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What is a graph? A graph is a diagram that shows the values of objects by using lines, bars and slices. There are a number of different kinds of graphs that can be created but two of the most common are charts and pies.

** Chart:** A chart is made up of a horizontal line and a vertical line. The horizontal line displays advancing numbers, letters or names going from left to right along the horizontal bottom line. The vertical line displays advancing numbers, letters or names going from the bottom to top along the vertical line.

** Pie:** A pie graph uses “slices” or “sections” to show size. For example, if you wanted to divide a pizza up to feed eight people, one slice of the pizza would be equal to 1/8 of the pie.

For each word problem below you will have to create your own graph (using either a chart or a pie) to determine what is the greater value, lesser value, equal value or negative value. (A negative value will be when the answer would fall below the horizontal line on a chart.)

1.

Four friends met in a park to discuss who they would invite to their Halloween party. Johnny was going to invite seven people, Joey was going to invite five people, Alex was going to invite nine people and Steven was going to invite four people. Using a chart graph, which two friends would bring the most people and the fewest people?

Alex and Joey

Alex and Steven

Johnny and Steven

Joey and Steven

Alex will be bringing 9 people so he will bring the most and Steven will bring 4 which is the least. Answer (b) Alex and Steven is the correct answer

2.

You have just opened your own fast food restaurant and you poll your customers as to what food items they would like to appear on your menu. Sixty-seven people wanted big hamburgers. Thirty-four people wanted corn dogs. Fifty-two people wanted tacos included. Twenty-three people wanted pizza. Eighty-one people wanted milk shakes and eighteen people wanted ice-cream sandwiches. Using a chart graph, which three top items will you include on your menu?

Milk shakes, big hamburgers and tacos

Milk shakes, big hamburgers and corn dogs

Tacos, corn dogs and pizza

Tacos, big hamburgers and corn dogs

Milk shakes received the most requests with 81 people requesting them. Big hamburgers came in second with 67 requests. Third place went to tacos with 52 people requesting it. Answer (a) milk shakes, big hamburgers and tacos is the correct answer

3.

At the middle school fall dance, students were asked which kind of music they would like played. Create a chart graph that shows that twenty-two percent said they wanted pop music. Twenty-eight percent wanted rock-n-roll music. Fourteen percent wanted country music. Three percent wanted jazz. Seven percent wanted Latin music and twenty-six percent wanted rap. What kind of value did those who wanted rock-n-roll music compare to those who wanted pop music?

Greater value

Lesser value

Equal value

Negative value

28% wanted rock-n-roll music while 22% wanted pop music. (28 > 22) Answer (a) is the correct answer

4.

The Johnson family went to their local amusement park to enjoy a fun filled day. Papa Johnson gave each of his three children twenty dollars to ride the rides. Create three pie charts showing how much each child spent. Charlie spent four dollars on bumper cars, three dollars on the slippery slope and eight dollars on the roller coaster. Mary spent seven dollars on the Scrambler, three dollars on the slippery slope, two dollars on the Ferris wheel and six dollars on the rocket ship. David spent nine dollars on the roller coaster, two dollars on the Scrambler and four dollars on the bumper cars. What kind of value did Charlie spend compared to what David spent?

Greater value

Lesser value

Equal value

Negative value

Charlie spent $4 on bumper cars, $3 on the slippery slope and $8 on the roller coaster. That is 4 + 3 + 8 = 15. Charlie spent $15. David spent $9 on the roller coaster, $2 on the Scrambler and $4 on bumper cars. That is 9 + 2 + 4 = 15. David spent $15. Charlie and David spent the same or equal amount so Answer (c) is the correct answer

5.

Staying with the Johnson family mentioned in Question 4, while Charlie, Mary and David were going on rides - Papa and Mama Johnson were playing games in the arcade. Each had twenty dollars to spend. Create two pie charts showing how much Papa and Mama spent. Papa Johnson spent eleven dollars on bowling, seven dollars on pinball machines and six dollars on shoot the duck. Mama Johnson spent twelve dollars on bingo, three dollars on pinball machines and four dollars on whack-a-mole. What kind of value did Papa spend with his twenty dollars?

Greater value

Lesser value

Equal value

Negative value

Papa spent $11 on bowling, $7 on pinball machines and $6 on shoot the duck. That is 11 + 7 + 6 = 24. $20 - $24 = -$4. Papa spent more money than he allotted so he spent into a negative value. Answer (d) is the correct answer

6.

