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Read a double bar graph · 8 practice problems

3.MD.B.3

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Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 medium

A class surveyed how many cars and how many trucks the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (blue and purple) side by side. For both cars and trucks, a blue bar and a purple bar are drawn next to each other.

For each item, compare the difference between the blue count and the purple count, and determine which item — cars or trucks — has the larger difference between the two colors.

The horizontal axis lists cars and trucks, and each item shows a pair of bars, one blue and one purple. The legend identifies the blue and purple bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (blue and purple) for each of two items: cars and trucks. For each item, find the difference between its two bars, then say which item has the larger blue-vs-purple difference.

Givens

Each item (cars, trucks) has a blue bar and a purple bar side by side
A legend tells which bar is blue and which is purple
Cars: blue = 10, purple = 6; Trucks: blue = 5, purple = 2

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For cars, the gap is the taller bar minus the shorter bar; do the same for trucks.

Cars: |10 - 6| = 4,\quad Trucks: |5 - 2| = 3

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 4 for cars and 3 for trucks.

4 > 3

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Cars have the larger difference between the blue and purple counts

4 · Reviewdoes it hold up?

The differences are 4 (cars) and 3 (trucks), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 2 medium

A class surveyed how many cats and how many dogs the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (orange and pink) side by side. For both cats and dogs, a orange bar and a pink bar are drawn next to each other.

For each item, compare the difference between the orange count and the pink count, and determine which item — cats or dogs — has the larger difference between the two colors.

The horizontal axis lists cats and dogs, and each item shows a pair of bars, one orange and one pink. The legend identifies the orange and pink bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (orange and pink) for each of two items: cats and dogs. For each item, find the difference between its two bars, then say which item has the larger orange-vs-pink difference.

Givens

Each item (cats, dogs) has a orange bar and a pink bar side by side
A legend tells which bar is orange and which is pink
Cats: orange = 4, pink = 9; Dogs: orange = 7, pink = 1

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For cats, the gap is the taller bar minus the shorter bar; do the same for dogs.

Cats: |4 - 9| = 5,\quad Dogs: |7 - 1| = 6

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 5 for cats and 6 for dogs.

5 < 6

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Dogs have the larger difference between the orange and pink counts

4 · Reviewdoes it hold up?

The differences are 5 (cats) and 6 (dogs), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 3 medium

A class surveyed how many colored pencils and how many crayons the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (orange and yellow-green) side by side. For both colored pencils and crayons, a orange bar and a yellow-green bar are drawn next to each other.

For each item, compare the difference between the orange count and the yellow-green count, and determine which item — colored pencils or crayons — has the larger difference between the two colors.

The horizontal axis lists colored pencils and crayons, and each item shows a pair of bars, one orange and one yellow-green. The legend identifies the orange and yellow-green bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (orange and yellow-green) for each of two items: colored pencils and crayons. For each item, find the difference between its two bars, then say which item has the larger orange-vs-yellow-green difference.

Givens

Each item (colored pencils, crayons) has a orange bar and a yellow-green bar side by side
A legend tells which bar is orange and which is yellow-green
Colored pencils: orange = 6, yellow-green = 4; Crayons: orange = 10, yellow-green = 4

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For colored pencils, the gap is the taller bar minus the shorter bar; do the same for crayons.

Colored pencils: |6 - 4| = 2,\quad Crayons: |10 - 4| = 6

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 2 for colored pencils and 6 for crayons.

2 < 6

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Crayons have the larger difference between the orange and yellow-green counts

4 · Reviewdoes it hold up?

The differences are 2 (colored pencils) and 6 (crayons), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 4 medium

A class surveyed how many books and how many magazines the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (red and green) side by side. For both books and magazines, a red bar and a green bar are drawn next to each other.

For each item, compare the difference between the red count and the green count, and determine which item — books or magazines — has the larger difference between the two colors.

The horizontal axis lists books and magazines, and each item shows a pair of bars, one red and one green. The legend identifies the red and green bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (red and green) for each of two items: books and magazines. For each item, find the difference between its two bars, then say which item has the larger red-vs-green difference.

Givens

Each item (books, magazines) has a red bar and a green bar side by side
A legend tells which bar is red and which is green
Books: red = 7, green = 2; Magazines: red = 6, green = 5

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For books, the gap is the taller bar minus the shorter bar; do the same for magazines.

Books: |7 - 2| = 5,\quad Magazines: |6 - 5| = 1

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 5 for books and 1 for magazines.

5 > 1

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Books have the larger difference between the red and green counts

4 · Reviewdoes it hold up?

The differences are 5 (books) and 1 (magazines), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 5 medium

A class surveyed how many cookies and how many cakes the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (purple and green) side by side. For both cookies and cakes, a purple bar and a green bar are drawn next to each other.

