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← 4-1 · Choose a scale that fits the largest value · Read and Scale a Data Graph

Choose a scale that fits the largest value · 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: 11 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 22 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1818 1010 1414 6464
  • (Number of students who like roses) == [ ] −(18+10+14)=- (18 + 10 + 14) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 22 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (18), lilies (10), and daisies (14), with a total of 64. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 2 students.

Givens
  • Tulip = 18, Lily = 10, Daisy = 14 students
  • Total = 64 students
  • One vertical grid square represents 2 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 2 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
64−(18+10+14)=64−42=2264 - (18 + 10 + 14) = 64 - 42 = 22
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 22 (rose), 18 (tulip), 10 (lily), 14 (daisy). The largest is 22, so the scale must reach at least 22 students.
max⁡(22,18,10,14)=22\max(22, 18, 10, 14) = 22
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 2 students, so divide the largest value by 2 to find how many squares are needed.
22÷2=1122 \div 2 = 11
If one square holds 2 students, then 22 students fill 11 squares exactly.
Answer: 11 squares

Review

11 squares at 2 students each reach 22 students, matching the largest value, and 22 is bigger than every other count, so 11 squares is the smallest scale that fits.

Guess and check (tool 6): 10 squares reach only 20 students, too short for 22; 11 squares reach 22, which works, confirming 11 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 2 each!
Variant 2 answer: 9 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 44 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 2424 1616 2828 104104
  • (Number of students who like roses) == [ ] −(24+16+28)=- (24 + 16 + 28) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 44 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (24), lilies (16), and daisies (28), with a total of 104. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 4 students.

Givens
  • Tulip = 24, Lily = 16, Daisy = 28 students
  • Total = 104 students
  • One vertical grid square represents 4 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 4 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
104−(24+16+28)=104−68=36104 - (24 + 16 + 28) = 104 - 68 = 36
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 36 (rose), 24 (tulip), 16 (lily), 28 (daisy). The largest is 36, so the scale must reach at least 36 students.
max⁡(36,24,16,28)=36\max(36, 24, 16, 28) = 36
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 4 students, so divide the largest value by 4 to find how many squares are needed.
36÷4=936 \div 4 = 9
If one square holds 4 students, then 36 students fill 9 squares exactly.
Answer: 9 squares

Review

9 squares at 4 students each reach 36 students, matching the largest value, and 36 is bigger than every other count, so 9 squares is the smallest scale that fits.

Guess and check (tool 6): 8 squares reach only 32 students, too short for 36; 9 squares reach 36, which works, confirming 9 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 4 each!
Variant 3 answer: 4 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 55 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1010 66 1414 5050
  • (Number of students who like roses) == [ ] −(10+6+14)=- (10 + 6 + 14) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 55 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (10), lilies (6), and daisies (14), with a total of 50. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 5 students.

Givens
  • Tulip = 10, Lily = 6, Daisy = 14 students
  • Total = 50 students
  • One vertical grid square represents 5 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 5 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
50−(10+6+14)=50−30=2050 - (10 + 6 + 14) = 50 - 30 = 20
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 20 (rose), 10 (tulip), 6 (lily), 14 (daisy). The largest is 20, so the scale must reach at least 20 students.
max⁡(20,10,6,14)=20\max(20, 10, 6, 14) = 20
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 5 students, so divide the largest value by 5 to find how many squares are needed.
20÷5=420 \div 5 = 4
If one square holds 5 students, then 20 students fill 4 squares exactly.
Answer: 4 squares

Review

4 squares at 5 students each reach 20 students, matching the largest value, and 20 is bigger than every other count, so 4 squares is the smallest scale that fits.

Guess and check (tool 6): 3 squares reach only 15 students, too short for 20; 4 squares reach 20, which works, confirming 4 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 5 each!
Variant 4 answer: 4 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 55 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1111 77 1313 5151
  • (Number of students who like roses) == [ ] −(11+7+13)=- (11 + 7 + 13) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 55 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (11), lilies (7), and daisies (13), with a total of 51. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 5 students.

Givens
  • Tulip = 11, Lily = 7, Daisy = 13 students
  • Total = 51 students
  • One vertical grid square represents 5 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 5 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
51−(11+7+13)=51−31=2051 - (11 + 7 + 13) = 51 - 31 = 20
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 20 (rose), 11 (tulip), 7 (lily), 13 (daisy). The largest is 20, so the scale must reach at least 20 students.
max⁡(20,11,7,13)=20\max(20, 11, 7, 13) = 20
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 5 students, so divide the largest value by 5 to find how many squares are needed.
20÷5=420 \div 5 = 4
If one square holds 5 students, then 20 students fill 4 squares exactly.
Answer: 4 squares

Review

4 squares at 5 students each reach 20 students, matching the largest value, and 20 is bigger than every other count, so 4 squares is the smallest scale that fits.

