Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Write a fixed-total sharing rule.
- Check the product remains constant.
- Restrict inputs when objects cannot be split.
Before you start
Divide whole numbers and evaluate a function for specified inputs.
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 classroom shares 60 markers equally among n groups, using every marker. How many markers does each group receive when there are 5 groups or 10 groups?
Why this math matters
When a fixed total is divided among more recipients, the share per recipient decreases. The change is not a fixed subtraction: doubling the recipient count halves the share. This constant-product structure is called inverse variation.
Set up the model
A useful answer starts with clear assumptions:
- All sixty markers are distributed equally, with no leftovers.
- Markers remain whole, and the group count is a positive integer.
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.
Understand why more groups mean fewer supplies per group
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A classroom shares 60 markers equally among n groups, using every marker. How many markers does each group receive when there are 5 groups or 10 groups?
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 invariant total
n × m = 60; m = 60/n
n counts groups and m counts markers per group. Their product must reconstruct the same sixty-marker collection.
Evaluate both group counts
m(5) = 60/5 = 12; m(10) = 60/10 = 6
Doubling the groups from five to ten halves the share from twelve to six. No new markers are introduced.
Check the allowed inputs
5 × 12 = 60; 10 × 6 = 60; 60/7 is not a whole number
The algebraic rule works for positive real inputs, but complete equal distribution of indivisible markers requires n to divide sixty.
The result
Five groups receive 12 markers each; ten groups receive 6 each.
The input zero is excluded because sharing among zero groups has no defined quotient. The graph decreases, but it is curved rather than a straight line: equal increases in n do not create equal decreases in m.
Common mistakes to catch
- Inverse variation does not mean merely any decreasing relationship.
- Rounding 60/7 cannot create an equal, complete distribution of sixty whole markers.
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
Share 72 counters equally among 8 groups. What is each share?
Show a hint
Divide the fixed total by the group count.
Reveal answer and explanation
9 counters
72/8 = 9 and 8 × 9 = 72, so all counters are used.
Practice 2
Using the original 60 markers, how many groups can receive exactly 15 markers each?
Show a hint
Use the product n × 15 = 60.
Reveal answer and explanation
4 groups
n = 60/15 = 4. Compared with five groups receiving twelve, fewer groups receive a larger share.
Take the idea with you
Check whether a product stays fixed before labelling a relationship inverse variation. State the domain imposed by real objects.
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: Count nested file folders with powers
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