Variant 1 easy answer: Chocolate Cookies cookies (range 100, vs the other's 80)

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints

Representative Problem

Givens

Unknowns

Constraints