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
- Calculate area with consistent length units.
- Apply a percentage allowance to the correct base.
- Round a package count up and explain why.
Before you start
Decimal multiplication, percentages, and division.
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 rectangular room measures 4.8 m by 3.6 m. A classroom estimate adds a 10% allowance to its area. If a box covers 1.8 m², how many whole boxes meet that target?
Why this math matters
Area turns lengths into a quantity of surface covering. Purchasing then adds a second constraint: material may come in whole packages. Separating measurement, an explicitly chosen allowance, and package rounding keeps the reasoning clear.
Set up the model
A useful answer starts with clear assumptions:
- The floor is a perfect rectangle with no cut-outs.
- The example uses a stated 10% allowance solely for arithmetic practice; real allowances depend on material, layout, and instructions.
- Each box covers 1.8 m², and only whole boxes are available. This is not an installation or purchasing specification.
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.
How much flooring would a room need?
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A rectangular room measures 4.8 m by 3.6 m. A classroom estimate adds a 10% allowance to its area. If a box covers 1.8 m², how many whole boxes meet that target?
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.
Calculate the room's area
A = 4.8 m × 3.6 m = 17.28 m²
Multiplying two lengths produces square metres. The perimeter would answer a different question: how far it is around the edge.
Add the stated allowance
target = 17.28 × 1.10 = 19.008 m²
A 10% allowance is 1.728 m². Adding it to 17.28 m² is the same as multiplying the original area by 1.10. Keep the unrounded value for the next step.
Convert coverage to boxes
19.008 m² ÷ 1.8 m²/box = 10.56 boxes
The square-metre units cancel, leaving boxes. Ten boxes provide only 18 m², below the stated target.
Round up and check
11 boxes × 1.8 m²/box = 19.8 m²
Eleven whole boxes cover at least 19.008 m². Their listed coverage is 2.52 m² more than the bare room area, before any cutting or waste.
The result
The classroom model requires 11 whole boxes to meet the area-plus-allowance target.
The 10% allowance and the extra coverage caused by buying whole boxes are different things. Here the allowance raises the target to 19.008 m², while package rounding raises purchased coverage to 19.8 m². Neither figure guarantees a particular real installation outcome.
Common mistakes to catch
- Using 2(4.8 + 3.6) gives perimeter in metres, not area in square metres.
- Rounding 10.56 to 10 leaves the order below the specified target.
- A 10% allowance means multiplying the original area by 1.10, not adding 10 square metres.
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 3 m by 4 m rectangle uses the same 10% arithmetic allowance. Each box covers 1.5 m². How many boxes meet the target?
Show a hint
Find area, multiply by 1.10, divide by coverage per box, then round up.
Reveal answer and explanation
9 boxes
Area = 12 m². The target is 13.2 m². Dividing by 1.5 m² per box gives 8.8 boxes, so 9 boxes provide 13.5 m².
Practice 2
A 5 m by 2.4 m rectangular floor contains a 1.2 m by 0.8 m rectangular cut-out. What is the remaining floor area before any allowance?
Show a hint
Subtract the cut-out's area from the large rectangle's area.
Reveal answer and explanation
11.04 m²
The large rectangle has area 12 m² and the cut-out has area 0.96 m². The remaining area is 12 − 0.96 = 11.04 m².
Take the idea with you
For a sketch of a wall, garden, or poster, decide whether the question needs length, area, or volume first. Draw and label every excluded region before calculating.
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: Break an L-shaped region into simple areas
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