← Find the value of one grid square · Read and Scale a Data Graph

Find the value of one grid square · 8 practice problems

3.MD.B.33.OA.A.3

Generated variants — 8

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

Variant 1 easy answer: 15 children

The bar graph shows the favorite pet chosen by the $36$ children in the survey. Find how many children chose Dog.

Bar graph "Favorite Pet": the horizontal axis lists the categories (Dog, Cat, Rabbit, Bird) and the vertical axis shows the number of children. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Dog $5$ squares, Cat $3$ squares, Rabbit $2$ squares, Bird $2$ squares.

Adding the number of grid squares for all the bars gives $5 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $36$ children, one grid square represents [ ] children.
Therefore the number of children who chose Dog is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 36 children chose each of 4 categories, but the vertical scale has no numbers. The bars are 5, 3, 2, 2 grid squares tall (Dog, Cat, Rabbit, Bird). Find how many children one grid square stands for, then find how many chose Dog.

Givens

Total children = 36
Bar heights in grid squares: Dog 5, Cat 3, Rabbit 2, Bird 2
The vertical scale has no numbers written on it

Unknowns

How many children one grid square represents
The number of children who chose Dog

Constraints

Every grid square represents the same number of children
The 4 bar values together account for all 36 children

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'children per square'. Total squares correspond to total children, so dividing 36 by the total squares gives the value of one square, which then scales the Dog bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

5 + 3 + 2 + 2 = 12

All the squares together stand for all the children.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 12 squares represent all 36 children, so one square represents 36 divided by 12.

36 \div 12 = 3

Sharing 36 children evenly across 12 squares gives 3 per square.

3Scale the Dog bar

#8 Analyze the Units 3.OA.A.3

The Dog bar is 5 squares tall, and each square is worth 3 children, so multiply.

5 \times 3 = 15

5 squares each worth 3 children make 15 children.

Answer: 15 children

4 · Reviewdoes it hold up?

Checking all bars at 3 per square: 15 + 9 + 6 + 6 = 36, matching the total, so the value-per-square and the Dog count are correct.

Another way: Look for a pattern (tool 5): once one square = 3, just multiply every bar height by 3 and confirm they sum to 36.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 36 by 12 for the unit value and multiplying 5 by 3 for Dog

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 2 easy answer: 12 students

The bar graph shows the favorite sport chosen by the $40$ students in the survey. Find how many students chose Soccer.

Bar graph "Favorite Sport": the horizontal axis lists the categories (Soccer, Basketball, Tennis, Swimming) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Soccer $6$ squares, Basketball $4$ squares, Tennis $5$ squares, Swimming $5$ squares.

Adding the number of grid squares for all the bars gives $6 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $40$ students, one grid square represents [ ] students.
Therefore the number of students who chose Soccer is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 40 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 6, 4, 5, 5 grid squares tall (Soccer, Basketball, Tennis, Swimming). Find how many students one grid square stands for, then find how many chose Soccer.

Givens

Total students = 40
Bar heights in grid squares: Soccer 6, Basketball 4, Tennis 5, Swimming 5
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Soccer

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 40 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 40 by the total squares gives the value of one square, which then scales the Soccer bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

6 + 4 + 5 + 5 = 20

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 20 squares represent all 40 students, so one square represents 40 divided by 20.

40 \div 20 = 2

Sharing 40 students evenly across 20 squares gives 2 per square.

3Scale the Soccer bar

#8 Analyze the Units 3.OA.A.3

The Soccer bar is 6 squares tall, and each square is worth 2 students, so multiply.

6 \times 2 = 12

6 squares each worth 2 students make 12 students.

Answer: 12 students

4 · Reviewdoes it hold up?

Checking all bars at 2 per square: 12 + 8 + 10 + 10 = 40, matching the total, so the value-per-square and the Soccer count are correct.

