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.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Represent equal groups with an equation.
- Apply an inverse operation to both sides.
- Check a proposed solution in the original statement.
Before you start
Multiply and divide whole numbers; interpret a letter as an unknown quantity.
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
Five identical classroom blocks have a total mass of 45 g. What is the mass of one block, and how can an equation justify the answer?
Why this math matters
An equation states a balance between two quantities. An inverse operation undoes the operation applied to the unknown while preserving that balance. This same logic supports unfamiliar equations after the arithmetic stops being obvious.
Set up the model
A useful answer starts with clear assumptions:
- Every block has the same mass.
- The stated total excludes packaging and is treated as exact in the exercise.
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.
Find an unknown mass with an inverse operation
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Five identical classroom blocks have a total mass of 45 g. What is the mass of one block, and how can an equation justify the answer?
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.
Name one block's mass
b = numerical mass in grams; 5b = 45
The coefficient five counts the blocks. The right side describes the entire group, while b describes just one member.
Undo multiplication
5b/5 = 45/5; b = 9
Dividing both sides by the same nonzero number preserves equality. It separates the total into five equal masses.
Return to the original problem
5 × 9 g = 45 g
Substitution confirms the five masses reproduce the measured total. Include grams when reporting the answer because a bare nine does not name the quantity.
The result
Each block has mass 9 g in this model.
The equation is more than a shortcut. If the blocks had unequal masses, dividing 45 by five would give their mean mass, not establish the mass of every individual block.
Common mistakes to catch
- Dividing only one side changes the equation instead of solving it.
- Equal grouping is an assumption; a total alone cannot determine unequal individual amounts.
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
A bag holds x counters. Adding 7 gives a total of 19. Find x.
Show a hint
Undo adding seven by subtracting seven from both sides.
Reveal answer and explanation
12 counters
x + 7 = 19 gives x = 12. The check is 12 + 7 = 19.
Practice 2
Four identical blocks total 30 g. What is one block's mass?
Show a hint
Use 4b = 30; the answer need not be a whole number.
Reveal answer and explanation
7.5 g
Divide both sides by four: b = 30/4 = 7.5. Four blocks of 7.5 g total 30 g.
Take the idea with you
Describe the operation hiding the unknown, then name the operation that reverses it. Verify the result in the original context.
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.
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