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Sum all data values read from a line graph · 8 practice problems

3.MD.B.34.NBT.B.4

Generated variants — 8

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

Variant 1 answer: 90 scones

The line graph shows the number of scones sold over 5 days at a tea house. Find the total number of scones sold.

The graph is titled "Scones Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of scones. The vertical axis is labeled 0, 30, 60; since 5 grid squares represent 30, each grid square represents $30 \div 5 = 6$ scones. The number sold each day is: 5th $12$ , 6th $24$ , 7th $18$ , 8th $30$ , 9th $6$ scones.

Show solution

Understand

A line graph of scones sold over 5 days shows 5th = 12, 6th = 24, 7th = 18, 8th = 30, 9th = 6 (each small square = 6 scones). I must find the total scones sold across all 5 days.

Givens

5th = 12, 6th = 24, 7th = 18, 8th = 30, 9th = 6 scones
Vertical axis labeled 0, 30, 60 with 5 squares per 30, so each square = 6
Need the sum over all the days

Unknowns

The total number of scones sold across the days

Constraints

Each value is read using the square value of 6 scones

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 6 scones: 5th = 12, 6th = 24, 7th = 18, 8th = 30, 9th = 6.

12,\ 24,\ 18,\ 30,\ 6

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 12 + 24 + 18 + 30 + 6 = 90.

12 + 24 + 18 + 30 + 6 = 90

Summing every day's value gives the running total for the period.

Answer: 90 scones

Review

Straight addition 12 + 24 + 18 + 30 + 6 = 90 matches. The total must be larger than the biggest single day (30), as a sum of positives must be, and 90 fits.

Count squares first (tool 5): days are 2 + 4 + 3 + 5 + 1 = 15 squares, and 15 x 6 = 90 scones - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 2 answer: 260 juices

The line graph shows the number of juices sold over 5 days at a juice bar. Find the total number of juices sold.

The graph is titled "Juices Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of juices. The vertical axis is labeled 0, 50, 100; since 5 grid squares represent 50, each grid square represents $50 \div 5 = 10$ juices. The number sold each day is: 5th $40$ , 6th $60$ , 7th $50$ , 8th $80$ , 9th $30$ juices.

Show solution

Understand

A line graph of juices sold over 5 days shows 5th = 40, 6th = 60, 7th = 50, 8th = 80, 9th = 30 (each small square = 10 juices). I must find the total juices sold across all 5 days.

Givens

5th = 40, 6th = 60, 7th = 50, 8th = 80, 9th = 30 juices
Vertical axis labeled 0, 50, 100 with 5 squares per 50, so each square = 10
Need the sum over all the days

Unknowns

The total number of juices sold across the days

Constraints

Each value is read using the square value of 10 juices

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 10 juices: 5th = 40, 6th = 60, 7th = 50, 8th = 80, 9th = 30.

40,\ 60,\ 50,\ 80,\ 30

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 40 + 60 + 50 + 80 + 30 = 260.

40 + 60 + 50 + 80 + 30 = 260

Summing every day's value gives the running total for the period.

Answer: 260 juices

Review

Straight addition 40 + 60 + 50 + 80 + 30 = 260 matches. The total must be larger than the biggest single day (80), as a sum of positives must be, and 260 fits.

Count squares first (tool 5): days are 4 + 6 + 5 + 8 + 3 = 26 squares, and 26 x 10 = 260 juices - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 3 answer: 148 donuts

The line graph shows the number of donuts sold over 5 days at a cafe. Find the total number of donuts sold.

The graph is titled "Donuts Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of donuts. The vertical axis is labeled 0, 20, 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ donuts. The number sold each day is: 5th $24$ , 6th $40$ , 7th $32$ , 8th $16$ , 9th $36$ donuts.

Show solution

Understand

A line graph of donuts sold over 5 days shows 5th = 24, 6th = 40, 7th = 32, 8th = 16, 9th = 36 (each small square = 4 donuts). I must find the total donuts sold across all 5 days.

Givens

5th = 24, 6th = 40, 7th = 32, 8th = 16, 9th = 36 donuts
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all the days

Unknowns

The total number of donuts sold across the days

Constraints

Each value is read using the square value of 4 donuts

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 4 donuts: 5th = 24, 6th = 40, 7th = 32, 8th = 16, 9th = 36.

24,\ 40,\ 32,\ 16,\ 36

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 24 + 40 + 32 + 16 + 36 = 148.