For each item, compare the difference between the purple count and the green count, and determine which item — cookies or cakes — has the larger difference between the two colors.

The horizontal axis lists cookies and cakes, and each item shows a pair of bars, one purple and one green. The legend identifies the purple and green bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (purple and green) for each of two items: cookies and cakes. For each item, find the difference between its two bars, then say which item has the larger purple-vs-green difference.

Givens

Each item (cookies, cakes) has a purple bar and a green bar side by side
A legend tells which bar is purple and which is green
Cookies: purple = 3, green = 8; Cakes: purple = 9, green = 2

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For cookies, the gap is the taller bar minus the shorter bar; do the same for cakes.

Cookies: |3 - 8| = 5,\quad Cakes: |9 - 2| = 7

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 5 for cookies and 7 for cakes.

5 < 7

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Cakes have the larger difference between the purple and green counts

4 · Reviewdoes it hold up?

The differences are 5 (cookies) and 7 (cakes), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 6 medium

A class surveyed how many pens and how many markers the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (blue and red) side by side. For both pens and markers, a blue bar and a red bar are drawn next to each other.

For each item, compare the difference between the blue count and the red count, and determine which item — pens or markers — has the larger difference between the two colors.

The horizontal axis lists pens and markers, and each item shows a pair of bars, one blue and one red. The legend identifies the blue and red bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (blue and red) for each of two items: pens and markers. For each item, find the difference between its two bars, then say which item has the larger blue-vs-red difference.

Givens

Each item (pens, markers) has a blue bar and a red bar side by side
A legend tells which bar is blue and which is red
Pens: blue = 8, red = 5; Markers: blue = 3, red = 9

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For pens, the gap is the taller bar minus the shorter bar; do the same for markers.

Pens: |8 - 5| = 3,\quad Markers: |3 - 9| = 6

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 3 for pens and 6 for markers.

3 < 6

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Markers have the larger difference between the blue and red counts

4 · Reviewdoes it hold up?

The differences are 3 (pens) and 6 (markers), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 7 medium

A class surveyed how many roses and how many tulips the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (red and yellow-green) side by side. For both roses and tulips, a red bar and a yellow-green bar are drawn next to each other.

For each item, compare the difference between the red count and the yellow-green count, and determine which item — roses or tulips — has the larger difference between the two colors.

The horizontal axis lists roses and tulips, and each item shows a pair of bars, one red and one yellow-green. The legend identifies the red and yellow-green bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (red and yellow-green) for each of two items: roses and tulips. For each item, find the difference between its two bars, then say which item has the larger red-vs-yellow-green difference.

Givens

Each item (roses, tulips) has a red bar and a yellow-green bar side by side
A legend tells which bar is red and which is yellow-green
Roses: red = 5, yellow-green = 5; Tulips: red = 8, yellow-green = 3

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For roses, the gap is the taller bar minus the shorter bar; do the same for tulips.

Roses: |5 - 5| = 0,\quad Tulips: |8 - 3| = 5

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 0 for roses and 5 for tulips.

0 < 5

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Tulips have the larger difference between the red and yellow-green counts

4 · Reviewdoes it hold up?

The differences are 0 (roses) and 5 (tulips), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Variant 8 medium

A class surveyed how many apples and how many oranges the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (green and yellow-green) side by side. For both apples and oranges, a green bar and a yellow-green bar are drawn next to each other.

For each item, compare the difference between the green count and the yellow-green count, and determine which item — apples or oranges — has the larger difference between the two colors.

The horizontal axis lists apples and oranges, and each item shows a pair of bars, one green and one yellow-green. The legend identifies the green and yellow-green bars.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A double bar graph shows two color counts (green and yellow-green) for each of two items: apples and oranges. For each item, find the difference between its two bars, then say which item has the larger green-vs-yellow-green difference.

Givens

Each item (apples, oranges) has a green bar and a yellow-green bar side by side
A legend tells which bar is green and which is yellow-green
Apples: green = 9, yellow-green = 3; Oranges: green = 4, yellow-green = 8

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

2 · Planchoose the strategy

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

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

3 · Execute2 carry out the plan

1Difference for each item

#7 Identify Subproblems 3.MD.B.3

For apples, the gap is the taller bar minus the shorter bar; do the same for oranges.

Apples: |9 - 3| = 6,\quad Oranges: |4 - 8| = 4

The height gap between the paired bars is how many more of one color there are.

2Compare the two gaps

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

Set the two gaps next to each other: 6 for apples and 4 for oranges.

6 > 4

The bigger the visible gap between a paired item's bars, the bigger the difference.

Answer: Apples have the larger difference between the green and yellow-green counts

4 · Reviewdoes it hold up?

The differences are 6 (apples) and 4 (oranges), so the named item matches the wider gap.

Another way: Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡Takeaway. This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!

Where next?

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