Guess and check (tool 6): 3 squares reach only 15 students, too short for 20; 4 squares reach 20, which works, confirming 4 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 5 each!
Variant 5 answer: 15 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 22 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1616 1212 2020 7878
  • (Number of students who like roses) == [ ] −(16+12+20)=- (16 + 12 + 20) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 22 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (16), lilies (12), and daisies (20), with a total of 78. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 2 students.

Givens
  • Tulip = 16, Lily = 12, Daisy = 20 students
  • Total = 78 students
  • One vertical grid square represents 2 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 2 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
78−(16+12+20)=78−48=3078 - (16 + 12 + 20) = 78 - 48 = 30
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 30 (rose), 16 (tulip), 12 (lily), 20 (daisy). The largest is 30, so the scale must reach at least 30 students.
max⁡(30,16,12,20)=30\max(30, 16, 12, 20) = 30
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 2 students, so divide the largest value by 2 to find how many squares are needed.
30÷2=1530 \div 2 = 15
If one square holds 2 students, then 30 students fill 15 squares exactly.
Answer: 15 squares

Review

15 squares at 2 students each reach 30 students, matching the largest value, and 30 is bigger than every other count, so 15 squares is the smallest scale that fits.

Guess and check (tool 6): 14 squares reach only 28 students, too short for 30; 15 squares reach 30, which works, confirming 15 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 2 each!
Variant 6 answer: 17 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 22 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 2222 1818 2626 100100
  • (Number of students who like roses) == [ ] −(22+18+26)=- (22 + 18 + 26) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 22 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (22), lilies (18), and daisies (26), with a total of 100. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 2 students.

Givens
  • Tulip = 22, Lily = 18, Daisy = 26 students
  • Total = 100 students
  • One vertical grid square represents 2 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 2 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
100−(22+18+26)=100−66=34100 - (22 + 18 + 26) = 100 - 66 = 34
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 34 (rose), 22 (tulip), 18 (lily), 26 (daisy). The largest is 34, so the scale must reach at least 34 students.
max⁡(34,22,18,26)=34\max(34, 22, 18, 26) = 34
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 2 students, so divide the largest value by 2 to find how many squares are needed.
34÷2=1734 \div 2 = 17
If one square holds 2 students, then 34 students fill 17 squares exactly.
Answer: 17 squares

Review

17 squares at 2 students each reach 34 students, matching the largest value, and 34 is bigger than every other count, so 17 squares is the smallest scale that fits.

Guess and check (tool 6): 16 squares reach only 32 students, too short for 34; 17 squares reach 34, which works, confirming 17 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 2 each!
Variant 7 answer: 5 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 55 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1515 99 2121 7070
  • (Number of students who like roses) == [ ] −(15+9+21)=- (15 + 9 + 21) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 55 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (15), lilies (9), and daisies (21), with a total of 70. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 5 students.

Givens
  • Tulip = 15, Lily = 9, Daisy = 21 students
  • Total = 70 students
  • One vertical grid square represents 5 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 5 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
70−(15+9+21)=70−45=2570 - (15 + 9 + 21) = 70 - 45 = 25
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 25 (rose), 15 (tulip), 9 (lily), 21 (daisy). The largest is 25, so the scale must reach at least 25 students.
max⁡(25,15,9,21)=25\max(25, 15, 9, 21) = 25
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 5 students, so divide the largest value by 5 to find how many squares are needed.
25÷5=525 \div 5 = 5
If one square holds 5 students, then 25 students fill 5 squares exactly.
Answer: 5 squares

Review

5 squares at 5 students each reach 25 students, matching the largest value, and 25 is bigger than every other count, so 5 squares is the smallest scale that fits.

Guess and check (tool 6): 4 squares reach only 20 students, too short for 25; 5 squares reach 25, which works, confirming 5 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 5 each!
Variant 8 answer: 7 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 33 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1313 99 1717 6060
  • (Number of students who like roses) == [ ] −(13+9+17)=- (13 + 9 + 17) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 33 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (13), lilies (9), and daisies (17), with a total of 60. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 3 students.