Another way: Look for a pattern (tool 5): once one square = 2, just multiply every bar height by 2 and confirm they sum to 40.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 40 by 20 for the unit value and multiplying 6 by 2 for Soccer

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 3 medium answer: 12 students

The bar graph shows the favorite color chosen by the $45$ students in the survey. Find how many students chose Red.

Bar graph "Favorite Color": the horizontal axis lists the categories (Red, Blue, Green, Yellow) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Red $4$ squares, Blue $6$ squares, Green $3$ squares, Yellow $2$ squares.

Adding the number of grid squares for all the bars gives $4 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $45$ students, one grid square represents [ ] students.
Therefore the number of students who chose Red is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 45 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 4, 6, 3, 2 grid squares tall (Red, Blue, Green, Yellow). Find how many students one grid square stands for, then find how many chose Red.

Givens

Total students = 45
Bar heights in grid squares: Red 4, Blue 6, Green 3, Yellow 2
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Red

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 45 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 45 by the total squares gives the value of one square, which then scales the Red bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

4 + 6 + 3 + 2 = 15

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 15 squares represent all 45 students, so one square represents 45 divided by 15.

45 \div 15 = 3

Sharing 45 students evenly across 15 squares gives 3 per square.

3Scale the Red bar

#8 Analyze the Units 3.OA.A.3

The Red bar is 4 squares tall, and each square is worth 3 students, so multiply.

4 \times 3 = 12

4 squares each worth 3 students make 12 students.

Answer: 12 students

4 · Reviewdoes it hold up?

Checking all bars at 3 per square: 12 + 18 + 9 + 6 = 45, matching the total, so the value-per-square and the Red count are correct.

Another way: Look for a pattern (tool 5): once one square = 3, just multiply every bar height by 3 and confirm they sum to 45.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 45 by 15 for the unit value and multiplying 4 by 3 for Red

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 4 medium answer: 16 students

The bar graph shows the most-admired historical figure chosen by the $46$ students in the survey. Find how many students chose Lincoln.

Bar graph "Most-Admired Historical Figure": the horizontal axis lists the categories (Lincoln, Washington, Franklin, Tubman) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Lincoln $8$ squares, Washington $7$ squares, Franklin $3$ squares, Tubman $5$ squares.

Adding the number of grid squares for all the bars gives $8 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $46$ students, one grid square represents [ ] students.
Therefore the number of students who chose Lincoln is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 46 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 8, 7, 3, 5 grid squares tall (Lincoln, Washington, Franklin, Tubman). Find how many students one grid square stands for, then find how many chose Lincoln.

Givens

Total students = 46
Bar heights in grid squares: Lincoln 8, Washington 7, Franklin 3, Tubman 5
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Lincoln

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 46 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 46 by the total squares gives the value of one square, which then scales the Lincoln bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

8 + 7 + 3 + 5 = 23

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 23 squares represent all 46 students, so one square represents 46 divided by 23.

46 \div 23 = 2

Sharing 46 students evenly across 23 squares gives 2 per square.

3Scale the Lincoln bar

#8 Analyze the Units 3.OA.A.3

The Lincoln bar is 8 squares tall, and each square is worth 2 students, so multiply.

8 \times 2 = 16

8 squares each worth 2 students make 16 students.

Answer: 16 students

4 · Reviewdoes it hold up?

Checking all bars at 2 per square: 16 + 14 + 6 + 10 = 46, matching the total, so the value-per-square and the Lincoln count are correct.

Another way: Look for a pattern (tool 5): once one square = 2, just multiply every bar height by 2 and confirm they sum to 46.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 46 by 23 for the unit value and multiplying 8 by 2 for Lincoln

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 5 medium answer: 9 people

The bar graph shows the favorite season chosen by the $54$ people in the survey. Find how many people chose Spring.

Bar graph "Favorite Season": the horizontal axis lists the categories (Spring, Summer, Fall, Winter) and the vertical axis shows the number of people. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Spring $3$ squares, Summer $5$ squares, Fall $4$ squares, Winter $6$ squares.

