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 3 chapters and video availability01 · Read and understand
What you will learn
- Explain special products using group models.
- Explain your method and check what the result means in the stated situation.
Before you start
Place value through hundreds, addition and subtraction, equal groups, and equal shares.
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
Compare 5 × 0 seedlings with 5 × 1 seedling.
Why this math matters
Check extreme cases of a repeated-group rule by imagining empty or single-item groups. 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.
Understand multiplication by zero and one
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Compare 5 × 0 seedlings with 5 × 1 seedling.
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
5 empty trays: 0 + 0 + 0 + 0 + 0
Empty groups contribute no objects.
Connect the parts
5 one-seedling trays: 1 + 1 + 1 + 1 + 1
Each nonempty group contributes one.
State and check the result
5 × 0 = 0; 5 × 1 = 5
Zero empties the product; one keeps the other factor's value.
The result
5 × 0 = 0; 5 × 1 = 5
Zero empties the product; one keeps the other factor's value.
Common mistakes to catch
- Zero behaves differently in addition and multiplication.
- One group is different from zero groups.
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 1 × 17?
Show a hint
One group contains all seventeen.
Reveal answer and explanation
17
Multiplying by one leaves the quantity unchanged.
Practice 2
Is 9 × 0 equal to 9 + 0?
Show a hint
The operations mean different things.
Reveal answer and explanation
No; 0 versus 9
Nine empty groups contain zero, while adding nothing to nine leaves nine.
Take the idea with you
Check extreme cases of a repeated-group rule by imagining empty or single-item groups.
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: Divide to count groups
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