Practice · Convert a pictograph into a frequency table · Sensim Math

Variant 1 easy

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	8	4	2	1	15

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	6	3	5	0	14

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 8, Eagle Peak 4, Mount Rainier 2, Cedar Butte 1 (total 15).
Mr. Diaz's class: Pine Ridge 6, Eagle Peak 3, Mount Rainier 5, Cedar Butte 0 (total 14).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 8+6=14, Eagle Peak 4+3=7, Mount Rainier 2+5=7, Cedar Butte 1+0=1.

8{+}6{=}14,\ 4{+}3{=}7,\ 2{+}5{=}7,\ 1{+}0{=}1

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

2Check the total

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

The combined votes should equal 15 + 14 = 29. Indeed 14 + 7 + 7 + 1 = 29, so no votes were lost.

14+7+7+1 = 29 = 15+14

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

3Pick the largest

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

The biggest combined count is 14 for Pine Ridge, more than Eagle Peak's 7, Mount Rainier's 7, Cedar Butte's 1.

14 > 7 > 7 > 1

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

Answer: Pine Ridge (14 votes combined)

4 · Reviewdoes it hold up?

Pine Ridge leads with a combined total of 14. All four totals sum to 29, matching 15+14, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Pine Ridge, giving the same choice without writing the sums.

Standardsmin 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 29.

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

Variant 2 easy

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	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	7	1	3	4	15

Mr. Diaz's class

Mountain	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	8	2	5	0	15

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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: Blue Lake 7, Red Canyon 1, Green Valley 3, Gold Mesa 4 (total 15).
Mr. Diaz's class: Blue Lake 8, Red Canyon 2, Green Valley 5, Gold Mesa 0 (total 15).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Blue Lake 7+8=15, Red Canyon 1+2=3, Green Valley 3+5=8, Gold Mesa 4+0=4.

7{+}8{=}15,\ 1{+}2{=}3,\ 3{+}5{=}8,\ 4{+}0{=}4

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

2Check the total

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

The combined votes should equal 15 + 15 = 30. Indeed 15 + 3 + 8 + 4 = 30, so no votes were lost.

15+3+8+4 = 30 = 15+15

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

3Pick the largest

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

The biggest combined count is 15 for Blue Lake, more than Green Valley's 8, Gold Mesa's 4, Red Canyon's 3.

15 > 8 > 4 > 3

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

Answer: Blue Lake (15 votes combined)

4 · Reviewdoes it hold up?

Blue Lake leads with a combined total of 15. All four totals sum to 30, matching 15+15, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Blue Lake, giving the same choice without writing the sums.

Standardsmin 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 30.

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

Variant 3 easy

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	2	7	3	5	17

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	4	8	2	1	15

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 2, Eagle Peak 7, Mount Rainier 3, Cedar Butte 5 (total 17).
Mr. Diaz's class: Pine Ridge 4, Eagle Peak 8, Mount Rainier 2, Cedar Butte 1 (total 15).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 2+4=6, Eagle Peak 7+8=15, Mount Rainier 3+2=5, Cedar Butte 5+1=6.

2{+}4{=}6,\ 7{+}8{=}15,\ 3{+}2{=}5,\ 5{+}1{=}6

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

2Check the total

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

The combined votes should equal 17 + 15 = 32. Indeed 6 + 15 + 5 + 6 = 32, so no votes were lost.

6+15+5+6 = 32 = 17+15

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

3Pick the largest

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

The biggest combined count is 15 for Eagle Peak, more than Pine Ridge's 6, Cedar Butte's 6, Mount Rainier's 5.

15 > 6 > 6 > 5

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

Answer: Eagle Peak (15 votes combined)

4 · Reviewdoes it hold up?

Eagle Peak leads with a combined total of 15. All four totals sum to 32, matching 17+15, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Eagle Peak, giving the same choice without writing the sums.

Standardsmin 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 32.

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

Variant 4 easy

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	3	3	9	4	19

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	2	6	5	1	14

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 3, Eagle Peak 3, Mount Rainier 9, Cedar Butte 4 (total 19).
Mr. Diaz's class: Pine Ridge 2, Eagle Peak 6, Mount Rainier 5, Cedar Butte 1 (total 14).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 3+2=5, Eagle Peak 3+6=9, Mount Rainier 9+5=14, Cedar Butte 4+1=5.

3{+}2{=}5,\ 3{+}6{=}9,\ 9{+}5{=}14,\ 4{+}1{=}5

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

2Check the total

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

The combined votes should equal 19 + 14 = 33. Indeed 5 + 9 + 14 + 5 = 33, so no votes were lost.

5+9+14+5 = 33 = 19+14

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

3Pick the largest

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

The biggest combined count is 14 for Mount Rainier, more than Eagle Peak's 9, Pine Ridge's 5, Cedar Butte's 5.

14 > 9 > 5 > 5

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

Answer: Mount Rainier (14 votes combined)

4 · Reviewdoes it hold up?