Adding the number of grid squares for all the bars gives $3 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $54$ people, one grid square represents [ ] people.
Therefore the number of people who chose Spring is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 54 people chose each of 4 categories, but the vertical scale has no numbers. The bars are 3, 5, 4, 6 grid squares tall (Spring, Summer, Fall, Winter). Find how many people one grid square stands for, then find how many chose Spring.

Givens

Total people = 54
Bar heights in grid squares: Spring 3, Summer 5, Fall 4, Winter 6
The vertical scale has no numbers written on it

Unknowns

How many people one grid square represents
The number of people who chose Spring

Constraints

Every grid square represents the same number of people
The 4 bar values together account for all 54 people

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'people per square'. Total squares correspond to total people, so dividing 54 by the total squares gives the value of one square, which then scales the Spring bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

3 + 5 + 4 + 6 = 18

All the squares together stand for all the people.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 18 squares represent all 54 people, so one square represents 54 divided by 18.

54 \div 18 = 3

Sharing 54 people evenly across 18 squares gives 3 per square.

3Scale the Spring bar

#8 Analyze the Units 3.OA.A.3

The Spring bar is 3 squares tall, and each square is worth 3 people, so multiply.

3 \times 3 = 9

3 squares each worth 3 people make 9 people.

Answer: 9 people

4 · Reviewdoes it hold up?

Checking all bars at 3 per square: 9 + 15 + 12 + 18 = 54, matching the total, so the value-per-square and the Spring count are correct.

Another way: Look for a pattern (tool 5): once one square = 3, just multiply every bar height by 3 and confirm they sum to 54.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 54 by 18 for the unit value and multiplying 3 by 3 for Spring

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 6 medium answer: 21 students

The bar graph shows the favorite fruit chosen by the $60$ students in the survey. Find how many students chose Apple.

Bar graph "Favorite Fruit": the horizontal axis lists the categories (Apple, Banana, Grape, Orange) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Apple $7$ squares, Banana $5$ squares, Grape $4$ squares, Orange $4$ squares.

Adding the number of grid squares for all the bars gives $7 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $60$ students, one grid square represents [ ] students.
Therefore the number of students who chose Apple is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 60 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 7, 5, 4, 4 grid squares tall (Apple, Banana, Grape, Orange). Find how many students one grid square stands for, then find how many chose Apple.

Givens

Total students = 60
Bar heights in grid squares: Apple 7, Banana 5, Grape 4, Orange 4
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Apple

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 60 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 60 by the total squares gives the value of one square, which then scales the Apple bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

7 + 5 + 4 + 4 = 20

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 20 squares represent all 60 students, so one square represents 60 divided by 20.

60 \div 20 = 3

Sharing 60 students evenly across 20 squares gives 3 per square.

3Scale the Apple bar

#8 Analyze the Units 3.OA.A.3

The Apple bar is 7 squares tall, and each square is worth 3 students, so multiply.

7 \times 3 = 21

7 squares each worth 3 students make 21 students.

Answer: 21 students

4 · Reviewdoes it hold up?

Checking all bars at 3 per square: 21 + 15 + 12 + 12 = 60, matching the total, so the value-per-square and the Apple count are correct.

Another way: Look for a pattern (tool 5): once one square = 3, just multiply every bar height by 3 and confirm they sum to 60.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 60 by 20 for the unit value and multiplying 7 by 3 for Apple

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 7 hard answer: 24 students

The bar graph shows the favorite subject chosen by the $72$ students in the survey. Find how many students chose Math.

Bar graph "Favorite Subject": the horizontal axis lists the categories (Math, Science, Art, Music) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Math $6$ squares, Science $3$ squares, Art $4$ squares, Music $5$ squares.

Adding the number of grid squares for all the bars gives $6 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $72$ students, one grid square represents [ ] students.
Therefore the number of students who chose Math is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 72 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 6, 3, 4, 5 grid squares tall (Math, Science, Art, Music). Find how many students one grid square stands for, then find how many chose Math.

