Convert a pictograph into a frequency table

3.MD.B.3 · take · grade 3

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

Ms. Reed's class and Mr. Diaz's class were each surveyed about which mountain they want to visit, and the results are shown in the tables below. If the two classes go on the field trip together, which mountain should they choose?

Ms. Reed's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	5	8	7	3	23

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	6	4	9	5	24

Show solution

Understand

Two classes each voted for a mountain to visit. To pick one mountain for both classes together, we add each mountain's votes across the two classes and choose the mountain with the most total votes.

Givens

Ms. Reed's class: Pine Ridge 5, Eagle Peak 8, Mount Rainier 7, Cedar Butte 3 (total 23).
Mr. Diaz's class: Pine Ridge 6, Eagle Peak 4, Mount Rainier 9, Cedar Butte 5 (total 24).
The two classes go together, so their votes should be combined.

Unknowns

Which single mountain the combined classes should choose.

Constraints

The best choice is the mountain with the greatest combined number of votes.

Plan

#15 Organize Information in More Ways · also uses: #2 Make a Systematic List

Merging the two separate tables into one combined frequency table (re-organizing the data) lets us compare totals. Listing each mountain's combined count makes the largest easy to spot.

Execute

#15 Organize Information in More Ways 3.MD.B.3

For each mountain, add Ms. Reed's count and Mr. Diaz's count: Pine Ridge 5+6=11, Eagle Peak 8+4=12, Mount Rainier 7+9=16, Cedar Butte 3+5=8.

5{+}6{=}11,\ 8{+}4{=}12,\ 7{+}9{=}16,\ 3{+}5{=}8

Combining two data tables into one is exactly the picture/bar-graph data sense Grade 3 develops.

#2 Make a Systematic List 3.OA.D.8

The combined votes should equal 23 + 24 = 47. Indeed 11 + 12 + 16 + 8 = 47, so no votes were lost.

11+12+16+8 = 47 = 23+24

Adding the parts to confirm they make the known total is a natural check.

#2 Make a Systematic List 3.MD.B.3

The biggest combined count is 16 for Mount Rainier, more than Eagle Peak's 12, Pine Ridge's 11, and Cedar Butte's 8.

16 > 12 > 11 > 8

Reading off the largest category from organized data is straightforward graph interpretation.

Answer: Mount Rainier (16 votes combined)

Review

Mount Rainier wins in Mr. Diaz's class (9) and is second in Ms. Reed's class (7), so its leading combined total of 16 is sensible. All four totals sum to 47, matching 23+24, so the data is accounted for.

Draw a single combined bar graph (Draw a Diagram): the tallest bar is Mount Rainier, giving the same choice without writing the sums.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Combining the two tables and comparing category counts to find the largest.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Adding category counts and checking against the total of 47.

💡 Stack the two tables into one and find the tallest count - that's Grade 3 graph reading!