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Read max, min, and gridline scale from a line graph · 8 practice problems

5.MD.B.23.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 easy

The line graph shows the number of cookies sold each day at Noah's stand. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Cookies Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of cookies. The vertical axis is labeled 0, 50, 100; since 5 grid squares represent 50, each grid square represents $50 \div 5 = 10$ cookies. The daily sales are: Mon $40$ , Tue $100$ , Wed $60$ , Thu $120$ , Fri $80$ cookies.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of cookies sold shows Mon = 40, Tue = 100, Wed = 60, Thu = 120, Fri = 80 (each small square = 10 cookies). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 40, Tue = 100, Wed = 60, Thu = 120, Fri = 80 cookies
Vertical axis labeled 0, 50, 100 with 5 squares per 50, so each square = 10
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 10 cookies

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Thu. It is 2 square(s) above 100, and each square is 10, so 100 + 2 x 10 = 120.

100 + 2\times 10 = 120

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Mon. It is 4 square(s) above 0, so 0 + 4 x 10 = 40.

0 + 4\times 10 = 40

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 120 - 40 = 80 cookies.

120 - 40 = 80

Max minus min gives the spread between the best and worst day.

Answer: 80 cookies

4 · Reviewdoes it hold up?

120 is the highest reading and 40 the lowest, and 120 - 40 = 80, which is 8 squares of 10 cookies (8 x 10 = 80) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 8 squares apart, and 8 x 10 = 80 cookies, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 10!

Variant 2 easy

The line graph shows the number of lemonades sold each day at the park kiosk. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Lemonades Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of lemonades. The vertical axis is labeled 0, 50, 100; since 5 grid squares represent 50, each grid square represents $50 \div 5 = 10$ lemonades. The daily sales are: Mon $80$ , Tue $60$ , Wed $100$ , Thu $140$ , Fri $120$ lemonades.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of lemonades sold shows Mon = 80, Tue = 60, Wed = 100, Thu = 140, Fri = 120 (each small square = 10 lemonades). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 80, Tue = 60, Wed = 100, Thu = 140, Fri = 120 lemonades
Vertical axis labeled 0, 50, 100 with 5 squares per 50, so each square = 10
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 10 lemonades

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Thu. It is 4 square(s) above 100, and each square is 10, so 100 + 4 x 10 = 140.

100 + 4\times 10 = 140

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Tue. It is 1 square(s) above 50, so 50 + 1 x 10 = 60.

50 + 1\times 10 = 60

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 140 - 60 = 80 lemonades.

140 - 60 = 80

Max minus min gives the spread between the best and worst day.

Answer: 80 lemonades

4 · Reviewdoes it hold up?

140 is the highest reading and 60 the lowest, and 140 - 60 = 80, which is 8 squares of 10 lemonades (8 x 10 = 80) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 8 squares apart, and 8 x 10 = 80 lemonades, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 10!

Variant 3 medium

The line graph shows the number of muffins sold each day at the corner cafe. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Muffins Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of muffins. The vertical axis is labeled 100, 200, 300; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ muffins. The daily sales are: Mon $160$ , Tue $120$ , Wed $200$ , Thu $180$ , Fri $240$ muffins.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of muffins sold shows Mon = 160, Tue = 120, Wed = 200, Thu = 180, Fri = 240 (each small square = 20 muffins). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 160, Tue = 120, Wed = 200, Thu = 180, Fri = 240 muffins
Vertical axis labeled 100, 200, 300 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 muffins

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Fri. It is 2 square(s) above 200, and each square is 20, so 200 + 2 x 20 = 240.

200 + 2\times 20 = 240

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Tue. It is 1 square(s) above 100, so 100 + 1 x 20 = 120.

100 + 1\times 20 = 120

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 240 - 120 = 120 muffins.

240 - 120 = 120

Max minus min gives the spread between the best and worst day.

Answer: 120 muffins

4 · Reviewdoes it hold up?

