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Use total and clues to fill missing bars · 8 practice problems

3.MD.B.34.OA.A.3

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Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy

The populations of two towns are being shown in a bar graph. Town A has a population of $40$ people. Town B's population is $7$ more than half of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $20$ , and $40$ . The horizontal axis lists Town A and Town B. Town A's bar is drawn up to $40$ , and Town B's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 40 people. Town B is 7 more than half of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 40 people
Town B = 7 more than half of Town A's population
Gridlines are marked at 0, 20, and 40

Unknowns

Town B's population
The height of Town B's bar

Constraints

Half of Town A must be computed before adding 7
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '7 more than half of Town A' breaks into two ordered subproblems: first take half of 40, then add 7. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1Half of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 40 people, so first find half of 40.

40 \div 2 = 20

Taking half of a number is dividing it into 2 equal parts.

2Add 7 more

#7 Identify Subproblems 4.OA.A.3

Town B is 7 more than that, so add 7 to 20.

20 + 7 = 27

'7 more than' means we increase the previous result by 7.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 27, on the same scale as Town A.

0 < 27 < 40

On the same scale, a value of 27 sits at the matching height.

Answer: Town B has 27 people

4 · Reviewdoes it hold up?

27 is 7 more than half of 40 (which is 20), so the bar height is sensible on the 40-scale.

Another way: Work backwards (tool 11): if Town B were exactly half of Town A it would be 20; the extra '7 more' nudges it to 27.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking half of Town A and then adding 7 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 2 easy

The populations of two towns are being shown in a bar graph. Town A has a population of $50$ people. Town B's population is $2$ more than a fifth of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $25$ , and $50$ . The horizontal axis lists Town A and Town B. Town A's bar is drawn up to $50$ , and Town B's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 50 people. Town B is 2 more than a fifth of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 50 people
Town B = 2 more than a fifth of Town A's population
Gridlines are marked at 0, 25, and 50

Unknowns

Town B's population
The height of Town B's bar

Constraints

A fifth of Town A must be computed before adding 2
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '2 more than a fifth of Town A' breaks into two ordered subproblems: first take a fifth of 50, then add 2. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1A fifth of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 50 people, so first find a fifth of 50.

50 \div 5 = 10

Taking a fifth of a number is dividing it into 5 equal parts.

2Add 2 more

#7 Identify Subproblems 4.OA.A.3

Town B is 2 more than that, so add 2 to 10.

10 + 2 = 12

'2 more than' means we increase the previous result by 2.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 12, on the same scale as Town A.

0 < 12 < 50

On the same scale, a value of 12 sits at the matching height.

Answer: Town B has 12 people

4 · Reviewdoes it hold up?

12 is 2 more than a fifth of 50 (which is 10), so the bar height is sensible on the 50-scale.

Another way: Work backwards (tool 11): if Town B were exactly a fifth of Town A it would be 10; the extra '2 more' nudges it to 12.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking a fifth of Town A and then adding 2 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 3 medium

The populations of two towns are being shown in a bar graph. Village A has a population of $60$ people. Village B's population is $4$ more than a third of Village A's population.

Find Village B's population, then draw the bar for Village B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $30$ , and $60$ . The horizontal axis lists Village A and Village B. Village A's bar is drawn up to $60$ , and Village B's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Village A is 60 people. Village B is 4 more than a third of Village A. Find Village B's population so its bar can be drawn.

Givens

Village A population = 60 people
Village B = 4 more than a third of Village A's population
Gridlines are marked at 0, 30, and 60

Unknowns

Village B's population
The height of Village B's bar

Constraints

A third of Village A must be computed before adding 4
The bar height matches the population on the same scale as Village A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '4 more than a third of Village A' breaks into two ordered subproblems: first take a third of 60, then add 4. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1A third of Village A

#7 Identify Subproblems 4.OA.A.3

Village A has 60 people, so first find a third of 60.

60 \div 3 = 20

Taking a third of a number is dividing it into 3 equal parts.

2Add 4 more

#7 Identify Subproblems 4.OA.A.3

Village B is 4 more than that, so add 4 to 20.

20 + 4 = 24

'4 more than' means we increase the previous result by 4.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Village B's bar reaches 24, on the same scale as Village A.

