Variant 1 easy

Representative Problem

The line graphs show how many chocolate cookies and how many strawberry cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Chocolate Cookies Sold": the vertical axis is the number sold, with each small grid square worth $50$ . The numbers sold are $100$ on day 4, $150$ on day 5, $200$ on day 6, $150$ on day 7.

Right graph, "Strawberry Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $190$ on day 4, $150$ on day 5, $170$ on day 6, $230$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Chocolate Cookies days 4-7 are 100, 150, 200, 150 (each small square = 50). Strawberry Cookies days 4-7 are 190, 150, 170, 230 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Chocolate Cookies sold: day4 = 100, day5 = 150, day6 = 200, day7 = 150
Strawberry Cookies sold: day4 = 190, day5 = 150, day6 = 170, day7 = 230
Chocolate Cookies graph small square = 50; Strawberry Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Chocolate Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the chocolate cookies graph (each square = 50), the most was 200 on day 6 and the least was 100 on day 4. The difference is 200 - 100.

200 - 100 = 100

Highest minus lowest gives the spread of one data set.

2Strawberry Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the strawberry cookies graph (each square = 10, axis cut by a wavy line), the most was 230 on day 7 and the least was 150 on day 5. The difference is 230 - 150.

230 - 150 = 80

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Chocolate Cookies's range is 100 and strawberry cookies's range is 80. Since 100 > 80, chocolate cookies has the larger difference between its best and worst day.

100 > 80

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Chocolate Cookies cookies (range 100, vs the other's 80)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 100 and 80, so chocolate cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Chocolate Cookies 2 squares x 50 = 100, Strawberry Cookies 8 squares x 10 = 80, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 2 easy

Representative Problem

The line graphs show how many chocolate cookies and how many strawberry cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Chocolate Cookies Sold": the vertical axis is the number sold, with each small grid square worth $40$ . The numbers sold are $80$ on day 4, $160$ on day 5, $200$ on day 6, $120$ on day 7.

Right graph, "Strawberry Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $210$ on day 4, $180$ on day 5, $240$ on day 6, $200$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Chocolate Cookies days 4-7 are 80, 160, 200, 120 (each small square = 40). Strawberry Cookies days 4-7 are 210, 180, 240, 200 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Chocolate Cookies sold: day4 = 80, day5 = 160, day6 = 200, day7 = 120
Strawberry Cookies sold: day4 = 210, day5 = 180, day6 = 240, day7 = 200
Chocolate Cookies graph small square = 40; Strawberry Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Chocolate Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the chocolate cookies graph (each square = 40), the most was 200 on day 6 and the least was 80 on day 4. The difference is 200 - 80.

200 - 80 = 120

Highest minus lowest gives the spread of one data set.

2Strawberry Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the strawberry cookies graph (each square = 10, axis cut by a wavy line), the most was 240 on day 6 and the least was 180 on day 5. The difference is 240 - 180.

240 - 180 = 60

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Chocolate Cookies's range is 120 and strawberry cookies's range is 60. Since 120 > 60, chocolate cookies has the larger difference between its best and worst day.

120 > 60

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Chocolate Cookies cookies (range 120, vs the other's 60)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 120 and 60, so chocolate cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Chocolate Cookies 3 squares x 40 = 120, Strawberry Cookies 6 squares x 10 = 60, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 3 medium

Representative Problem

The line graphs show how many almond cookies and how many cocoa cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Almond Cookies Sold": the vertical axis is the number sold, with each small grid square worth $40$ . The numbers sold are $120$ on day 4, $80$ on day 5, $160$ on day 6, $200$ on day 7.

Right graph, "Cocoa Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $260$ on day 4, $280$ on day 5, $250$ on day 6, $300$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Almond Cookies days 4-7 are 120, 80, 160, 200 (each small square = 40). Cocoa Cookies days 4-7 are 260, 280, 250, 300 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Almond Cookies sold: day4 = 120, day5 = 80, day6 = 160, day7 = 200
Cocoa Cookies sold: day4 = 260, day5 = 280, day6 = 250, day7 = 300
Almond Cookies graph small square = 40; Cocoa Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Almond Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the almond cookies graph (each square = 40), the most was 200 on day 7 and the least was 80 on day 5. The difference is 200 - 80.

200 - 80 = 120

Highest minus lowest gives the spread of one data set.

2Cocoa Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the cocoa cookies graph (each square = 10, axis cut by a wavy line), the most was 300 on day 7 and the least was 250 on day 6. The difference is 300 - 250.

300 - 250 = 50

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Almond Cookies's range is 120 and cocoa cookies's range is 50. Since 120 > 50, almond cookies has the larger difference between its best and worst day.

