Test Bank for Reconceptualizing Mathematics, 3e Judith

Test Bank for Reconceptualizing Mathematics, 3e Judith Sowder, Larry Sowder, Susan Nickerson (All Chapters Download link at the end of this File)

Chapter_01_Reasoning_About_Quantities

• 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.

• 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.

• 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.

• 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.

• How can the term "big" be quantified?

ANSWER: Possible answers include: height; weight; popularity; etc.

• 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.

• 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 1 / 2

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

• 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?

• 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?

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

• All in part A are related, but in different ways.
• Jennie's starting time, Jennie's exit time, speed Jennie traveled, Cassie's starting time, speed

Cassie traveled

• 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?

• List eight quantities involved in this problem.
• Sketch a diagram to show the relevant sums and differences in this situation.
• 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.

• 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

• There are other praiseworthy drawings possible, but the diagram below suggests the solution (for

the total number of sandwiches) pretty easily.

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