Sum all data values read from 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 number of soft pretzels sold over 5 days at a bakery. Find the total number of pretzels sold.

The graph is titled "Soft Pretzels Sold." The horizontal axis shows the date (the 5th, 6th, 7th, 8th, and 9th), and the vertical axis shows the number of pretzels. The vertical axis is labeled 0, 20, and 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ pretzels. The number sold each day is: the 5th $32$ , the 6th $16$ , the 7th $28$ , the 8th $52$ , and the 9th $36$ pretzels.

Show solution

Understand

A line graph of soft pretzels sold over 5 days shows the 5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36 (each small square = 4 pretzels). I must find the total pretzels sold across all five days.

Givens

5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36 pretzels
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all five days

Unknowns

The total number of pretzels sold across the five days

Constraints

Each value is read using the square value of 4 pretzels

Plan

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

I read each day's value off the graph using the square size, then add the five numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

#1 Draw a Diagram 3.MD.B.3

Using each square = 4 pretzels: 5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36.

32,\ 16,\ 28,\ 52,\ 36

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Group friendly pairs: (32 + 28) = 60 and (16 + 36) = 52; that gives 60 + 52 = 112, then add 52 for the 8th: 112 + 52 = 164.

(32+28) + (16+36) + 52 = 60 + 52 + 52 = 164

Pairing numbers to make tens keeps the multi-digit addition simple.

Answer: 164 pretzels

Review

Straight addition 32 + 16 + 28 + 52 + 36 = 164 matches. The total should be a few hundred since each day is in the tens, and 164 fits; it is also larger than the biggest single day (52), as a sum of positives must be.

Count squares first (tool 5): days are 8 + 4 + 7 + 13 + 9 = 41 squares, and 41 x 4 = 164 pretzels - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the five daily counts into a total

💡 Read each day with the right square size, then add - pairing numbers to make tens makes it easy!