Givens
  • Tulip = 13, Lily = 9, Daisy = 17 students
  • Total = 60 students
  • One vertical grid square represents 3 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 3 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
60−(13+9+17)=60−39=2160 - (13 + 9 + 17) = 60 - 39 = 21
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 21 (rose), 13 (tulip), 9 (lily), 17 (daisy). The largest is 21, so the scale must reach at least 21 students.
max⁡(21,13,9,17)=21\max(21, 13, 9, 17) = 21
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 3 students, so divide the largest value by 3 to find how many squares are needed.
21÷3=721 \div 3 = 7
If one square holds 3 students, then 21 students fill 7 squares exactly.
Answer: 7 squares

Review

7 squares at 3 students each reach 21 students, matching the largest value, and 21 is bigger than every other count, so 7 squares is the smallest scale that fits.

Guess and check (tool 6): 6 squares reach only 18 students, too short for 21; 7 squares reach 21, which works, confirming 7 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 3 each!
Variant 9 answer: 14 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 22 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 2020 1414 1818 8080
  • (Number of students who like roses) == [ ] −(20+14+18)=- (20 + 14 + 18) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 22 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (20), lilies (14), and daisies (18), with a total of 80. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 2 students.

Givens
  • Tulip = 20, Lily = 14, Daisy = 18 students
  • Total = 80 students
  • One vertical grid square represents 2 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 2 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
80−(20+14+18)=80−52=2880 - (20 + 14 + 18) = 80 - 52 = 28
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 28 (rose), 20 (tulip), 14 (lily), 18 (daisy). The largest is 28, so the scale must reach at least 28 students.
max⁡(28,20,14,18)=28\max(28, 20, 14, 18) = 28
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 2 students, so divide the largest value by 2 to find how many squares are needed.
28÷2=1428 \div 2 = 14
If one square holds 2 students, then 28 students fill 14 squares exactly.
Answer: 14 squares

Review

14 squares at 2 students each reach 28 students, matching the largest value, and 28 is bigger than every other count, so 14 squares is the smallest scale that fits.

Guess and check (tool 6): 13 squares reach only 26 students, too short for 28; 14 squares reach 28, which works, confirming 14 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 2 each!
Variant 10 answer: 6 squares

Representative Problem

The table shows the favorite flowers of the students at Mia's school. If this table is drawn as a bar graph in which one vertical grid square represents 44 students, find the least number of vertical grid squares the scale must have.

Table "Favorite Flower":

Flower Rose Tulip Lily Daisy Total
Number of students (?) 1212 88 1616 6060
  • (Number of students who like roses) == [ ] −(12+8+16)=- (12 + 8 + 16) = [ ] (students)
  • Since [ ] students like roses, the vertical scale must reach at least [ ] students.
  • If one vertical grid square represents 44 students, the vertical scale needs at least [ ] squares.
Show solution

Understand

A table lists how many students like roses, tulips (12), lilies (8), and daisies (16), with a total of 60. First find the missing rose count, then decide how many vertical grid squares a bar graph needs if one square stands for 4 students.

Givens
  • Tulip = 12, Lily = 8, Daisy = 16 students
  • Total = 60 students
  • One vertical grid square represents 4 students
Unknowns
  • The number of students who like roses
  • The least number of vertical grid squares the scale must have
Constraints
  • The scale must reach at least the largest single value
  • Each grid square stands for exactly 4 students

Plan

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

This is a two-step task: first recover the missing value from the total (a subtraction subproblem), then convert the largest value into grid squares using the 'students per square' unit.

Execute

#7 Identify Subproblems 3.MD.B.3
Subtract the three known categories from the total to get the number of students who like roses.
60−(12+8+16)=60−36=2460 - (12 + 8 + 16) = 60 - 36 = 24
A total is the sum of its parts, so the missing part is the total minus the known parts.
#7 Identify Subproblems 3.MD.B.3
Compare the four counts: 24 (rose), 12 (tulip), 8 (lily), 16 (daisy). The largest is 24, so the scale must reach at least 24 students.
max⁡(24,12,8,16)=24\max(24, 12, 8, 16) = 24
The tallest bar sets how high the scale must go.
#8 Analyze the Units 3.MD.B.3
Each grid square is worth 4 students, so divide the largest value by 4 to find how many squares are needed.
24÷4=624 \div 4 = 6
If one square holds 4 students, then 24 students fill 6 squares exactly.
Answer: 6 squares

Review

6 squares at 4 students each reach 24 students, matching the largest value, and 24 is bigger than every other count, so 6 squares is the smallest scale that fits.

Guess and check (tool 6): 5 squares reach only 20 students, too short for 24; 6 squares reach 24, which works, confirming 6 is the least.

Standards · min grade 3

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Choosing a vertical scale that fits the largest data value and counting the needed grid squares
💡 This only needs Grade 3 bar-graph sense: find the biggest value, then count squares worth 4 each!