Mount Rainier leads with a combined total of 14. All four totals sum to 33, matching 19+14, so the data is accounted for.

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

Standardsmin 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 33.

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

Variant 5 medium

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	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	9	3	4	2	18

Mr. Diaz's class

Mountain	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	7	1	5	6	19

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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: Blue Lake 9, Red Canyon 3, Green Valley 4, Gold Mesa 2 (total 18).
Mr. Diaz's class: Blue Lake 7, Red Canyon 1, Green Valley 5, Gold Mesa 6 (total 19).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Blue Lake 9+7=16, Red Canyon 3+1=4, Green Valley 4+5=9, Gold Mesa 2+6=8.

9{+}7{=}16,\ 3{+}1{=}4,\ 4{+}5{=}9,\ 2{+}6{=}8

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

2Check the total

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

The combined votes should equal 18 + 19 = 37. Indeed 16 + 4 + 9 + 8 = 37, so no votes were lost.

16+4+9+8 = 37 = 18+19

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

3Pick the largest

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

The biggest combined count is 16 for Blue Lake, more than Green Valley's 9, Gold Mesa's 8, Red Canyon's 4.

16 > 9 > 8 > 4

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

Answer: Blue Lake (16 votes combined)

4 · Reviewdoes it hold up?

Blue Lake leads with a combined total of 16. All four totals sum to 37, matching 18+19, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Blue Lake, giving the same choice without writing the sums.

Standardsmin 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 37.

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

Variant 6 medium

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	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	4	9	2	5	20

Mr. Diaz's class

Mountain	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	3	6	4	1	14

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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: Blue Lake 4, Red Canyon 9, Green Valley 2, Gold Mesa 5 (total 20).
Mr. Diaz's class: Blue Lake 3, Red Canyon 6, Green Valley 4, Gold Mesa 1 (total 14).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Blue Lake 4+3=7, Red Canyon 9+6=15, Green Valley 2+4=6, Gold Mesa 5+1=6.

4{+}3{=}7,\ 9{+}6{=}15,\ 2{+}4{=}6,\ 5{+}1{=}6

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

2Check the total

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

The combined votes should equal 20 + 14 = 34. Indeed 7 + 15 + 6 + 6 = 34, so no votes were lost.

7+15+6+6 = 34 = 20+14

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

3Pick the largest

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

The biggest combined count is 15 for Red Canyon, more than Blue Lake's 7, Green Valley's 6, Gold Mesa's 6.

15 > 7 > 6 > 6

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

Answer: Red Canyon (15 votes combined)

4 · Reviewdoes it hold up?

Red Canyon leads with a combined total of 15. All four totals sum to 34, matching 20+14, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Red Canyon, giving the same choice without writing the sums.

Standardsmin 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 34.

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

Variant 7 medium

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	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	2	5	7	3	17

Mr. Diaz's class

Mountain	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	6	1	9	4	20

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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: Blue Lake 2, Red Canyon 5, Green Valley 7, Gold Mesa 3 (total 17).
Mr. Diaz's class: Blue Lake 6, Red Canyon 1, Green Valley 9, Gold Mesa 4 (total 20).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Blue Lake 2+6=8, Red Canyon 5+1=6, Green Valley 7+9=16, Gold Mesa 3+4=7.

2{+}6{=}8,\ 5{+}1{=}6,\ 7{+}9{=}16,\ 3{+}4{=}7

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

2Check the total

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

The combined votes should equal 17 + 20 = 37. Indeed 8 + 6 + 16 + 7 = 37, so no votes were lost.

8+6+16+7 = 37 = 17+20

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

3Pick the largest

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

The biggest combined count is 16 for Green Valley, more than Blue Lake's 8, Gold Mesa's 7, Red Canyon's 6.

16 > 8 > 7 > 6

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

Answer: Green Valley (16 votes combined)

4 · Reviewdoes it hold up?

Green Valley leads with a combined total of 16. All four totals sum to 37, matching 17+20, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Green Valley, giving the same choice without writing the sums.

Standardsmin 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 37.

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

Variant 8 medium

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	4	6	1	9	20

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	3	2	5	8	18

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 4, Eagle Peak 6, Mount Rainier 1, Cedar Butte 9 (total 20).
Mr. Diaz's class: Pine Ridge 3, Eagle Peak 2, Mount Rainier 5, Cedar Butte 8 (total 18).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 4+3=7, Eagle Peak 6+2=8, Mount Rainier 1+5=6, Cedar Butte 9+8=17.

4{+}3{=}7,\ 6{+}2{=}8,\ 1{+}5{=}6,\ 9{+}8{=}17

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

2Check the total

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

The combined votes should equal 20 + 18 = 38. Indeed 7 + 8 + 6 + 17 = 38, so no votes were lost.

7+8+6+17 = 38 = 20+18

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

3Pick the largest

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

The biggest combined count is 17 for Cedar Butte, more than Eagle Peak's 8, Pine Ridge's 7, Mount Rainier's 6.

