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 5 chapters and video availability01 · Read and understand
What you will learn
- Relate outputs of two multiplication patterns.
- Explain your method and check what the result means in the stated situation.
Before you start
Multi-digit operations, equivalent fractions, decimal place value, and rectangular area.
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
For inputs 1, 2, 3, rule A multiplies by 2 and rule B multiplies by 6. How are the outputs related?
Why this math matters
Use paired tables to distinguish an additive change from a multiplicative relationship. 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.
Compare two rules in a table
PausedQuestion: Start with the question. Paused.
Question
Start with the question
For inputs 1, 2, 3, rule A multiplies by 2 and rule B multiplies by 6. How are the outputs related?
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
A outputs: 2, 4, 6
Use the same inputs for the first rule.
Connect the parts
B outputs: 6, 12, 18
Apply the second rule to those same inputs.
State and check the result
B is 3 times A for every listed input
Since 6n = 3(2n), the relationship holds for all allowed inputs.
The result
B is 3 times A for every listed input
Since 6n = 3(2n), the relationship holds for all allowed inputs.
Common mistakes to catch
- Compare outputs for the same input.
- Three more and three times describe different relationships.
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
Rule C is 5n and D is 10n. How are their outputs related?
Show a hint
Factor ten as two times five.
Reveal answer and explanation
D is twice C
10n = 2(5n).
Practice 2
If A = 2n and B = 2n + 3, is B always three times A?
Show a hint
Compare an added amount with a multiplier.
Reveal answer and explanation
No; B is three more than A
For n=2 the outputs are four and seven, not four and twelve.
Take the idea with you
Use paired tables to distinguish an additive change from a multiplicative relationship.
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 space using unit cubes
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