120 > 50

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Almond Cookies cookies (range 120, vs the other's 50)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 120 and 50, so almond cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Almond Cookies 3 squares x 40 = 120, Cocoa Cookies 5 squares x 10 = 50, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 4 medium

Representative Problem

The line graphs show how many butter cookies and how many mint cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Butter Cookies Sold": the vertical axis is the number sold, with each small grid square worth $50$ . The numbers sold are $200$ on day 4, $350$ on day 5, $300$ on day 6, $250$ on day 7.

Right graph, "Mint Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $180$ on day 4, $160$ on day 5, $210$ on day 6, $200$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Butter Cookies days 4-7 are 200, 350, 300, 250 (each small square = 50). Mint Cookies days 4-7 are 180, 160, 210, 200 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Butter Cookies sold: day4 = 200, day5 = 350, day6 = 300, day7 = 250
Mint Cookies sold: day4 = 180, day5 = 160, day6 = 210, day7 = 200
Butter Cookies graph small square = 50; Mint Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Butter Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the butter cookies graph (each square = 50), the most was 350 on day 5 and the least was 200 on day 4. The difference is 350 - 200.

350 - 200 = 150

Highest minus lowest gives the spread of one data set.

2Mint Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the mint cookies graph (each square = 10, axis cut by a wavy line), the most was 210 on day 6 and the least was 160 on day 5. The difference is 210 - 160.

210 - 160 = 50

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Butter Cookies's range is 150 and mint cookies's range is 50. Since 150 > 50, butter cookies has the larger difference between its best and worst day.

150 > 50

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Butter Cookies cookies (range 150, vs the other's 50)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 150 and 50, so butter cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Butter Cookies 3 squares x 50 = 150, Mint Cookies 5 squares x 10 = 50, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 5 medium

Representative Problem

The line graphs show how many vanilla cookies and how many lemon cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Vanilla Cookies Sold": the vertical axis is the number sold, with each small grid square worth $30$ . The numbers sold are $60$ on day 4, $120$ on day 5, $90$ on day 6, $150$ on day 7.

Right graph, "Lemon Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $320$ on day 4, $290$ on day 5, $350$ on day 6, $310$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Vanilla Cookies days 4-7 are 60, 120, 90, 150 (each small square = 30). Lemon Cookies days 4-7 are 320, 290, 350, 310 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Vanilla Cookies sold: day4 = 60, day5 = 120, day6 = 90, day7 = 150
Lemon Cookies sold: day4 = 320, day5 = 290, day6 = 350, day7 = 310
Vanilla Cookies graph small square = 30; Lemon Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Vanilla Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the vanilla cookies graph (each square = 30), the most was 150 on day 7 and the least was 60 on day 4. The difference is 150 - 60.

150 - 60 = 90

Highest minus lowest gives the spread of one data set.

2Lemon Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the lemon cookies graph (each square = 10, axis cut by a wavy line), the most was 350 on day 6 and the least was 290 on day 5. The difference is 350 - 290.

350 - 290 = 60

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Vanilla Cookies's range is 90 and lemon cookies's range is 60. Since 90 > 60, vanilla cookies has the larger difference between its best and worst day.

90 > 60

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Vanilla Cookies cookies (range 90, vs the other's 60)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 90 and 60, so vanilla cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Vanilla Cookies 3 squares x 30 = 90, Lemon Cookies 6 squares x 10 = 60, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 6 medium

Representative Problem

The line graphs show how many peanut cookies and how many maple cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Peanut Cookies Sold": the vertical axis is the number sold, with each small grid square worth $20$ . The numbers sold are $100$ on day 4, $240$ on day 5, $160$ on day 6, $280$ on day 7.

Right graph, "Maple Cookies Sold": the vertical axis is the number sold, with each small grid square worth $30$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $330$ on day 4, $360$ on day 5, $300$ on day 6, $390$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Peanut Cookies days 4-7 are 100, 240, 160, 280 (each small square = 20). Maple Cookies days 4-7 are 330, 360, 300, 390 (each small square = 30, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Peanut Cookies sold: day4 = 100, day5 = 240, day6 = 160, day7 = 280
Maple Cookies sold: day4 = 330, day5 = 360, day6 = 300, day7 = 390
Peanut Cookies graph small square = 20; Maple Cookies graph small square = 30
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Peanut Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the peanut cookies graph (each square = 20), the most was 280 on day 7 and the least was 100 on day 4. The difference is 280 - 100.

280 - 100 = 180

Highest minus lowest gives the spread of one data set.

2Maple Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the maple cookies graph (each square = 30, axis cut by a wavy line), the most was 390 on day 7 and the least was 300 on day 6. The difference is 390 - 300.

390 - 300 = 90

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Peanut Cookies's range is 180 and maple cookies's range is 90. Since 180 > 90, peanut cookies has the larger difference between its best and worst day.

