Practice · One labelled bar fixes the scale for every other bar · Sensim Math

Variant 1 easy answer: 264 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $55\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 5 cm stands for 55 square metres, and we want the whole field.

Givens

Potato takes 8 cm of the bar.
Sweet potato takes 6 cm of the bar.
Corn takes 5 cm of the bar.
Beans takes 3 cm of the bar.
Other takes 2 cm of the bar.
The corn's share is 55 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 5 cm is 55 square metres.

55 \div 5 = 11

Each centimetre is 11 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

8 + 6 + 5 + 3 + 2 = 24

The bar is 24 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

24 \times 11 = 264

The field is 264 square metres.

Answer: 264 m²

4 · Reviewdoes it hold up?

Working back: 11 square metres per centimetre times the corn's 5 cm is 55 square metres, exactly the figure we were given.

Another way: The corn is 5 of the bar's 24 cm, so it is that fraction of the field; dividing 55 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 2 easy answer: 405 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $60\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 4 cm stands for 60 square metres, and we want the whole field.

Givens

Potato takes 10 cm of the bar.
Sweet potato takes 8 cm of the bar.
Corn takes 4 cm of the bar.
Beans takes 3 cm of the bar.
Other takes 2 cm of the bar.
The corn's share is 60 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 4 cm is 60 square metres.

60 \div 4 = 15

Each centimetre is 15 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

10 + 8 + 4 + 3 + 2 = 27

The bar is 27 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

27 \times 15 = 405

The field is 405 square metres.

Answer: 405 m²

4 · Reviewdoes it hold up?

Working back: 15 square metres per centimetre times the corn's 4 cm is 60 square metres, exactly the figure we were given.

Another way: The corn is 4 of the bar's 27 cm, so it is that fraction of the field; dividing 60 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 3 easy answer: 416 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $65\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 5 cm stands for 65 square metres, and we want the whole field.

Givens

Potato takes 12 cm of the bar.
Sweet potato takes 8 cm of the bar.
Corn takes 5 cm of the bar.
Beans takes 4 cm of the bar.
Other takes 3 cm of the bar.
The corn's share is 65 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 5 cm is 65 square metres.

65 \div 5 = 13

Each centimetre is 13 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

12 + 8 + 5 + 4 + 3 = 32

The bar is 32 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

32 \times 13 = 416

The field is 416 square metres.

Answer: 416 m²

4 · Reviewdoes it hold up?

Working back: 13 square metres per centimetre times the corn's 5 cm is 65 square metres, exactly the figure we were given.

Another way: The corn is 5 of the bar's 32 cm, so it is that fraction of the field; dividing 65 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 4 easy answer: 390 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $75\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 5 cm stands for 75 square metres, and we want the whole field.

Givens

Potato takes 9 cm of the bar.
Sweet potato takes 6 cm of the bar.
Corn takes 5 cm of the bar.
Beans takes 4 cm of the bar.
Other takes 2 cm of the bar.
The corn's share is 75 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 5 cm is 75 square metres.

75 \div 5 = 15

Each centimetre is 15 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

9 + 6 + 5 + 4 + 2 = 26

The bar is 26 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

26 \times 15 = 390

The field is 390 square metres.

Answer: 390 m²

4 · Reviewdoes it hold up?

Working back: 15 square metres per centimetre times the corn's 5 cm is 75 square metres, exactly the figure we were given.

Another way: The corn is 5 of the bar's 26 cm, so it is that fraction of the field; dividing 75 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 5 medium answer: 434 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $84\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 6 cm stands for 84 square metres, and we want the whole field.

Givens

Potato takes 10 cm of the bar.
Sweet potato takes 7 cm of the bar.
Corn takes 6 cm of the bar.
Beans takes 5 cm of the bar.
Other takes 3 cm of the bar.
The corn's share is 84 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 6 cm is 84 square metres.

