Use a Graph: Homework

Sketch the graph first, then read it: the scale, what each bar or point means, and what happens next.

Part A — Sketch It, Then Read It / 8

Each graph is described in words, and the numbers are made up. Sketch the graph on scrap paper first, then answer.

1.
A bar graph shows cups of lemonade sold: Monday 14, Tuesday 9, Wednesday 16, Thursday 11. Each cup costs $0.75. How much money came in on the two best days?Answer
2.
A line graph shows the temperature: 6 am 48 degrees, 9 am 55, noon 67, 3 pm 74. Between which two readings did the temperature rise the most, and by how much?Answer
3.
A line graph shows a plant: 2 cm at week 1, 5 cm at week 2, 8 cm at week 3. Keeping the line going the same way, how tall will it be at week 6?Answer
4.
A double bar graph shows pizza sales for two classes. Class A: September 40, October 52. Class B: September 35, October 61. How many more did Class B grow than Class A?Answer
5.
A circle graph shows how you spend a $60 allowance. Half goes to savings, a quarter goes to games, and the rest goes to snacks. How much goes to snacks?Answer
6.
A bar graph's scale counts by 5s starting at 0. One bar ends exactly halfway between the 15 line and the 20 line. How tall is the bar?Answer
7.
A line graph shows weekly sales. Store A: week 1 is 20, week 2 is 35, week 3 is 50. Store B: 60, 55, 50. Keep both lines going the same way. In week 4, how many more does Store A sell than Store B?Answer
8.
Which skill? For each, say whether you would read a graph (U3-L1) or make a table (U3-L2). (a) You are handed a finished bar graph and asked which month sold the most. (b) You are handed a loose list of the favorite colors of 20 students and asked how many chose blue.Answer

Real numbers from the U.S. Census, in millions of people. Imagine them as a bar graph, one bar for each year.

Think it through, then write your answer and one sentence about how you knew.

1.
A bar graph's scale starts at 100 instead of 0. One bar is 105 tall and another is 110. The second bar looks more than twice as tall. Why is the graph misleading, and what would an honest graph look like?Answer
2.
A line graph goes up by 10 each week for three weeks. A friend says it will keep going up by 10, so in week 100 the value will be 1,000. When is it not safe to extend a graph like this? Give an example.Answer

Write your own, then solve it yourself.

1.
Make up a bar graph problem with four bars. Describe the bars, then ask a question that takes two steps to answer. Give the answer.Answer

Total / 16

Graded by

Notes

Part A — the answer.

$22.50. The best days are Wednesday and Monday: (16 + 14) × 0.75.
12 degrees, from 9 am to noon. The other jumps were 7 and 7.
17 cm. It grows 3 cm each week, and week 6 is five weeks after week 1.
14 more. Class B grew 26 and Class A grew 12.
$15
17.5
20 more. Store A is 65 and Store B is 45.
(a) Read a graph. Find the tallest bar, check its label and the scale. (b) Make a table. Tally each color into a row, then count the blue tally.

Part B — the answers.

a. 0 to 350 by 50s. The scale has to reach the greatest number, 331.4, and 100 is too small. b. 180.1 million c. 75.2 million, from 1950 to 1980. But it covers 30 years and the other two cover 20, so it is not quite fair. d. 381.4 million e. 180 million

Part C — one correct answer, and what a good explanation says.

The bars are cut off at 100, so you are only seeing the part above 100: a 5 and a 10. The real numbers are only a little different. An honest graph starts its scale at 0, and then 110 looks only a little taller than 105.
Answers vary. A trend can stop or turn. A plant stops growing when it is full height, and sales level off. Extending the line is a guess that works for a short stretch, not for a long one.

Part D — what a good problem looks like.

Answers vary. A good one needs two steps, such as bars of 6, 9, 4 and 12 books, asking how many more the top bar is than the average of the other three: 12 - (6 + 9 + 4) ÷ 3 = 12 - 6.33... = 5.67.