Estimate an unmeasured midpoint value on a line graph

5.MD.B.2 · adapt · grade 5

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

The line graph shows the temperature recorded in a town. Estimate the temperature at about 1:00 p.m., in $^\circ\mathrm{C}$ .

The graph is titled "Town Temperature." The horizontal axis shows the time (8 a.m., 10 a.m., 12 noon, 2 p.m., 4 p.m.), and the vertical axis shows the temperature in $^\circ\mathrm{C}$ . The vertical axis is labeled 5, 10, and 15; since 5 grid squares represent 5, each grid square represents $5 \div 5 = 1\,^\circ\mathrm{C}$ . The recorded temperatures are: 8 a.m. $6\,^\circ\mathrm{C}$ , 10 a.m. $8\,^\circ\mathrm{C}$ , 12 noon $11\,^\circ\mathrm{C}$ , 2 p.m. $15\,^\circ\mathrm{C}$ , and 4 p.m. $12\,^\circ\mathrm{C}$ . The temperature at 1:00 p.m. was not recorded, so estimate it as the midpoint of the temperatures at 12 noon and 2 p.m.

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Understand

A line graph of town temperature shows 8 a.m. = 6, 10 a.m. = 8, 12 noon = 11, 2 p.m. = 15, 4 p.m. = 12 degrees C (each square = 1 degree). 1:00 p.m. was not measured; I estimate it as the midpoint of the 12 noon and 2 p.m. readings.

Givens

8 a.m. = 6 degrees C, 10 a.m. = 8 degrees C, 12 noon = 11 degrees C, 2 p.m. = 15 degrees C, 4 p.m. = 12 degrees C
Each small grid square = 1 degree C
1:00 p.m. is exactly halfway between 12 noon and 2 p.m.
Estimate 1 p.m. as the midpoint of the 12 noon and 2 p.m. temperatures

Unknowns

The estimated temperature at about 1:00 p.m. in degrees C

Constraints

1 p.m. lies between the two measured times, so its value should sit between 11 and 15

Plan

#5 Look for a Pattern · also uses: #1 Draw a Diagram

On a line graph the segment between two points rises steadily, so the value halfway across is the average of the two endpoints. 1 p.m. is the halfway time between 12 noon and 2 p.m., so I take the midpoint of 11 and 15.

Execute

#5 Look for a Pattern 5.MD.B.2

1 p.m. is halfway between 12 noon (11 degrees) and 2 p.m. (15 degrees). Add them: 11 + 15 = 26.

11 + 15 = 26

The connecting line climbs evenly, so the middle is the average of the ends.

#1 Draw a Diagram 5.MD.B.2

Divide the sum by 2 to find the midpoint value: 26 / 2 = 13 degrees C.

26 \div 2 = 13

On the graph 13 sits exactly halfway up the segment, matching 1 p.m. halfway across.

Answer: 13 degrees C

Review

13 lies between 11 (noon) and 15 (2 p.m.), as it must for a time in between, and it is exactly in the middle, which fits 1 p.m. being the middle time. The magnitude is sensible for an early-afternoon temperature.

Use the rise (tool 8 / units): the temperature climbed 4 degrees over 2 hours, so it rises 2 degrees per hour; one hour past noon gives 11 + 2 = 13 degrees C.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the noon and 2 p.m. values and estimating the in-between point

💡 Halfway across a line segment means halfway up - just average the two end values!