Martha and her three best friends wanted to lose weight before spring break. Martha had to lose fifteen pounds. Janet wanted to lose nineteen pounds. Carol wanted to lose six pounds and Allison wanted to lose twenty-four pounds. Martha wound up losing half of what she wanted to. Janet lost sixty percent of what she wanted to. Carol lost ninety percent of what she wanted to and Allison lost sixty-eight percent of what she wanted to. By creating a chart graph, which girl lost the most pounds?

Janet

Allison

Martha

Carol

Martha wanted to lose 15 pounds but only lost half of that or 50%. 15 ÷ 2 = 7.5 pounds -- Janet wanted to lose 19 pounds but lost 60% of that. 19 ÷ 100% = .19, .19 x 60 = 11.4 pounds. Carol wanted to lose 6 pounds and lost 90% of that. 6 ÷100 = .06, .06 x 90 = 5.4 pounds. Finally, Allison wanted to lose 24 pounds but lost only 68% of that. 24 ÷ 100 = .24, .24 x 68 = 16.32 pounds -- Allison lost the most pounds so Answer (b) is correct

7.

Mr. Atkins bought thirty-two new math books for his fifth period class. Four of the books had missing odd page numbers and had to be returned. Three other books were teacher’s copies showing all of the answers so two of those had to be returned as well. Mrs. Wilson had an extra copy of the same book so she gave her extra copy to Mr. Atkins. Two dogs jumped through the window and stole two of the books, shredding them in the school yard. Using a pie graph, how many of the new books was Mr. Atkins able to keep?

29

24

26

25

Mr. Atkins started with 32 new books and had to return 4 for missing pages. That is 32 - 4 = 28. Next he had 3 teacher’s copies so he returned 2 of those. That is 28 - 2 = 26. Mrs. Wilson gave him 1 extra copy. That is 26 + 1 = 27. Then 2 crazy dogs came in and stole and destroyed 2 copies. That is 27 - 2 = 25. Mr. Atkins was able to keep 25 copies of the new math book. Answer (d) is the correct answer

8.

For our civics class we had to watch the election results of our local candidates. Boyner, Carlson, Jefferson and Wilcox were all running for mayor. There were 100,000 votes to be captured. Create a chart graph that shows the four candidates and the percentage of votes. (NOTE: 100,000 equals 100%.) Boyner got twenty-three percent of the votes. Carlson got twenty-two percent of the votes. Jefferson got twenty-seven percent of the votes and Wilcox got twenty-eight percent of the votes. How many more votes did Wilcox get over Carlson?

50,000

60,000

6,000

600

Boyner got 23% of the votes. 100,000 ÷ 100 = 1,000 – that makes 1,000 votes equals 1% so 23 x 1000 = 23000. Boyner got 23,000 votes. Carlson got 22% so that would be 22 x 1000 = 22000. Carlson got 22,000 votes. Jefferson got 27% so that would be 27 x 1000 = 27000. Jefferson got 27,000 votes. Wilcox got 28% so that would be 28 x 1000 = 28000. Wilcox got 28,000 votes. 28,000 – 22,000 = 6,000. Wilcox got 6,000 more votes than Carlson. Answer (c) is the correct answer

9.

My grandparents started a college savings account for each of their four grandchildren, Phillip, Patricia, Kelly and Michael. When each grandchild graduated there was $12,000 in their fund. Phillip took sixty-five percent of his fund for his first year of college. Patricia took forty-nine percent of her fund. Kelly took sixty-one percent of her fund and Michael took twenty-two percent of his. Create a chart graph to show each grandchild and the percentage of their college fund they took out their first year. Who took out $7,320.00?

Kelly

Michael

Phillip

Patricia

We know they each had $12,000 which is equal to 100% of their funds. 12000 ÷ 100 = 120. $120 equals 1% of the college fund. Phillip took out 65% form his fund so we multiply 65 x 120 = $7,800. Patricia took out 49% so we multiply 49 x 120 = $5,880. Kelly took out 61% so we multiply 61 x 120 = $7,320. Finally, Michael took out 22% or 22 x 120 = $2,640. Answer (a) Kelly is the correct answer

10.

Returning to the Johnson family mentioned in Questions 4 and 5, Papa and Mama Johnson were playing games in the arcade and each had twenty dollars to spend. Looking at the two pie charts created earlier, we learned that Papa Johnson spent eleven dollars on bowling, seven dollars on pinball machines and six dollars on shoot the duck while Mama Johnson spent twelve dollars on bingo, three dollars on pinball machines and four dollars on whack-a-mole. What kind of value did Mama spend with her twenty dollars?

Greater value

Lesser value

Equal value

Negative value

Mama spent $12 on bingo, $3 on pinball machines and $4 on whack-a-mole. That is 12 + 3 + 4 = 19. Mama spent $19 of her $20 so she spent less than she could have. Answer (b) is the correct answer