below zero.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A reading of −6°C rises by 11°C. Find the new reading.
Show a hint
Use six degrees to reach zero first.
Reveal answer and explanation
5°C
−6 + 11 = 5. There are five degrees of warming left after reaching zero.
Practice 2
A temperature changes from 3°C to −8°C. Find the signed change and the size of the drop.
Show a hint
Signed change equals final minus initial.
Reveal answer and explanation
−11°C change; an 11°C drop
−8 − 3 = −11. Its absolute value is 11, which describes the magnitude of the decrease.
Take the idea with you
Use the same position-versus-change distinction for elevator floors or a game score that allows negative values.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Mix a colour using parts, not guesses
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