24 + 40 + 32 + 16 + 36 = 148

Summing every day's value gives the running total for the period.

Answer: 148 donuts

Review

Straight addition 24 + 40 + 32 + 16 + 36 = 148 matches. The total must be larger than the biggest single day (40), as a sum of positives must be, and 148 fits.

Count squares first (tool 5): days are 6 + 10 + 8 + 4 + 9 = 37 squares, and 37 x 4 = 148 donuts - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 4 answer: 208 burritos

The line graph shows the number of burritos sold over 5 days at a food truck. Find the total number of burritos sold.

The graph is titled "Burritos Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of burritos. The vertical axis is labeled 0, 20, 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ burritos. The number sold each day is: 5th $44$ , 6th $28$ , 7th $52$ , 8th $36$ , 9th $48$ burritos.

Show solution

Understand

A line graph of burritos sold over 5 days shows 5th = 44, 6th = 28, 7th = 52, 8th = 36, 9th = 48 (each small square = 4 burritos). I must find the total burritos sold across all 5 days.

Givens

5th = 44, 6th = 28, 7th = 52, 8th = 36, 9th = 48 burritos
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all the days

Unknowns

The total number of burritos sold across the days

Constraints

Each value is read using the square value of 4 burritos

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 4 burritos: 5th = 44, 6th = 28, 7th = 52, 8th = 36, 9th = 48.

44,\ 28,\ 52,\ 36,\ 48

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 44 + 28 + 52 + 36 + 48 = 208.

44 + 28 + 52 + 36 + 48 = 208

Summing every day's value gives the running total for the period.

Answer: 208 burritos

Review

Straight addition 44 + 28 + 52 + 36 + 48 = 208 matches. The total must be larger than the biggest single day (52), as a sum of positives must be, and 208 fits.

Count squares first (tool 5): days are 11 + 7 + 13 + 9 + 12 = 52 squares, and 52 x 4 = 208 burritos - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 5 answer: 136 waffles

The line graph shows the number of waffles sold over 5 days at a diner. Find the total number of waffles sold.

The graph is titled "Waffles Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of waffles. The vertical axis is labeled 0, 20, 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ waffles. The number sold each day is: 5th $28$ , 6th $12$ , 7th $44$ , 8th $20$ , 9th $32$ waffles.

Show solution

Understand

A line graph of waffles sold over 5 days shows 5th = 28, 6th = 12, 7th = 44, 8th = 20, 9th = 32 (each small square = 4 waffles). I must find the total waffles sold across all 5 days.

Givens

5th = 28, 6th = 12, 7th = 44, 8th = 20, 9th = 32 waffles
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all the days

Unknowns

The total number of waffles sold across the days

Constraints

Each value is read using the square value of 4 waffles

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 4 waffles: 5th = 28, 6th = 12, 7th = 44, 8th = 20, 9th = 32.

28,\ 12,\ 44,\ 20,\ 32

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 28 + 12 + 44 + 20 + 32 = 136.

28 + 12 + 44 + 20 + 32 = 136

Summing every day's value gives the running total for the period.

Answer: 136 waffles

Review

Straight addition 28 + 12 + 44 + 20 + 32 = 136 matches. The total must be larger than the biggest single day (44), as a sum of positives must be, and 136 fits.

Count squares first (tool 5): days are 7 + 3 + 11 + 5 + 8 = 34 squares, and 34 x 4 = 136 waffles - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 6 answer: 164 soft pretzels

The line graph shows the number of soft pretzels sold over 5 days at a bakery. Find the total number of soft pretzels sold.

The graph is titled "Soft Pretzels Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of soft pretzels. The vertical axis is labeled 0, 20, 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ soft pretzels. The number sold each day is: 5th $32$ , 6th $16$ , 7th $28$ , 8th $52$ , 9th $36$ soft pretzels.

Show solution

Understand

A line graph of soft pretzels sold over 5 days shows 5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36 (each small square = 4 soft pretzels). I must find the total soft pretzels sold across all 5 days.

Givens

5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36 soft pretzels
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all the days

Unknowns

The total number of soft pretzels sold across the days

Constraints

Each value is read using the square value of 4 soft pretzels

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 4 soft pretzels: 5th = 32, 6th = 16, 7th = 28, 8th = 52, 9th = 36.

32,\ 16,\ 28,\ 52,\ 36

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 32 + 16 + 28 + 52 + 36 = 164.

