Practice · Find the value of one grid interval · Sensim Math

Variant 1 easy

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $16$ students in all, find how many students live in Town C.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $1$ circle, Town B has $1$ circle, Town C has $4$ circles, Town D has $2$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $8$ circles in all and $16$ students, how many students does one circle represent?

(3) Town C has $4$ circles, so the number of students living in Town C is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 16 students all together. I need to find how many students live in Town C.

Givens

Circle counts: Town A = 1, Town B = 1, Town C = 4, Town D = 2.
The four towns have 16 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town C.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 1 + 1 + 4 + 2 = 8 circles in all.

1 + 1 + 4 + 2 = 8

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

8 circles stand for 16 students, so one circle stands for 16 / 8 = 2 students.

16 \div 8 = 2

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town C

#8 Analyze the Units 3.MD.B.3

Town C has 4 circles and each circle is 2 students, so Town C has 2 x 4 = 8 students.

2 \times 4 = 8

Multiplying circles by students-per-circle gives the town's real value.

Answer: 8 students

4 · Reviewdoes it hold up?

Check the whole graph with 2 per circle: A=2, B=2, C=8, D=4, totaling 2 + 2 + 8 + 4 = 16, which matches the given total. So Town C = 8 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town C's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 2 easy

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $18$ students in all, find how many students live in Town C.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $2$ circles, Town B has $2$ circles, Town C has $4$ circles, Town D has $1$ circle. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $9$ circles in all and $18$ students, how many students does one circle represent?

(3) Town C has $4$ circles, so the number of students living in Town C is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 18 students all together. I need to find how many students live in Town C.

Givens

Circle counts: Town A = 2, Town B = 2, Town C = 4, Town D = 1.
The four towns have 18 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town C.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 2 + 2 + 4 + 1 = 9 circles in all.

2 + 2 + 4 + 1 = 9

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

9 circles stand for 18 students, so one circle stands for 18 / 9 = 2 students.

18 \div 9 = 2

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town C

#8 Analyze the Units 3.MD.B.3

Town C has 4 circles and each circle is 2 students, so Town C has 2 x 4 = 8 students.

2 \times 4 = 8

Multiplying circles by students-per-circle gives the town's real value.

Answer: 8 students

4 · Reviewdoes it hold up?

Check the whole graph with 2 per circle: A=4, B=4, C=8, D=2, totaling 4 + 4 + 8 + 2 = 18, which matches the given total. So Town C = 8 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town C's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 3 medium

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $20$ students in all, find how many students live in Town B.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $3$ circles, Town B has $3$ circles, Town C has $2$ circles, Town D has $2$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $10$ circles in all and $20$ students, how many students does one circle represent?

(3) Town B has $3$ circles, so the number of students living in Town B is $\square\times3=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 20 students all together. I need to find how many students live in Town B.

Givens

Circle counts: Town A = 3, Town B = 3, Town C = 2, Town D = 2.
The four towns have 20 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town B.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 3 + 3 + 2 + 2 = 10 circles in all.

3 + 3 + 2 + 2 = 10

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

10 circles stand for 20 students, so one circle stands for 20 / 10 = 2 students.

20 \div 10 = 2

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town B

#8 Analyze the Units 3.MD.B.3

Town B has 3 circles and each circle is 2 students, so Town B has 2 x 3 = 6 students.

2 \times 3 = 6

Multiplying circles by students-per-circle gives the town's real value.

Answer: 6 students

4 · Reviewdoes it hold up?

Check the whole graph with 2 per circle: A=6, B=6, C=4, D=4, totaling 6 + 6 + 4 + 4 = 20, which matches the given total. So Town B = 6 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town B's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 4 easy

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $20$ students in all, find how many students live in Town D.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $1$ circle, Town B has $3$ circles, Town C has $2$ circles, Town D has $4$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $10$ circles in all and $20$ students, how many students does one circle represent?

(3) Town D has $4$ circles, so the number of students living in Town D is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 20 students all together. I need to find how many students live in Town D.

Givens

Circle counts: Town A = 1, Town B = 3, Town C = 2, Town D = 4.
The four towns have 20 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town D.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 1 + 3 + 2 + 4 = 10 circles in all.

1 + 3 + 2 + 4 = 10

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

10 circles stand for 20 students, so one circle stands for 20 / 10 = 2 students.

20 \div 10 = 2

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town D

#8 Analyze the Units 3.MD.B.3

Town D has 4 circles and each circle is 2 students, so Town D has 2 x 4 = 8 students.