17 > 8 > 7 > 6

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

Answer: Cedar Butte (17 votes combined)

4 · Reviewdoes it hold up?

Cedar Butte leads with a combined total of 17. All four totals sum to 38, matching 20+18, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Cedar Butte, giving the same choice without writing the sums.

Standardsmin 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 38.

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

Variant 9 hard

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	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	5	2	6	8	21

Mr. Diaz's class

Mountain	Blue Lake	Red Canyon	Green Valley	Gold Mesa	Total
Students	1	4	3	7	15

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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: Blue Lake 5, Red Canyon 2, Green Valley 6, Gold Mesa 8 (total 21).
Mr. Diaz's class: Blue Lake 1, Red Canyon 4, Green Valley 3, Gold Mesa 7 (total 15).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Blue Lake 5+1=6, Red Canyon 2+4=6, Green Valley 6+3=9, Gold Mesa 8+7=15.

5{+}1{=}6,\ 2{+}4{=}6,\ 6{+}3{=}9,\ 8{+}7{=}15

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

2Check the total

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

The combined votes should equal 21 + 15 = 36. Indeed 6 + 6 + 9 + 15 = 36, so no votes were lost.

6+6+9+15 = 36 = 21+15

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

3Pick the largest

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

The biggest combined count is 15 for Gold Mesa, more than Green Valley's 9, Blue Lake's 6, Red Canyon's 6.

15 > 9 > 6 > 6

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

Answer: Gold Mesa (15 votes combined)

4 · Reviewdoes it hold up?

Gold Mesa leads with a combined total of 15. All four totals sum to 36, matching 21+15, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Gold Mesa, giving the same choice without writing the sums.

Standardsmin 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 36.

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

Variant 10 hard

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	9	2	4	6	21

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	3	5	1	7	16

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 9, Eagle Peak 2, Mount Rainier 4, Cedar Butte 6 (total 21).
Mr. Diaz's class: Pine Ridge 3, Eagle Peak 5, Mount Rainier 1, Cedar Butte 7 (total 16).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 9+3=12, Eagle Peak 2+5=7, Mount Rainier 4+1=5, Cedar Butte 6+7=13.

9{+}3{=}12,\ 2{+}5{=}7,\ 4{+}1{=}5,\ 6{+}7{=}13

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

2Check the total

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

The combined votes should equal 21 + 16 = 37. Indeed 12 + 7 + 5 + 13 = 37, so no votes were lost.

12+7+5+13 = 37 = 21+16

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

3Pick the largest

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

The biggest combined count is 13 for Cedar Butte, more than Pine Ridge's 12, Eagle Peak's 7, Mount Rainier's 5.

13 > 12 > 7 > 5

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

Answer: Cedar Butte (13 votes combined)

4 · Reviewdoes it hold up?

Cedar Butte leads with a combined total of 13. All four totals sum to 37, matching 21+16, so the data is accounted for.

Another way: Draw a single combined bar graph (Draw a Diagram): the tallest bar is Cedar Butte, giving the same choice without writing the sums.

Standardsmin 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 37.

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

Variant 11 hard

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	6	3	8	2	19

Mr. Diaz's class

Mountain	Pine Ridge	Eagle Peak	Mount Rainier	Cedar Butte	Total
Students	5	4	7	6	22

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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 6, Eagle Peak 3, Mount Rainier 8, Cedar Butte 2 (total 19).
Mr. Diaz's class: Pine Ridge 5, Eagle Peak 4, Mount Rainier 7, Cedar Butte 6 (total 22).
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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class's count: Pine Ridge 6+5=11, Eagle Peak 3+4=7, Mount Rainier 8+7=15, Cedar Butte 2+6=8.

6{+}5{=}11,\ 3{+}4{=}7,\ 8{+}7{=}15,\ 2{+}6{=}8

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

2Check the total

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

The combined votes should equal 19 + 22 = 41. Indeed 11 + 7 + 15 + 8 = 41, so no votes were lost.

11+7+15+8 = 41 = 19+22

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

3Pick the largest

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

The biggest combined count is 15 for Mount Rainier, more than Pine Ridge's 11, Cedar Butte's 8, Eagle Peak's 7.

15 > 11 > 8 > 7

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

Answer: Mount Rainier (15 votes combined)

4 · Reviewdoes it hold up?

Mount Rainier leads with a combined total of 15. All four totals sum to 41, matching 19+22, so the data is accounted for.

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

Standardsmin 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 41.

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

Variant 12 hard

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

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Add each mountain across both classes

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

For each mountain, add Ms. Reed's class's count and Mr. Diaz's class'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.

2Check the total

#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.

3Pick the largest

#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, 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)

4 · Reviewdoes it hold up?

Mount Rainier leads with a combined total of 16. All four totals sum to 47, matching 23+24, so the data is accounted for.

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

Standardsmin 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.

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

Convert a pictograph into a frequency table · 12 practice problems

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