1.Give an example of a quantity. What is a possible value for your example?

Name: Class: Date: Chapter 1 Copyright MacmillanLearning. Poweredby Cognero.Page 1 1.Give an example of a quantity. What is a possible value for your example?ANSWER: A possible example is the length of this room. A possible value is 20 feet.

2.Name five quantities that you have dealt with so far today.ANSWER: Possible answers include: distance from home to class; time spent traveling from home to class; amount of gasoline purchased; amount of milk drunk at breakfast; amount of money spent on a Starbucks coffee; etc.

3.Name three quantities that relate to you, and tell how they are measured.ANSWER: Possible answers include: weight (in pounds or kilograms); height (in inches); arm span (inches); shoe size (standard sizes for shoes); waist size (in inches); etc.

4.Would student motivation be difficult or easy to quantify? Explain. Tell how you might go about quantifying student motivation in this class.ANSWER: Probably difficult. Factors influencing motivation might include: need for a passing grade; desire to understand content; parental pressure; peer pressure; etc. A scale (such as 1 low to 10 high) could be designed to measure these factors.

5.How can the term "big" be quantified?ANSWER: Possible answers include: height; weight; popularity; etc.

6.Give two quantities that one could have in mind when he/she says, "This has been a good day." ANSWER: Possible answers include: outside temperature; amount of work accomplished; amount of time spent playing ball and/or picnicking; etc.

7.List at least five relevant quantities that are involved with this problem situation. For each quantity, if the value is given, write it next to the quantity. If the value is not given, write the unit you would use to measure it.Pat and Li left the starting line at the same time, running in opposite directions on a 400-meter, oval-shaped race track. Pat was running at a constant rate of 175 meters per minute. They met each other for the first time after they had been running for 1.5 minutes. How far had Pat run when Li completely finished one lap?ANSWER: Sample answers (quantity, value or unit if value unknown; other units possible—e.g., seconds instead of minutes): Length of track, 400 meters Pat's speed, 175 meters per minute Time until they meet for first time, 1.5 minutes Distance Pat has traveled when they meet for first time, meters Distance Li has traveled when they meet for the first time, meters Li's speed, meters per minute Time for Li to run one lap, minutes Time for Pat to run one lap, minutes Distance Pat has run when Li finished one lap, meters (The above are relevant to one solution, but the following are quantities in the situation as well.) Difference in time for one lap for Pat and Li, seconds or minutes Difference in speeds, Pat and Li, meters per minute 8.Carry out a quantitative analysis of the following problem situation by answering each of the questions that follow.Jennie got on the freeway at 2:00 PM, using the entrance closest to her home, and traveled at 55 mph to the College Avenue exit, where she turned off at 2:12 PM. Her roommate Cassie had finished her morning classes and was headed home at about the same time. Cassie entered the freeway from the College Avenue entrance at 2:08 PM and traveled to the home exit at 60 mph. At what time did Cassie arrive at the exit ramp to go home?A.What quantities here are critical?B.What quantities here are related?Reconceptualizing Mathematics, 4e Judith Sowder, Larry Sowder, Susan Nickerson, Ian Whitacre (Test Bank All Chapters, 100% Original Verified, A+ Grade) 1 / 4

Name: Class: Date: Chapter 1 Copyright MacmillanLearning. Poweredby Cognero.Page 2 C.For what quantities do I know the value?D.For what quantities do I need to know the value?ANSWER: A. Jennie's starting time, Jennie's exit time, time Jennie traveled, speed Jennie traveled, distance Jennie traveled, Cassie's starting time, distance Cassie traveled, speed Cassie traveled, time Cassie traveled B.The distance each traveled is the quantity related to both Jennie and Cassie.C.Jennie's starting time, Jennie's exit time, speed Jennie traveled, Cassie's starting time, speed Cassie traveled D.Time Jennie traveled, distance Jennie traveled (= distance Cassie traveled), time Cassie traveled (to get Cassie's exit ramp time)

9.Consider this problem situation:

The school cafeteria is ready to serve two kinds of sandwiches, tuna and ham, and two kinds of pizza, pepperoni and vegetarian. There are 48 servings of pizza prepared. There are eight more tuna sandwiches prepared than there are servings of pepperoni pizza. There are four fewer ham sandwiches prepared than there are servings of vegetarian pizza. Altogether, how many sandwiches are prepared?A.List eight quantities involved in this problem.B.Sketch a diagram to show the relevant sums and differences in this situation.C.Solve the problem.ANSWER: It will be difficult for your students to avoid algebra or trial and error on this problem; decide whether you wish to prohibit the use of algebra. You might also consider omitting part C.A.For example: number of kinds of sandwiches, number of kinds of pizza, number of servings of pizza prepared, difference in number of tuna sandwiches prepared versus number of servings of pepperoni pizza, difference in number of ham sandwiches prepared versus number of servings of vegetarian pizza, total number of sandwiches prepared, number of tuna sandwiches prepared, number of ham sandwiches prepared, number of servings of pepperoni pizza, number of servings of vegetarian pizza, difference in number of tuna sandwiches and number of ham sandwiches B.There are other praiseworthy drawings possible, but the diagram below suggests the solution (for the total number of sandwiches) pretty easily.C.There are 52 sandwiches prepared in all (8 + 48 − 4).