32 + 16 + 28 + 52 + 36 = 164

Summing every day's value gives the running total for the period.

Answer: 164 soft pretzels

Review

Straight addition 32 + 16 + 28 + 52 + 36 = 164 matches. The total must be larger than the biggest single day (52), as a sum of positives must be, and 164 fits.

Count squares first (tool 5): days are 8 + 4 + 7 + 13 + 9 = 41 squares, and 41 x 4 = 164 soft pretzels - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 7 answer: 196 croissants

The line graph shows the number of croissants sold over 5 days at a bakeshop. Find the total number of croissants sold.

The graph is titled "Croissants Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of croissants. The vertical axis is labeled 0, 20, 40; since 5 grid squares represent 20, each grid square represents $20 \div 5 = 4$ croissants. The number sold each day is: 5th $48$ , 6th $24$ , 7th $40$ , 8th $56$ , 9th $28$ croissants.

Show solution

Understand

A line graph of croissants sold over 5 days shows 5th = 48, 6th = 24, 7th = 40, 8th = 56, 9th = 28 (each small square = 4 croissants). I must find the total croissants sold across all 5 days.

Givens

5th = 48, 6th = 24, 7th = 40, 8th = 56, 9th = 28 croissants
Vertical axis labeled 0, 20, 40 with 5 squares per 20, so each square = 4
Need the sum over all the days

Unknowns

The total number of croissants sold across the days

Constraints

Each value is read using the square value of 4 croissants

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 4 croissants: 5th = 48, 6th = 24, 7th = 40, 8th = 56, 9th = 28.

48,\ 24,\ 40,\ 56,\ 28

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 48 + 24 + 40 + 56 + 28 = 196.

48 + 24 + 40 + 56 + 28 = 196

Summing every day's value gives the running total for the period.

Answer: 196 croissants

Review

Straight addition 48 + 24 + 40 + 56 + 28 = 196 matches. The total must be larger than the biggest single day (56), as a sum of positives must be, and 196 fits.

Count squares first (tool 5): days are 12 + 6 + 10 + 14 + 7 = 49 squares, and 49 x 4 = 196 croissants - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!

Variant 8 answer: 140 cupcakes

The line graph shows the number of cupcakes sold over 5 days at a stand. Find the total number of cupcakes sold.

The graph is titled "Cupcakes Sold." The horizontal axis shows the date (5th, 6th, 7th, 8th, 9th), and the vertical axis shows the number of cupcakes. The vertical axis is labeled 0, 25, 50; since 5 grid squares represent 25, each grid square represents $25 \div 5 = 5$ cupcakes. The number sold each day is: 5th $20$ , 6th $35$ , 7th $15$ , 8th $40$ , 9th $30$ cupcakes.

Show solution

Understand

A line graph of cupcakes sold over 5 days shows 5th = 20, 6th = 35, 7th = 15, 8th = 40, 9th = 30 (each small square = 5 cupcakes). I must find the total cupcakes sold across all 5 days.

Givens

5th = 20, 6th = 35, 7th = 15, 8th = 40, 9th = 30 cupcakes
Vertical axis labeled 0, 25, 50 with 5 squares per 25, so each square = 5
Need the sum over all the days

Unknowns

The total number of cupcakes sold across the days

Constraints

Each value is read using the square value of 5 cupcakes

Plan

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

I read each day's value off the graph using the square size, then add the numbers. Reading the points is the diagram step; the addition is a straightforward subproblem.

Execute

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

Using each square = 5 cupcakes: 5th = 20, 6th = 35, 7th = 15, 8th = 40, 9th = 30.

20,\ 35,\ 15,\ 40,\ 30

Each dot's height times the square value gives that day's count.

#7 Identify Subproblems 4.NBT.B.4

Add the 5 daily counts: 20 + 35 + 15 + 40 + 30 = 140.

20 + 35 + 15 + 40 + 30 = 140

Summing every day's value gives the running total for the period.

Answer: 140 cupcakes

Review

Straight addition 20 + 35 + 15 + 40 + 30 = 140 matches. The total must be larger than the biggest single day (40), as a sum of positives must be, and 140 fits.

Count squares first (tool 5): days are 4 + 7 + 3 + 8 + 6 = 28 squares, and 28 x 5 = 140 cupcakes - the same total.

Standards · min grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading each day's value using the scaled gridlines
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the daily counts into a total

💡 Read each day with the right square size, then add them all up!