0 < 24 < 60

On the same scale, a value of 24 sits at the matching height.

Answer: Village B has 24 people

4 · Reviewdoes it hold up?

24 is 4 more than a third of 60 (which is 20), so the bar height is sensible on the 60-scale.

Another way: Work backwards (tool 11): if Village B were exactly a third of Village A it would be 20; the extra '4 more' nudges it to 24.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking a third of Village A and then adding 4 to find Village B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Village B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 4 medium

The populations of two towns are being shown in a bar graph. Town A has a population of $80$ people. Town B's population is $5$ more than half of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $40$ , and $80$ . The horizontal axis lists Town A and Town B. Town A's bar is drawn up to $80$ , and Town B's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 80 people. Town B is 5 more than half of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 80 people
Town B = 5 more than half of Town A's population
Gridlines are marked at 0, 40, and 80

Unknowns

Town B's population
The height of Town B's bar

Constraints

Half of Town A must be computed before adding 5
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '5 more than half of Town A' breaks into two ordered subproblems: first take half of 80, then add 5. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1Half of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 80 people, so first find half of 80.

80 \div 2 = 40

Taking half of a number is dividing it into 2 equal parts.

2Add 5 more

#7 Identify Subproblems 4.OA.A.3

Town B is 5 more than that, so add 5 to 40.

40 + 5 = 45

'5 more than' means we increase the previous result by 5.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 45, on the same scale as Town A.

0 < 45 < 80

On the same scale, a value of 45 sits at the matching height.

Answer: Town B has 45 people

4 · Reviewdoes it hold up?

45 is 5 more than half of 80 (which is 40), so the bar height is sensible on the 80-scale.

Another way: Work backwards (tool 11): if Town B were exactly half of Town A it would be 40; the extra '5 more' nudges it to 45.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking half of Town A and then adding 5 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 5 medium

The populations of two towns are being shown in a bar graph. North Town has a population of $90$ people. South Town's population is $6$ more than a third of North Town's population.

Find South Town's population, then draw the bar for South Town to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $45$ , and $90$ . The horizontal axis lists North Town and South Town. North Town's bar is drawn up to $90$ , and South Town's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. North Town is 90 people. South Town is 6 more than a third of North Town. Find South Town's population so its bar can be drawn.

Givens

North Town population = 90 people
South Town = 6 more than a third of North Town's population
Gridlines are marked at 0, 45, and 90

Unknowns

South Town's population
The height of South Town's bar

Constraints

A third of North Town must be computed before adding 6
The bar height matches the population on the same scale as North Town

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '6 more than a third of North Town' breaks into two ordered subproblems: first take a third of 90, then add 6. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1A third of North Town

#7 Identify Subproblems 4.OA.A.3

North Town has 90 people, so first find a third of 90.

90 \div 3 = 30

Taking a third of a number is dividing it into 3 equal parts.

2Add 6 more

#7 Identify Subproblems 4.OA.A.3

South Town is 6 more than that, so add 6 to 30.

30 + 6 = 36

'6 more than' means we increase the previous result by 6.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

South Town's bar reaches 36, on the same scale as North Town.

0 < 36 < 90

On the same scale, a value of 36 sits at the matching height.

Answer: South Town has 36 people

4 · Reviewdoes it hold up?

36 is 6 more than a third of 90 (which is 30), so the bar height is sensible on the 90-scale.

Another way: Work backwards (tool 11): if South Town were exactly a third of North Town it would be 30; the extra '6 more' nudges it to 36.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking a third of North Town and then adding 6 to find South Town
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing South Town's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 6 hard

The populations of two towns are being shown in a bar graph. Town A has a population of $100$ people. Town B's population is $1$ more than a fifth of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

The vertical axis shows population (number of people), with gridlines marked at $0$ , $50$ , and $100$ . The horizontal axis lists Town A and Town B. Town A's bar is drawn up to $100$ , and Town B's bar is still empty.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 100 people. Town B is 1 more than a fifth of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 100 people
Town B = 1 more than a fifth of Town A's population
Gridlines are marked at 0, 50, and 100

Unknowns

Town B's population
The height of Town B's bar

Constraints

A fifth of Town A must be computed before adding 1
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '1 more than a fifth of Town A' breaks into two ordered subproblems: first take a fifth of 100, then add 1. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1A fifth of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 100 people, so first find a fifth of 100.