2 \times 4 = 8

Multiplying circles by students-per-circle gives the town's real value.

Answer: 8 students

4 · Reviewdoes it hold up?

Check the whole graph with 2 per circle: A=2, B=6, C=4, D=8, totaling 2 + 6 + 4 + 8 = 20, which matches the given total. So Town D = 8 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town D's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 5 medium

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $24$ students in all, find how many students live in Town A.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $3$ circles, Town B has $1$ circle, Town C has $2$ circles, Town D has $2$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $8$ circles in all and $24$ students, how many students does one circle represent?

(3) Town A has $3$ circles, so the number of students living in Town A is $\square\times3=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 24 students all together. I need to find how many students live in Town A.

Givens

Circle counts: Town A = 3, Town B = 1, Town C = 2, Town D = 2.
The four towns have 24 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town A.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 3 + 1 + 2 + 2 = 8 circles in all.

3 + 1 + 2 + 2 = 8

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

8 circles stand for 24 students, so one circle stands for 24 / 8 = 3 students.

24 \div 8 = 3

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town A

#8 Analyze the Units 3.MD.B.3

Town A has 3 circles and each circle is 3 students, so Town A has 3 x 3 = 9 students.

3 \times 3 = 9

Multiplying circles by students-per-circle gives the town's real value.

Answer: 9 students

4 · Reviewdoes it hold up?

Check the whole graph with 3 per circle: A=9, B=3, C=6, D=6, totaling 9 + 3 + 6 + 6 = 24, which matches the given total. So Town A = 9 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town A's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 6 medium

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $24$ students in all, find how many students live in Town A.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $5$ circles, Town B has $1$ circle, Town C has $2$ circles, Town D has $4$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $12$ circles in all and $24$ students, how many students does one circle represent?

(3) Town A has $5$ circles, so the number of students living in Town A is $\square\times5=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 24 students all together. I need to find how many students live in Town A.

Givens

Circle counts: Town A = 5, Town B = 1, Town C = 2, Town D = 4.
The four towns have 24 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town A.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 5 + 1 + 2 + 4 = 12 circles in all.

5 + 1 + 2 + 4 = 12

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

12 circles stand for 24 students, so one circle stands for 24 / 12 = 2 students.

24 \div 12 = 2

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town A

#8 Analyze the Units 3.MD.B.3

Town A has 5 circles and each circle is 2 students, so Town A has 2 x 5 = 10 students.

2 \times 5 = 10

Multiplying circles by students-per-circle gives the town's real value.

Answer: 10 students

4 · Reviewdoes it hold up?

Check the whole graph with 2 per circle: A=10, B=2, C=4, D=8, totaling 10 + 2 + 4 + 8 = 24, which matches the given total. So Town A = 10 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town A's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 7 medium

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $27$ students in all, find how many students live in Town C.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $1$ circle, Town B has $2$ circles, Town C has $4$ circles, Town D has $2$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $9$ circles in all and $27$ students, how many students does one circle represent?

(3) Town C has $4$ circles, so the number of students living in Town C is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 27 students all together. I need to find how many students live in Town C.

Givens

Circle counts: Town A = 1, Town B = 2, Town C = 4, Town D = 2.
The four towns have 27 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town C.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 1 + 2 + 4 + 2 = 9 circles in all.

1 + 2 + 4 + 2 = 9

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

9 circles stand for 27 students, so one circle stands for 27 / 9 = 3 students.

27 \div 9 = 3

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town C

#8 Analyze the Units 3.MD.B.3

Town C has 4 circles and each circle is 3 students, so Town C has 3 x 4 = 12 students.

3 \times 4 = 12

Multiplying circles by students-per-circle gives the town's real value.

Answer: 12 students

4 · Reviewdoes it hold up?

Check the whole graph with 3 per circle: A=3, B=6, C=12, D=6, totaling 3 + 6 + 12 + 6 = 27, which matches the given total. So Town C = 12 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town C's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 8 hard

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $30$ students in all, find how many students live in Town A.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $4$ circles, Town B has $2$ circles, Town C has $1$ circle, Town D has $3$ circles. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $10$ circles in all and $30$ students, how many students does one circle represent?

(3) Town A has $4$ circles, so the number of students living in Town A is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 30 students all together. I need to find how many students live in Town A.

Givens

Circle counts: Town A = 4, Town B = 2, Town C = 1, Town D = 3.
The four towns have 30 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town A.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 4 + 2 + 1 + 3 = 10 circles in all.