10.Considering the following problem situation:

Two trains leave from different stations and travel toward each other on parallel tracks. They leave at the same time. The stations are 217 miles apart. One train travels at 65 mph, and the other travels at 72 mph. How long after they leave their stations do they meet each other?List six quantities in the problem (note that you are not asked to solve this problem). If a value is given, write it next to the quantity. If no value is given, write an appropriate unit of measure.ANSWER: Sample answers (quantity, value or unit if value unknown): Distance between stations, 217 miles Speed of one train, 65 miles per hours Speed of other train, 72 miles per hour Total speed of the two trains, miles per hour Time until trains meet, hours (or minutes) Distance first train has traveled when they meet, miles Distance second train has traveled when they meet, miles 2 / 4

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• Carry out a quantitative analysis of the following problem situation by answering each of the questions that

follow, and then solve the problem:

A butcher had two pieces of bologna, A and B, with A weighing 3 1/3 times as much as B. After the butcher cut 1.8 pounds off A, A was still 2 1/3 times as heavy as B. How many pounds does piece B weigh?

• What quantities here are critical?
• What quantities here are related?
• For what quantities do I know the value?
• For what quantities do I need to know the value?
• Use a diagram to find the weight of B, in pounds.

ANSWER: A. Weights of pieces A and B before and after cut, comparison (ratio) of pieces before cut, comparison (ratio) of pieces after cut, weight of piece cut from A

• Same as in part A, along with weight of B
• Weight cut from A, ratio of A to B before cut, ratio of A to B after cut
• Weight of B

E. Before cut: 1.8 pounds

After cut:

Piece B must weigh 1.8 pounds.

12. Consider the following problem situation:

Two boats simultaneously left a pier and traveled in opposite directions. One traveled at a speed of 18 nautical miles per hour and the other at 22 nautical miles per hour. How far apart were they after 2.5 h?List five relevant quantities that are involved in this problem. For each quantity, if a value is given, write it next to the quantity. If value is not given, write the unit you would use to measure it and its value if possible.

ANSWER: Speed of first boat, 18 nautical miles per hour

Speed of second boat, 22 nautical miles per hour Distance traveled by first boat in 2.5 h, nautical miles: 2.5 × 18 = 45 n.m. 3 / 4

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Distance traveled by second boat in 2.5 h, nautical miles: 2.5 × 22 = 55 n.m.

Total distance between boats at 2.5 h, nautical miles: 45 n.m. + 55 n.m. = 100 n.m.

• My brother and I go to the same school. My brother takes 50 minutes to walk to school, and I take 40

minutes. If he gets a 49-minute head start one day, can I catch him before he gets to school? Explain without referring to any shortcut in your explanation.

(Hint: Do not do a lot of calculation.)

ANSWER: No. Brother needs only one more minute to get to school, and in one minute, I can travel only 1/40 of the distance to school.

• My sister can walk from school to home in 40 minutes. I can walk from school to home in 30 minutes. But

today I stayed for some extra help, and my sister was already 2/5 of the way home when I started.If I walk at my usual speed, can I catch my sister before she gets home?If YES, exactly what fraction of the trip have we covered when I catch her?If NO, exactly what fraction of the trip have I covered when my sister gets home?In either case, write enough (words, numbers, drawings) to make your thinking clear.ANSWER: (Yes/No) Explanation, including fraction of the trip: No, I cannot catch up with my sister. My sister has 3/5 of the way to go, which should take 3/5 of 40 minutes, or 24 minutes before arriving at home. But in 24 minutes, I can cover only 24/30, or 4/5, of the way home. On the diagram, my sister is at the second dot (16 minutes) when I begin and has 24 minutes of walking before arrival. In those 24 minutes, I can walk only to X.

• The big dog weighs five times as much as the little dog. The little dog weighs 2/3 as much as the medium-

sized dog. The medium-sized dog weighs 9 pounds more than the little dog. How much does the big dog weigh?

• List three quantities associated with this problem. If possible, give the associated value.
• Draw a diagram to represent the quantities in this problem.
• This diagram was provided by a fifth-grader. Tell why it is not helpful.
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