Problem
Knowing what 1 cm stands for gives the whole
A bar graph splits a field by crop, given in centimeters, and one crop's real area is known. We need the area of the whole field.
Data & probabilityRatios
Your answer
How to solve
Strategy Analyze the Units — On a bar graph, length and quantity are locked together at a fixed rate. Find what one centimeter is worth, and every other section can be read the same way -- including the whole bar at once.
1STEP 1
Find what one centimeter is worth
The corn's 85 m² is drawn as 5 cm, so divide.
85 ÷ 5 = 17
Each centimeter stands for 17 m².
6.RP.A.2Analyze The UnitsEach centimetre of the bar stands for .
Why?
The bar is drawn so that equal lengths mean equal areas everywhere along it, so its whole length is made of centimetres that each stand for the same amount.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The corn's is five of those centimetres and covers , so finding one centimetre's worth is the division that undoes taking five.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Measure the whole bar
The whole field is the five sections laid end to end.
11 + 7 + 5 + 4 + 3 = 30
The bar is 30 cm long.
6.SP.B.4Identify Subproblems3STEP 3
Scale the whole bar up
Every centimeter is worth 17 m², so multiply.
30 × 17 = 510
The field is 510 m².
6.RP.A.2Work BackwardsAnswer
510 m²
Check the corn's share both ways: 5 out of 30 cm is one sixth, and 510 ÷ 6 = 85 m², the area given.
Takeaway
On a bar graph, work out what one centimeter is worth and the whole graph opens up.
- Find what one centimeter is worth
- Measure the whole bar
- Scale the whole bar up