240 is the highest reading and 120 the lowest, and 240 - 120 = 120, which is 6 squares of 20 muffins (6 x 20 = 120) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 6 squares apart, and 6 x 20 = 120 muffins, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Variant 4 medium

The line graph shows the number of bagels sold each day at Ava's bakery. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Bagels Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of bagels. The vertical axis is labeled 200, 300, 400; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ bagels. The daily sales are: Mon $220$ , Tue $360$ , Wed $280$ , Thu $300$ , Fri $340$ bagels.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of bagels sold shows Mon = 220, Tue = 360, Wed = 280, Thu = 300, Fri = 340 (each small square = 20 bagels). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 220, Tue = 360, Wed = 280, Thu = 300, Fri = 340 bagels
Vertical axis labeled 200, 300, 400 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 bagels

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Tue. It is 3 square(s) above 300, and each square is 20, so 300 + 3 x 20 = 360.

300 + 3\times 20 = 360

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Mon. It is 1 square(s) above 200, so 200 + 1 x 20 = 220.

200 + 1\times 20 = 220

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 360 - 220 = 140 bagels.

360 - 220 = 140

Max minus min gives the spread between the best and worst day.

Answer: 140 bagels

4 · Reviewdoes it hold up?

360 is the highest reading and 220 the lowest, and 360 - 220 = 140, which is 7 squares of 20 bagels (7 x 20 = 140) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 7 squares apart, and 7 x 20 = 140 bagels, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Variant 5 medium

The line graph shows the number of pizzas sold each day at Ruby's pizzeria. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Pizzas Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of pizzas. The vertical axis is labeled 200, 300, 400; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ pizzas. The daily sales are: Mon $240$ , Tue $300$ , Wed $260$ , Thu $360$ , Fri $320$ pizzas.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of pizzas sold shows Mon = 240, Tue = 300, Wed = 260, Thu = 360, Fri = 320 (each small square = 20 pizzas). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 240, Tue = 300, Wed = 260, Thu = 360, Fri = 320 pizzas
Vertical axis labeled 200, 300, 400 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 pizzas

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Thu. It is 3 square(s) above 300, and each square is 20, so 300 + 3 x 20 = 360.

300 + 3\times 20 = 360

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Mon. It is 2 square(s) above 200, so 200 + 2 x 20 = 240.

200 + 2\times 20 = 240

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 360 - 240 = 120 pizzas.

360 - 240 = 120

Max minus min gives the spread between the best and worst day.

Answer: 120 pizzas

4 · Reviewdoes it hold up?

360 is the highest reading and 240 the lowest, and 360 - 240 = 120, which is 6 squares of 20 pizzas (6 x 20 = 120) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 6 squares apart, and 6 x 20 = 120 pizzas, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Variant 6 medium

The line graph shows the number of smoothies sold each day at Leo's juice bar. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Smoothies Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of smoothies. The vertical axis is labeled 300, 400, 500; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ smoothies. The daily sales are: Mon $340$ , Tue $420$ , Wed $360$ , Thu $480$ , Fri $400$ smoothies.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of smoothies sold shows Mon = 340, Tue = 420, Wed = 360, Thu = 480, Fri = 400 (each small square = 20 smoothies). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 340, Tue = 420, Wed = 360, Thu = 480, Fri = 400 smoothies
Vertical axis labeled 300, 400, 500 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 smoothies

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Thu. It is 4 square(s) above 400, and each square is 20, so 400 + 4 x 20 = 480.

400 + 4\times 20 = 480

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Mon. It is 2 square(s) above 300, so 300 + 2 x 20 = 340.

300 + 2\times 20 = 340

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 480 - 340 = 140 smoothies.

480 - 340 = 140

Max minus min gives the spread between the best and worst day.

Answer: 140 smoothies

4 · Reviewdoes it hold up?