Givens

Total students = 72
Bar heights in grid squares: Math 6, Science 3, Art 4, Music 5
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Math

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 72 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 72 by the total squares gives the value of one square, which then scales the Math bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

6 + 3 + 4 + 5 = 18

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 18 squares represent all 72 students, so one square represents 72 divided by 18.

72 \div 18 = 4

Sharing 72 students evenly across 18 squares gives 4 per square.

3Scale the Math bar

#8 Analyze the Units 3.OA.A.3

The Math bar is 6 squares tall, and each square is worth 4 students, so multiply.

6 \times 4 = 24

6 squares each worth 4 students make 24 students.

Answer: 24 students

4 · Reviewdoes it hold up?

Checking all bars at 4 per square: 24 + 12 + 16 + 20 = 72, matching the total, so the value-per-square and the Math count are correct.

Another way: Look for a pattern (tool 5): once one square = 4, just multiply every bar height by 4 and confirm they sum to 72.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 72 by 18 for the unit value and multiplying 6 by 4 for Math

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!

Variant 8 hard answer: 32 students

The bar graph shows the favorite lunch chosen by the $80$ students in the survey. Find how many students chose Pizza.

Bar graph "Favorite Lunch": the horizontal axis lists the categories (Pizza, Burger, Pasta, Salad) and the vertical axis shows the number of students. The vertical scale has no numbers written on it. The height of each bar, counted in grid squares, is: Pizza $8$ squares, Burger $4$ squares, Pasta $3$ squares, Salad $5$ squares.

Adding the number of grid squares for all the bars gives $8 +$ [ ] $+$ [ ] $+$ [ ] $=$ [ ] (squares).
Since [ ] squares represent $80$ students, one grid square represents [ ] students.
Therefore the number of students who chose Pizza is [ ].

Show solution

1 · Understandwhat's really being asked

A bar graph shows how many of 80 students chose each of 4 categories, but the vertical scale has no numbers. The bars are 8, 4, 3, 5 grid squares tall (Pizza, Burger, Pasta, Salad). Find how many students one grid square stands for, then find how many chose Pizza.

Givens

Total students = 80
Bar heights in grid squares: Pizza 8, Burger 4, Pasta 3, Salad 5
The vertical scale has no numbers written on it

Unknowns

How many students one grid square represents
The number of students who chose Pizza

Constraints

Every grid square represents the same number of students
The 4 bar values together account for all 80 students

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

The key is the unit 'students per square'. Total squares correspond to total students, so dividing 80 by the total squares gives the value of one square, which then scales the Pizza bar.

3 · Execute3 carry out the plan

1Add up all the grid squares

#7 Identify Subproblems 3.MD.B.3

Sum the heights of all the bars to get the total number of grid squares used.

8 + 4 + 3 + 5 = 20

All the squares together stand for all the students.

2Find people per square

#8 Analyze the Units 3.OA.A.3

Those 20 squares represent all 80 students, so one square represents 80 divided by 20.

80 \div 20 = 4

Sharing 80 students evenly across 20 squares gives 4 per square.

3Scale the Pizza bar

#8 Analyze the Units 3.OA.A.3

The Pizza bar is 8 squares tall, and each square is worth 4 students, so multiply.

8 \times 4 = 32

8 squares each worth 4 students make 32 students.

Answer: 32 students

4 · Reviewdoes it hold up?

Checking all bars at 4 per square: 32 + 16 + 12 + 20 = 80, matching the total, so the value-per-square and the Pizza count are correct.

Another way: Look for a pattern (tool 5): once one square = 4, just multiply every bar height by 4 and confirm they sum to 80.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading bar heights in grid squares and relating them to the total
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing 80 by 20 for the unit value and multiplying 8 by 4 for Pizza

💡Takeaway. This only needs Grade 3 division: share the total over all the squares to learn what one square is worth!