Sensim Math · Depth 한국어

← 2-2 · Find the value of one grid interval · Read and Scale a Data Graph

Find the value of one grid interval · 10 practice problems

3.MD.B.3

Generated variants — 10

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

Variant 1 answer: 12 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 3030 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 44 circles, Town B has 22 circles, Town C has 11 circle, Town D has 33 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 1010 circles in all and 3030 students, how many students does one circle represent?

(3) Town A has 44 circles, so the number of students living in Town A is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=104 + 2 + 1 + 3 = 10
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
10 circles stand for 30 students, so one circle stands for 30 / 10 = 3 students.
30÷10=330 \div 10 = 3
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
3×4=123 \times 4 = 12
Multiplying circles by students-per-circle gives the town's real value.
Answer: 12 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 2 answer: 6 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 2020 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 33 circles, Town B has 33 circles, Town C has 22 circles, Town D has 22 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 1010 circles in all and 2020 students, how many students does one circle represent?

(3) Town B has 33 circles, so the number of students living in Town B is □×3=□\square\times3=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=103 + 3 + 2 + 2 = 10
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
10 circles stand for 20 students, so one circle stands for 20 / 10 = 2 students.
20÷10=220 \div 10 = 2
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
2×3=62 \times 3 = 6
Multiplying circles by students-per-circle gives the town's real value.
Answer: 6 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 3 answer: 15 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 3333 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 22 circles, Town B has 55 circles, Town C has 33 circles, Town D has 11 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 1111 circles in all and 3333 students, how many students does one circle represent?

(3) Town B has 55 circles, so the number of students living in Town B is □×5=□\square\times5=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=112 + 5 + 3 + 1 = 11
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
11 circles stand for 33 students, so one circle stands for 33 / 11 = 3 students.
33÷11=333 \div 11 = 3
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
3×5=153 \times 5 = 15
Multiplying circles by students-per-circle gives the town's real value.
Answer: 15 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 4 answer: 16 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 4040 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 22 circles, Town B has 44 circles, Town C has 33 circles, Town D has 11 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 1010 circles in all and 4040 students, how many students does one circle represent?

(3) Town B has 44 circles, so the number of students living in Town B is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=102 + 4 + 3 + 1 = 10
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
10 circles stand for 40 students, so one circle stands for 40 / 10 = 4 students.
40÷10=440 \div 10 = 4
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
4×4=164 \times 4 = 16
Multiplying circles by students-per-circle gives the town's real value.
Answer: 16 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 5 answer: 12 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 2727 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 11 circle, Town B has 22 circles, Town C has 44 circles, Town D has 22 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 99 circles in all and 2727 students, how many students does one circle represent?

(3) Town C has 44 circles, so the number of students living in Town C is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=91 + 2 + 4 + 2 = 9
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
9 circles stand for 27 students, so one circle stands for 27 / 9 = 3 students.
27÷9=327 \div 9 = 3
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
3×4=123 \times 4 = 12
Multiplying circles by students-per-circle gives the town's real value.
Answer: 12 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 6 answer: 8 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 1616 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 11 circle, Town B has 11 circle, Town C has 44 circles, Town D has 22 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 88 circles in all and 1616 students, how many students does one circle represent?

(3) Town C has 44 circles, so the number of students living in Town C is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=81 + 1 + 4 + 2 = 8
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
8 circles stand for 16 students, so one circle stands for 16 / 8 = 2 students.
16÷8=216 \div 8 = 2
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
2×4=82 \times 4 = 8
Multiplying circles by students-per-circle gives the town's real value.
Answer: 8 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 7 answer: 8 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 1818 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 22 circles, Town B has 22 circles, Town C has 44 circles, Town D has 11 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 99 circles in all and 1818 students, how many students does one circle represent?

(3) Town C has 44 circles, so the number of students living in Town C is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=92 + 2 + 4 + 1 = 9
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
9 circles stand for 18 students, so one circle stands for 18 / 9 = 2 students.
18÷9=218 \div 9 = 2
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
2×4=82 \times 4 = 8
Multiplying circles by students-per-circle gives the town's real value.
Answer: 8 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 8 answer: 8 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 2020 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 11 circle, Town B has 33 circles, Town C has 22 circles, Town D has 44 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 1010 circles in all and 2020 students, how many students does one circle represent?

(3) Town D has 44 circles, so the number of students living in Town D is □×4=□\square\times4=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=101 + 3 + 2 + 4 = 10
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
10 circles stand for 20 students, so one circle stands for 20 / 10 = 2 students.
20÷10=220 \div 10 = 2
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
2×4=82 \times 4 = 8
Multiplying circles by students-per-circle gives the town's real value.
Answer: 8 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 9 answer: 9 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 2424 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 33 circles, Town B has 11 circle, Town C has 22 circles, Town D has 22 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 88 circles in all and 2424 students, how many students does one circle represent?

(3) Town A has 33 circles, so the number of students living in Town A is □×3=□\square\times3=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=83 + 1 + 2 + 2 = 8
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
8 circles stand for 24 students, so one circle stands for 24 / 8 = 3 students.
24÷8=324 \div 8 = 3
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
3×3=93 \times 3 = 9
Multiplying circles by students-per-circle gives the town's real value.
Answer: 9 students

Review

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.

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

Standards · min 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.
💡 This only needs the Grade 3 idea that one picture stands for a set number -- find that, then multiply!
Variant 10 answer: 10 students

The number of students living in four towns was surveyed and shown in a picture graph. When the four towns have 2424 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 55 circles, Town B has 11 circle, Town C has 22 circles, Town D has 44 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 1212 circles in all and 2424 students, how many students does one circle represent?

(3) Town A has 55 circles, so the number of students living in Town A is □×5=□\square\times5=\square students.

Number of students by town Number Town A B C D
Show solution

Understand

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.

Plan

#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.

Execute

#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=125 + 1 + 2 + 4 = 12
Reading and totaling the symbols is how you interpret a scaled picture graph.
#8 Analyze the Units 3.MD.B.3
12 circles stand for 24 students, so one circle stands for 24 / 12 = 2 students.
24÷12=224 \div 12 = 2
Sharing the students equally among the circles tells the value of each circle (the scale).
#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.
2×5=102 \times 5 = 10
Multiplying circles by students-per-circle gives the town's real value.
Answer: 10 students

Review

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.

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

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