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 6 chapters and video availability01 · Read and understand
What you will learn
- Find additive opposites and distinguish them from reciprocals.
- Explain your method and check what the result means in the stated situation.
Before you start
Fraction and decimal operations, whole-number factors, measurement units, and reading simple tables.
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
What is the opposite of −4.5, and why?
Why this math matters
Use reflection and cancellation to reason about changes that undo each other. The worked example shows how to connect the situation, its mathematical representation, and a check on the result.
Set up the model
A useful answer starts with clear assumptions:
- Use the units, grouping rules, and reference whole stated in the question.
- Treat the supplied counts and measurements as exact within the classroom model, unless an estimate or a random outcome is requested.
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.
Opposite numbers reflect across zero
PausedQuestion: Start with the question. Paused.
Question
Start with the question
What is the opposite of −4.5, and why?
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 situation
−4.5 is 4.5 units left of zero
Use the signed number line.
Connect the parts
Reflect to 4.5 units right of zero
Reflection keeps distance and reverses direction.
State and check the result
Opposite = 4.5; −4.5 + 4.5 = 0
Opposites cancel when added.
The result
Opposite = 4.5; −4.5 + 4.5 = 0
Opposites cancel when added.
Common mistakes to catch
- Opposite and reciprocal name different operations.
- The opposite of a negative number is positive.
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
What is the opposite of zero?
Show a hint
Zero already lies at the center of reflection.
Reveal answer and explanation
0
Reflecting zero leaves the same point, and 0 + 0 = 0.
Practice 2
Is the opposite of 3 equal to 1/3?
Show a hint
Opposites add to zero; reciprocals multiply to one.
Reveal answer and explanation
No; the opposite is −3
3 + (−3) = 0, whereas 3 × 1/3 = 1.
Take the idea with you
Use reflection and cancellation to reason about changes that undo each other.
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: Plot points in all four quadrants
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