84 \div 6 = 14

Each centimetre is 14 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

10 + 7 + 6 + 5 + 3 = 31

The bar is 31 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

31 \times 14 = 434

The field is 434 square metres.

Answer: 434 m²

4 · Reviewdoes it hold up?

Working back: 14 square metres per centimetre times the corn's 6 cm is 84 square metres, exactly the figure we were given.

Another way: The corn is 6 of the bar's 31 cm, so it is that fraction of the field; dividing 84 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 6 medium answer: 510 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $85\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 5 cm stands for 85 square metres, and we want the whole field.

Givens

Potato takes 11 cm of the bar.
Sweet potato takes 7 cm of the bar.
Corn takes 5 cm of the bar.
Beans takes 4 cm of the bar.
Other takes 3 cm of the bar.
The corn's share is 85 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 5 cm is 85 square metres.

85 \div 5 = 17

Each centimetre is 17 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

11 + 7 + 5 + 4 + 3 = 30

The bar is 30 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

30 \times 17 = 510

The field is 510 square metres.

Answer: 510 m²

4 · Reviewdoes it hold up?

Working back: 17 square metres per centimetre times the corn's 5 cm is 85 square metres, exactly the figure we were given.

Another way: The corn is 5 of the bar's 30 cm, so it is that fraction of the field; dividing 85 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 7 medium answer: 495 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $90\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 6 cm stands for 90 square metres, and we want the whole field.

Givens

Potato takes 12 cm of the bar.
Sweet potato takes 9 cm of the bar.
Corn takes 6 cm of the bar.
Beans takes 4 cm of the bar.
Other takes 2 cm of the bar.
The corn's share is 90 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 6 cm is 90 square metres.

90 \div 6 = 15

Each centimetre is 15 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

12 + 9 + 6 + 4 + 2 = 33

The bar is 33 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

33 \times 15 = 495

The field is 495 square metres.

Answer: 495 m²

4 · Reviewdoes it hold up?

Working back: 15 square metres per centimetre times the corn's 6 cm is 90 square metres, exactly the figure we were given.

Another way: The corn is 6 of the bar's 33 cm, so it is that fraction of the field; dividing 90 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 8 medium answer: 516 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $96\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 8 cm stands for 96 square metres, and we want the whole field.

Givens

Potato takes 15 cm of the bar.
Sweet potato takes 11 cm of the bar.
Corn takes 8 cm of the bar.
Beans takes 5 cm of the bar.
Other takes 4 cm of the bar.
The corn's share is 96 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 8 cm is 96 square metres.

96 \div 8 = 12

Each centimetre is 12 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

15 + 11 + 8 + 5 + 4 = 43

The bar is 43 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

43 \times 12 = 516

The field is 516 square metres.

Answer: 516 m²

4 · Reviewdoes it hold up?

Working back: 12 square metres per centimetre times the corn's 8 cm is 96 square metres, exactly the figure we were given.

Another way: The corn is 8 of the bar's 43 cm, so it is that fraction of the field; dividing 96 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 9 hard answer: 564 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $108\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 9 cm stands for 108 square metres, and we want the whole field.

Givens

Potato takes 16 cm of the bar.
Sweet potato takes 12 cm of the bar.
Corn takes 9 cm of the bar.
Beans takes 6 cm of the bar.
Other takes 4 cm of the bar.
The corn's share is 108 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 9 cm is 108 square metres.

108 \div 9 = 12

Each centimetre is 12 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

16 + 12 + 9 + 6 + 4 = 47

The bar is 47 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

47 \times 12 = 564

The field is 564 square metres.

Answer: 564 m²

4 · Reviewdoes it hold up?

Working back: 12 square metres per centimetre times the corn's 9 cm is 108 square metres, exactly the figure we were given.

Another way: The corn is 9 of the bar's 47 cm, so it is that fraction of the field; dividing 108 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 10 hard answer: 680 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $120\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 6 cm stands for 120 square metres, and we want the whole field.