180 > 90

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Peanut Cookies cookies (range 180, vs the other's 90)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 180 and 90, so peanut cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Peanut Cookies 9 squares x 20 = 180, Maple Cookies 3 squares x 30 = 90, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 7 hard

Representative Problem

The line graphs show how many sugar cookies and how many ginger cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Sugar Cookies Sold": the vertical axis is the number sold, with each small grid square worth $50$ . The numbers sold are $150$ on day 4, $300$ on day 5, $450$ on day 6, $300$ on day 7.

Right graph, "Ginger Cookies Sold": the vertical axis is the number sold, with each small grid square worth $20$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $420$ on day 4, $400$ on day 5, $460$ on day 6, $410$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Sugar Cookies days 4-7 are 150, 300, 450, 300 (each small square = 50). Ginger Cookies days 4-7 are 420, 400, 460, 410 (each small square = 20, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Sugar Cookies sold: day4 = 150, day5 = 300, day6 = 450, day7 = 300
Ginger Cookies sold: day4 = 420, day5 = 400, day6 = 460, day7 = 410
Sugar Cookies graph small square = 50; Ginger Cookies graph small square = 20
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Sugar Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the sugar cookies graph (each square = 50), the most was 450 on day 6 and the least was 150 on day 4. The difference is 450 - 150.

450 - 150 = 300

Highest minus lowest gives the spread of one data set.

2Ginger Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the ginger cookies graph (each square = 20, axis cut by a wavy line), the most was 460 on day 6 and the least was 400 on day 5. The difference is 460 - 400.

460 - 400 = 60

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Sugar Cookies's range is 300 and ginger cookies's range is 60. Since 300 > 60, sugar cookies has the larger difference between its best and worst day.

300 > 60

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Sugar Cookies cookies (range 300, vs the other's 60)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 300 and 60, so sugar cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Sugar Cookies 6 squares x 50 = 300, Ginger Cookies 3 squares x 20 = 60, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Variant 8 hard

Representative Problem

The line graphs show how many honey cookies and how many cream cookies a bakery sold each day. For which kind of cookie is the difference between its best-selling day and its worst-selling day larger?

(Figure) Two line graphs shown side by side. On both graphs the horizontal axis is the date — day $4$ , day $5$ , day $6$ , day $7$ .

Left graph, "Honey Cookies Sold": the vertical axis is the number sold, with each small grid square worth $30$ . The numbers sold are $90$ on day 4, $180$ on day 5, $270$ on day 6, $90$ on day 7.

Right graph, "Cream Cookies Sold": the vertical axis is the number sold, with each small grid square worth $10$ (the lower part of the axis is cut off with a wavy line). The numbers sold are $510$ on day 4, $540$ on day 5, $500$ on day 6, $520$ on day 7.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Two line graphs show daily cookie sales. Honey Cookies days 4-7 are 90, 180, 270, 90 (each small square = 30). Cream Cookies days 4-7 are 510, 540, 500, 520 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.

Givens

Honey Cookies sold: day4 = 90, day5 = 180, day6 = 270, day7 = 90
Cream Cookies sold: day4 = 510, day5 = 540, day6 = 500, day7 = 520
Honey Cookies graph small square = 30; Cream Cookies graph small square = 10
The two graphs use different vertical scales

Unknowns

Which cookie has the larger gap between its best-selling and worst-selling day

Constraints

Values must be read using each graph's own square size, not the apparent height

2 · Planchoose the strategy

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Because the graphs use different square sizes, comparing point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: each cookie's range, and compare those two numbers.

3 · Execute3 carry out the plan

1Honey Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the honey cookies graph (each square = 30), the most was 270 on day 6 and the least was 90 on day 4. The difference is 270 - 90.

270 - 90 = 180

Highest minus lowest gives the spread of one data set.

2Cream Cookies range

#7 Identify Subproblems 5.MD.B.2

Reading the cream cookies graph (each square = 10, axis cut by a wavy line), the most was 540 on day 5 and the least was 500 on day 6. The difference is 540 - 500.

540 - 500 = 40

I use the actual numbers, not how tall the line looks, because the squares are worth different amounts.

3Compare the two ranges

#15 Organize Information in More Ways 5.MD.B.2

Honey Cookies's range is 180 and cream cookies's range is 40. Since 180 > 40, honey cookies has the larger difference between its best and worst day.

180 > 40

Once both data sets are in real numbers, a plain comparison answers the question.

Answer: Honey Cookies cookies (range 180, vs the other's 40)

4 · Reviewdoes it hold up?

A line can look taller or steeper only because its squares are worth a different amount; reading each graph by its own scale, not by appearance, gives ranges 180 and 40, so honey cookies wins.

Another way: Convert each swing into squares and multiply by each square value: Honey Cookies 6 squares x 30 = 180, Cream Cookies 4 squares x 10 = 40, confirming the comparison.

Standardsmin grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading values from each graph's scale and comparing the ranges

💡Takeaway. When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

Compare line graphs that use different gridline scales · 8 practice problems

Generated variants — 8

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Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Where next?