Sensim Math · Depth 한국어

4-2 · Line Graphs

Read max, min, and gridline scale from a line graph

5.MD.B.23.MD.B.3 · adapt · grade 5

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

▶ Practice — 8 problems

The line graph shows the number of ice cream cones sold each day at Mia's ice cream shop. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Ice Cream Cones Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of cones sold. The vertical axis is labeled 500, 600, and 700; since 5 grid squares represent 100, each grid square represents 100÷5=20100 \div 5 = 20 cones. The daily sales are: Monday 520520, Tuesday 660660, Wednesday 580580, Thursday 740740, and Friday 680680 cones.

Ice Cream Cones Sold (cones) 500 600 700 Mon Tue Wed Thu Fri
Show solution

Understand

A line graph of ice cream cones sold shows Mon = 520, Tue = 660, Wed = 580, Thu = 740, Fri = 680 (each small square = 20 cones). I must find the difference between the busiest day's count and the slowest day's count.

Givens
  • Monday = 520, Tuesday = 660, Wednesday = 580, Thursday = 740, Friday = 680 cones
  • Vertical axis labeled 500, 600, 700 with 5 squares per 100, so each square = 20
  • Highest point is the busiest day; lowest point is the slowest day
Unknowns
  • The difference between the most cones sold on a day and the fewest
Constraints
  • Read counts using the square value of 20 cones

Plan

#1 Draw a Diagram · also uses: #7 Identify Subproblems

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

Execute

#1 Draw a Diagram 3.MD.B.3
The highest point is Thursday. It is two squares above 700, and each square is 20, so 700 + 2 x 20 = 740 cones.
700+2×20=740700 + 2\times 20 = 740
The tallest dot marks the biggest value on the graph.
#1 Draw a Diagram 3.MD.B.3
The lowest point is Monday. It is one square above 500, so 500 + 20 = 520 cones.
500+20=520500 + 20 = 520
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 740 - 520 = 220 cones.
740−520=220740 - 520 = 220
Max minus min gives the spread between the best and worst day.
Answer: 220 cones

Review

740 is the highest reading and 520 the lowest, and 740 - 520 = 220, which is 11 squares of 20 cones (11 x 20 = 220) - consistent with the grid. The difference is less than either total, as a difference should be.

Count squares first (tool 5): the top and bottom dots are 11 squares apart, and 11 x 20 = 220 cones, giving the same answer without reading exact numbers.

Standards · min grade 5

  • 3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
  • 5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph
💡 Highest dot minus lowest dot - just remember each square here is worth 20!