480 is the highest reading and 340 the lowest, and 480 - 340 = 140, which is 7 squares of 20 smoothies (7 x 20 = 140) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 7 squares apart, and 7 x 20 = 140 smoothies, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Variant 7 hard

The line graph shows the number of tacos sold each day at Sol's taco truck. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Tacos Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of tacos. The vertical axis is labeled 500, 600, 700; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ tacos. The daily sales are: Mon $620$ , Tue $540$ , Wed $700$ , Thu $660$ , Fri $580$ tacos.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of tacos sold shows Mon = 620, Tue = 540, Wed = 700, Thu = 660, Fri = 580 (each small square = 20 tacos). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 620, Tue = 540, Wed = 700, Thu = 660, Fri = 580 tacos
Vertical axis labeled 500, 600, 700 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 tacos

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Wed. It is 0 square(s) above 700, and each square is 20, so 700 + 0 x 20 = 700.

700 + 0\times 20 = 700

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Tue. It is 2 square(s) above 500, so 500 + 2 x 20 = 540.

500 + 2\times 20 = 540

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 700 - 540 = 160 tacos.

700 - 540 = 160

Max minus min gives the spread between the best and worst day.

Answer: 160 tacos

4 · Reviewdoes it hold up?

700 is the highest reading and 540 the lowest, and 700 - 540 = 160, which is 8 squares of 20 tacos (8 x 20 = 160) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 8 squares apart, and 8 x 20 = 160 tacos, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Variant 8 hard

The line graph shows the number of ice cream cones sold each day at Mia's ice cream shop. Find the difference between the number sold on the busiest day and the number sold on the slowest day.

The graph is titled "Ice Cream Cones Sold." The horizontal axis shows the day of the week (Mon, Tue, Wed, Thu, Fri), and the vertical axis shows the number of ice cream cones. The vertical axis is labeled 500, 600, 700; since 5 grid squares represent 100, each grid square represents $100 \div 5 = 20$ ice cream cones. The daily sales are: Mon $520$ , Tue $660$ , Wed $580$ , Thu $740$ , Fri $680$ ice cream cones.

Your answer

Show solution

1 · Understandwhat's really being asked

A line graph of ice cream cones sold shows Mon = 520, Tue = 660, Wed = 580, Thu = 740, Fri = 680 (each small square = 20 ice cream cones). I must find the difference between the busiest day's count and the slowest day's count.

Givens

Mon = 520, Tue = 660, Wed = 580, Thu = 740, Fri = 680 ice cream cones
Vertical axis labeled 500, 600, 700 with 5 squares per 100, so each square = 20
Highest point is the busiest day; lowest point is the slowest day

Unknowns

The difference between the most sold on a day and the fewest

Constraints

Read counts using the square value of 20 ice cream cones

2 · Planchoose the strategy

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

On a line graph the highest dot is the maximum and the lowest dot is the minimum, so I read those two points off the graph and then subtract. The work splits into find-max, find-min, subtract.

3 · Execute3 carry out the plan

1Find the busiest day

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

The highest point is Thu. It is 2 square(s) above 700, and each square is 20, so 700 + 2 x 20 = 740.

700 + 2\times 20 = 740

The tallest dot marks the biggest value on the graph.

2Find the slowest day

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

The lowest point is Mon. It is 1 square(s) above 500, so 500 + 1 x 20 = 520.

500 + 1\times 20 = 520

The lowest dot marks the smallest value.

3Subtract

#7 Identify Subproblems 5.MD.B.2

The difference between the busiest and slowest day is 740 - 520 = 220 ice cream cones.

740 - 520 = 220

Max minus min gives the spread between the best and worst day.

Answer: 220 ice cream cones

4 · Reviewdoes it hold up?

740 is the highest reading and 520 the lowest, and 740 - 520 = 220, which is 11 squares of 20 ice cream cones (11 x 20 = 220) - consistent with the grid. The difference is less than either total, as a difference should be.

Another way: Count squares first (tool 5): the top and bottom dots are 11 squares apart, and 11 x 20 = 220 ice cream cones, giving the same answer without reading exact numbers.

Standardsmin grade 5

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Finding the max, min, and their difference from the graph

💡Takeaway. Highest dot minus lowest dot - just remember each square here is worth 20!

Where next?

← Back to the problem: Read max, min, and gridline scale from a line graph