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← 4-2 · Read max, min, and gridline scale from a line graph · Read and Scale a Data Graph

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

5.MD.B.23.MD.B.3

Generated variants — 8

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

Variant 1 answer: 140 bagels

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÷5=20100 \div 5 = 20 bagels. The daily sales are: Mon 220220, Tue 360360, Wed 280280, Thu 300300, Fri 340340 bagels.

Bagels Sold (bagels) 200 300 400 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+3×20=360300 + 3\times 20 = 360
The tallest dot marks the biggest value on the graph.
#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+1×20=220200 + 1\times 20 = 220
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 360 - 220 = 140 bagels.
360−220=140360 - 220 = 140
Max minus min gives the spread between the best and worst day.
Answer: 140 bagels

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 2 answer: 120 muffins

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÷5=20100 \div 5 = 20 muffins. The daily sales are: Mon 160160, Tue 120120, Wed 200200, Thu 180180, Fri 240240 muffins.

Muffins Sold (muffins) 100 200 300 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+2×20=240200 + 2\times 20 = 240
The tallest dot marks the biggest value on the graph.
#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+1×20=120100 + 1\times 20 = 120
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 240 - 120 = 120 muffins.
240−120=120240 - 120 = 120
Max minus min gives the spread between the best and worst day.
Answer: 120 muffins

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 3 answer: 140 smoothies

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÷5=20100 \div 5 = 20 smoothies. The daily sales are: Mon 340340, Tue 420420, Wed 360360, Thu 480480, Fri 400400 smoothies.

Smoothies Sold (smoothies) 300 400 500 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+4×20=480400 + 4\times 20 = 480
The tallest dot marks the biggest value on the graph.
#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+2×20=340300 + 2\times 20 = 340
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 480 - 340 = 140 smoothies.
480−340=140480 - 340 = 140
Max minus min gives the spread between the best and worst day.
Answer: 140 smoothies

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 4 answer: 120 pizzas

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÷5=20100 \div 5 = 20 pizzas. The daily sales are: Mon 240240, Tue 300300, Wed 260260, Thu 360360, Fri 320320 pizzas.

Pizzas Sold (pizzas) 200 300 400 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+3×20=360300 + 3\times 20 = 360
The tallest dot marks the biggest value on the graph.
#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+2×20=240200 + 2\times 20 = 240
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 360 - 240 = 120 pizzas.
360−240=120360 - 240 = 120
Max minus min gives the spread between the best and worst day.
Answer: 120 pizzas

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 5 answer: 220 ice cream cones

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÷5=20100 \div 5 = 20 ice cream cones. The daily sales are: Mon 520520, Tue 660660, Wed 580580, Thu 740740, Fri 680680 ice cream cones.

Ice Cream Cones Sold (ice cream cones) 500 600 700 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+2×20=740700 + 2\times 20 = 740
The tallest dot marks the biggest value on the graph.
#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+1×20=520500 + 1\times 20 = 520
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 740 - 520 = 220 ice cream cones.
740−520=220740 - 520 = 220
Max minus min gives the spread between the best and worst day.
Answer: 220 ice cream cones

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 6 answer: 80 lemonades

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÷5=1050 \div 5 = 10 lemonades. The daily sales are: Mon 8080, Tue 6060, Wed 100100, Thu 140140, Fri 120120 lemonades.

Lemonades Sold (lemonades) 0 50 100 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+4×10=140100 + 4\times 10 = 140
The tallest dot marks the biggest value on the graph.
#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+1×10=6050 + 1\times 10 = 60
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 140 - 60 = 80 lemonades.
140−60=80140 - 60 = 80
Max minus min gives the spread between the best and worst day.
Answer: 80 lemonades

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 10!
Variant 7 answer: 160 tacos

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÷5=20100 \div 5 = 20 tacos. The daily sales are: Mon 620620, Tue 540540, Wed 700700, Thu 660660, Fri 580580 tacos.

Tacos Sold (tacos) 500 600 700 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+0×20=700700 + 0\times 20 = 700
The tallest dot marks the biggest value on the graph.
#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+2×20=540500 + 2\times 20 = 540
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 700 - 540 = 160 tacos.
700−540=160700 - 540 = 160
Max minus min gives the spread between the best and worst day.
Answer: 160 tacos

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 20!
Variant 8 answer: 80 cookies

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÷5=1050 \div 5 = 10 cookies. The daily sales are: Mon 4040, Tue 100100, Wed 6060, Thu 120120, Fri 8080 cookies.

Cookies Sold (cookies) 0 50 100 Mon Tue Wed Thu Fri
Show solution

Understand

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

Plan

#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.

Execute

#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+2×10=120100 + 2\times 10 = 120
The tallest dot marks the biggest value on the graph.
#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+4×10=400 + 4\times 10 = 40
The lowest dot marks the smallest value.
#7 Identify Subproblems 5.MD.B.2
The difference between the busiest and slowest day is 120 - 40 = 80 cookies.
120−40=80120 - 40 = 80
Max minus min gives the spread between the best and worst day.
Answer: 80 cookies

Review

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.

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.

Standards · min 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
💡 Highest dot minus lowest dot - just remember each square here is worth 10!