Givens

Potato takes 13 cm of the bar.
Sweet potato takes 8 cm of the bar.
Corn takes 6 cm of the bar.
Beans takes 4 cm of the bar.
Other takes 3 cm of the bar.
The corn's share is 120 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 6 cm is 120 square metres.

120 \div 6 = 20

Each centimetre is 20 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

13 + 8 + 6 + 4 + 3 = 34

The bar is 34 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

34 \times 20 = 680

The field is 680 square metres.

Answer: 680 m²

4 · Reviewdoes it hold up?

Working back: 20 square metres per centimetre times the corn's 6 cm is 120 square metres, exactly the figure we were given.

Another way: The corn is 6 of the bar's 34 cm, so it is that fraction of the field; dividing 120 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 11 hard answer: 689 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $130\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 10 cm stands for 130 square metres, and we want the whole field.

Givens

Potato takes 18 cm of the bar.
Sweet potato takes 13 cm of the bar.
Corn takes 10 cm of the bar.
Beans takes 7 cm of the bar.
Other takes 5 cm of the bar.
The corn's share is 130 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 10 cm is 130 square metres.

130 \div 10 = 13

Each centimetre is 13 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

18 + 13 + 10 + 7 + 5 = 53

The bar is 53 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

53 \times 13 = 689

The field is 689 square metres.

Answer: 689 m²

4 · Reviewdoes it hold up?

Working back: 13 square metres per centimetre times the corn's 10 cm is 130 square metres, exactly the figure we were given.

Another way: The corn is 10 of the bar's 53 cm, so it is that fraction of the field; dividing 130 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

Variant 12 hard answer: 780 m²

The bar graph shows the area of Junseo's field planted with each crop. If the corn takes up $140\ \text{m}^2$ , what is the area of the whole field, in $\text{m}^2$ ?

Show solution

1 · Understandwhat's really being asked

A bar graph splits a field into five crops by length. The corn's 7 cm stands for 140 square metres, and we want the whole field.

Givens

Potato takes 14 cm of the bar.
Sweet potato takes 10 cm of the bar.
Corn takes 7 cm of the bar.
Beans takes 5 cm of the bar.
Other takes 3 cm of the bar.
The corn's share is 140 square metres.

Unknowns

The area of the whole field.

Constraints

The bar is drawn to scale, so equal lengths mean equal areas.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#1 Draw a Diagram

The graph is in centimetres and the field is in square metres, and nothing on the picture connects them. The one crop with an area printed is the exchange rate -- find square metres per centimetre, then apply it to the whole bar.

3 · Execute3 carry out the plan

1Find what one centimetre stands for

#8 Analyze the Units 6.RP.A.2

The corn's 7 cm is 140 square metres.

140 \div 7 = 20

Each centimetre is 20 square metres.

2Measure the whole bar

#1 Draw a Diagram 6.SP.B.4

Add every section's length.

14 + 10 + 7 + 5 + 3 = 39

The bar is 39 cm long.

3Apply the rate to the whole bar

#8 Analyze the Units 6.RP.A.2

Every centimetre stands for the same area, so multiply.

39 \times 20 = 780

The field is 780 square metres.

Answer: 780 m²

4 · Reviewdoes it hold up?

Working back: 20 square metres per centimetre times the corn's 7 cm is 140 square metres, exactly the figure we were given.

Another way: The corn is 7 of the bar's 39 cm, so it is that fraction of the field; dividing 140 by that fraction reaches the same total without ever naming a rate.

Standardsmin grade 6

6.SP.B.4 Display numerical data in plots (dot, histogram, box) — Reading lengths off a divided bar graph.
6.RP.A.2 Understand unit rate a/b associated with a ratio — Using square metres per centimetre as a unit rate.

💡Takeaway. A graph in centimetres tells you nothing until one bar is labelled. That label is the exchange rate for all of them.

One labelled bar fixes the scale for every other bar · 12 practice problems

Generated variants — 12

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Constraints

Givens

Unknowns

Constraints