4 + 2 + 1 + 3 = 10

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

10 circles stand for 30 students, so one circle stands for 30 / 10 = 3 students.

30 \div 10 = 3

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town A

#8 Analyze the Units 3.MD.B.3

Town A has 4 circles and each circle is 3 students, so Town A has 3 x 4 = 12 students.

3 \times 4 = 12

Multiplying circles by students-per-circle gives the town's real value.

Answer: 12 students

4 · Reviewdoes it hold up?

Check the whole graph with 3 per circle: A=12, B=6, C=3, D=9, totaling 12 + 6 + 3 + 9 = 30, which matches the given total. So Town A = 12 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town A's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 9 hard

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $33$ students in all, find how many students live in Town B.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $2$ circles, Town B has $5$ circles, Town C has $3$ circles, Town D has $1$ circle. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $11$ circles in all and $33$ students, how many students does one circle represent?

(3) Town B has $5$ circles, so the number of students living in Town B is $\square\times5=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 33 students all together. I need to find how many students live in Town B.

Givens

Circle counts: Town A = 2, Town B = 5, Town C = 3, Town D = 1.
The four towns have 33 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town B.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 2 + 5 + 3 + 1 = 11 circles in all.

2 + 5 + 3 + 1 = 11

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

11 circles stand for 33 students, so one circle stands for 33 / 11 = 3 students.

33 \div 11 = 3

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town B

#8 Analyze the Units 3.MD.B.3

Town B has 5 circles and each circle is 3 students, so Town B has 3 x 5 = 15 students.

3 \times 5 = 15

Multiplying circles by students-per-circle gives the town's real value.

Answer: 15 students

4 · Reviewdoes it hold up?

Check the whole graph with 3 per circle: A=6, B=15, C=9, D=3, totaling 6 + 15 + 9 + 3 = 33, which matches the given total. So Town B = 15 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town B's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Variant 10 hard

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have $40$ students in all, find how many students live in Town B.

Number of students by town

The horizontal axis lists the towns (A, B, C, D). Town A has $2$ circles, Town B has $4$ circles, Town C has $3$ circles, Town D has $1$ circle. (The number of students that one circle represents is not given.)

(1) Counting all the circles in the graph, how many are there?

(2) Since there are $10$ circles in all and $40$ students, how many students does one circle represent?

(3) Town B has $4$ circles, so the number of students living in Town B is $\square\times4=\square$ students.

Your answer

Show solution

1 · Understandwhat's really being asked

A picture graph shows students by town using circles, but the value of one circle is not given. The four towns have 40 students all together. I need to find how many students live in Town B.

Givens

Circle counts: Town A = 2, Town B = 4, Town C = 3, Town D = 1.
The four towns have 40 students in all.
Every circle stands for the same number of students (unknown).

Unknowns

How many students one circle represents.
The number of students in Town B.

Constraints

Total circles times students-per-circle equals the total students.

2 · Planchoose the strategy

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

One circle is a unit standing for some students. Counting all circles and matching them to the total students gives the value of one circle; then I scale the target town's circles by that unit. This is unit reasoning broken into small steps.

3 · Execute3 carry out the plan

1Count all the circles

#7 Identify Subproblems 3.MD.B.3

Add the circles in every column: 2 + 4 + 3 + 1 = 10 circles in all.

2 + 4 + 3 + 1 = 10

Reading and totaling the symbols is how you interpret a scaled picture graph.

2Find what one circle is worth

#8 Analyze the Units 3.MD.B.3

10 circles stand for 40 students, so one circle stands for 40 / 10 = 4 students.

40 \div 10 = 4

Sharing the students equally among the circles tells the value of each circle (the scale).

3Scale Town B

#8 Analyze the Units 3.MD.B.3

Town B has 4 circles and each circle is 4 students, so Town B has 4 x 4 = 16 students.

4 \times 4 = 16

Multiplying circles by students-per-circle gives the town's real value.

Answer: 16 students

4 · Reviewdoes it hold up?

Check the whole graph with 4 per circle: A=8, B=16, C=12, D=4, totaling 8 + 16 + 12 + 4 = 40, which matches the given total. So Town B = 16 is consistent.

Another way: Find the scale once, then multiply each town's circle count by it; the target town follows the same rule.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Finding the scale (students per circle) and reading Town B's value from the scaled graph.

💡Takeaway. This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!

Find the value of one grid interval · 10 practice problems

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