100 \div 5 = 20

Taking a fifth of a number is dividing it into 5 equal parts.

2Add 1 more

#7 Identify Subproblems 4.OA.A.3

Town B is 1 more than that, so add 1 to 20.

20 + 1 = 21

'1 more than' means we increase the previous result by 1.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 21, on the same scale as Town A.

0 < 21 < 100

On the same scale, a value of 21 sits at the matching height.

Answer: Town B has 21 people

4 · Reviewdoes it hold up?

21 is 1 more than a fifth of 100 (which is 20), so the bar height is sensible on the 100-scale.

Another way: Work backwards (tool 11): if Town B were exactly a fifth of Town A it would be 20; the extra '1 more' nudges it to 21.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking a fifth of Town A and then adding 1 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 7 hard

The populations of two towns are being shown in a bar graph. Town A has a population of $100$ people. Town B's population is $10$ more than a quarter of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 100 people. Town B is 10 more than a quarter of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 100 people
Town B = 10 more than a quarter of Town A's population
Gridlines are marked at 0, 50, and 100

Unknowns

Town B's population
The height of Town B's bar

Constraints

A quarter of Town A must be computed before adding 10
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '10 more than a quarter of Town A' breaks into two ordered subproblems: first take a quarter of 100, then add 10. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1A quarter of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 100 people, so first find a quarter of 100.

100 \div 4 = 25

Taking a quarter of a number is dividing it into 4 equal parts.

2Add 10 more

#7 Identify Subproblems 4.OA.A.3

Town B is 10 more than that, so add 10 to 25.

25 + 10 = 35

'10 more than' means we increase the previous result by 10.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 35, on the same scale as Town A.

0 < 35 < 100

On the same scale, a value of 35 sits at the matching height.

Answer: Town B has 35 people

4 · Reviewdoes it hold up?

35 is 10 more than a quarter of 100 (which is 25), so the bar height is sensible on the 100-scale.

Another way: Work backwards (tool 11): if Town B were exactly a quarter of Town A it would be 25; the extra '10 more' nudges it to 35.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking a quarter of Town A and then adding 10 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

Variant 8 medium

The populations of two towns are being shown in a bar graph. Town A has a population of $100$ people. Town B's population is $3$ more than half of Town A's population.

Find Town B's population, then draw the bar for Town B to complete the graph.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph compares two towns' populations. Town A is 100 people. Town B is 3 more than half of Town A. Find Town B's population so its bar can be drawn.

Givens

Town A population = 100 people
Town B = 3 more than half of Town A's population
Gridlines are marked at 0, 50, and 100

Unknowns

Town B's population
The height of Town B's bar

Constraints

Half of Town A must be computed before adding 3
The bar height matches the population on the same scale as Town A

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #11 Work Backwards

The phrase '3 more than half of Town A' breaks into two ordered subproblems: first take half of 100, then add 3. Order matters, so we build the value step by step.

3 · Execute3 carry out the plan

1Half of Town A

#7 Identify Subproblems 4.OA.A.3

Town A has 100 people, so first find half of 100.

100 \div 2 = 50

Taking half of a number is dividing it into 2 equal parts.

2Add 3 more

#7 Identify Subproblems 4.OA.A.3

Town B is 3 more than that, so add 3 to 50.

50 + 3 = 53

'3 more than' means we increase the previous result by 3.

3Draw the bar

#7 Identify Subproblems 3.MD.B.3

Town B's bar reaches 53, on the same scale as Town A.

0 < 53 < 100

On the same scale, a value of 53 sits at the matching height.

Answer: Town B has 53 people

4 · Reviewdoes it hold up?

53 is 3 more than half of 100 (which is 50), so the bar height is sensible on the 100-scale.

Another way: Work backwards (tool 11): if Town B were exactly half of Town A it would be 50; the extra '3 more' nudges it to 53.

Standardsmin grade 4

4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Taking half of Town A and then adding 3 to find Town B
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Placing Town B's bar at the correct height on the population scale

💡Takeaway. This only needs Grade 4 'do it in order' thinking: divide first, then add!

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