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.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to add signed changes on a number line.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Positive and negative positions on a number line.
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 temperature starts at −7°C, rises by 12°C, then falls by 4°C. What is the final temperature?
Why this math matters
Signed addition combines a starting position with a directed change. Draw a directed number line for changes in elevation, position, or a measured deviation from a reference.
Set up the model
A useful answer starts with clear assumptions:
- The changes happen in the stated order.
- All temperatures and changes use degrees Celsius.
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.
Add signed changes on a number line
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A temperature starts at −7°C, rises by 12°C, then falls by 4°C. What is the final temperature?
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.
Represent the quantities
start = −7; first change = +12
A rise is a positive change even if the starting temperature is negative.
Apply the relationship
−7 + 12 = 5; second change = −4
Cross zero after moving seven units upward, then continue five more.
Check and interpret
5 + (−4) = 1°C
The total change is +8°C, which moves −7°C to 1°C.
The result
5 + (−4) = 1°C
The total change is +8°C, which moves −7°C to 1°C.
Common mistakes to catch
- A negative starting value does not make every later change negative.
- The magnitude of a change is nonnegative, but its signed value includes direction.
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
An elevator starts at floor −2 and rises 7 numbered floors. Where does it stop?
Show a hint
Move seven units in the positive direction.
Reveal answer and explanation
Floor 5
−2 + 7 = 5.
Practice 2
What change moves a position from 3 to −8?
Show a hint
Find final position minus starting position.
Reveal answer and explanation
−11 units
−8 − 3 = −11; the movement is eleven units in the negative direction.
Take the idea with you
Draw a directed number line for changes in elevation, position, or a measured deviation from a reference.
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: Explain subtraction of a negative number
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