Choose a scale that fits the largest value

3.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

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 $2$ 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	(?)	$18$	$10$	$14$	$64$

(Number of students who like roses) $=$ [ ] $- (18 + 10 + 14) =$ [ ] (students)
Since [ ] students like roses, the vertical scale must reach at least [ ] students.
If one vertical grid square represents $2$ 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 = 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

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 \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!