Data & Graphs

Problem

Set the scale, then complete the graph

I must complete a 'Students per Class' picture graph for four classes. The grid already shows Class 2 with 3 circles and Class 3 with 4 circles. Using the conditions (Class 1 = 16 students, Class 2 is 4 fewer than Class 3, and all four classes total 56), I set the value of one grid square and fill in the missing classes.
Students per Class Number of students Class Class 1 Class 2 Class 3 Class 4
Measurement & data
Your answer
How to solve
Strategy Analyze the Units — The difference of 1 circle between Class 2 and Class 3 must equal the 4-student difference, which fixes the scale (one circle = 4 students). With the scale known I work out each class in small steps and use the total of 56 to finish.
1STEP 1

Find the value of one grid square

Class 3 has one more circle than Class 2 but only 4 more students, so that one circle stands for 4 students.

4 students ÷ 1 circle = 4 students per circle
2STEP 2

Find Class 2 and Class 3 in students

At 4 students per circle, Class 2 = 3 × 4 = 12 students and Class 3 = 4 × 4 = 16 students (16 - 12 = 4, as required).

3 × 4 = 12, 4 × 4 = 16
3STEP 3

Find Class 4 using the total

The four classes total 56. Subtract the three known classes: 56 - 16 - 12 - 16 = 12, so Class 4 has 12 students.

56 - 16 - 12 - 16 = 12
4STEP 4

Complete the graph

Divide each count by 4: Class 1 = 4 circles, Class 2 = 3, Class 3 = 4, Class 4 = 3 circles; draw each column from the bottom up.

16 ÷ 4 = 4, 12 ÷ 4 = 3
Answer
One square = 4 students; Class 1 = 16 (4 circles), Class 2 = 12 (3 circles), Class 3 = 16 (4 circles), Class 4 = 12 (3 circles).
Add the completed counts: 16 + 12 + 16 + 12 = 56, matching the total, and Class 2 (12) is exactly 4 fewer than Class 3 (16). Both conditions hold.
Takeaway

This only needs the Grade 3 idea that one circle's difference equals the student difference — that sets the scale!

  • Find the value of one grid square
  • Find Class 2 and Class 3 in students
  • Find Class 4 using the total
  • Complete the graph
Where next?
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