Question 1

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

Accepted Answer

A possible example is the length of this room. A possible value is 20 feet.

Question 2

Name five quantities that you have dealt with so far today.

Accepted 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.

Question 3

Name three quantities that relate to you, and tell how they are measured.

Accepted 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.

Question 4

Would student motivation be difficult or easy to quantify? Explain. Tell how you might go about quantifying student motivation in this class.

Accepted Answer

The answer of Would student motivation be difficult or easy...

Question 5

How can the term "big" be quantified?

Accepted Answer

The answer of How can the term "big" be quantified?...

Question 6

Give two quantities that one could have in mind when he/she says, "This has been a good day."

Accepted Answer

The answer of Give two quantities that one could have...

Question 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, rumning in opposite direct. 400 -meter, oval-shaped race track. Pat was running at a constant rate of 1 minute. They met each other for the first time after they had been rumning $f$ minutes. How for had Pat nun when Li completely finished one lap?

Accepted Answer

The answer of List at least five relevant quantities that...

Question 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?
C) For what quantities do I know the value?
D) For what quantities do I need to know the value?

Accepted Answer

The answer of Carry out a quantitative analysis of the...

Question 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.

Accepted Answer

The answer of Consider this problem situation:
The school cafeteria is...

Question 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.

Accepted Answer

The answer of Considering the following problem situation:
Two trains leave...

Question 11

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

Accepted Answer

The answer of Carry out a quantitative analysis of the...

Question 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 hours?
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.

Accepted Answer

The answer of Consider the following problem situation:
Two boats simultaneously...

Question 13

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 short-cut in your explanation. (Hint: Do not do a lot of calculation.)

Accepted Answer

The answer of My brother and I go to the...

Question 14

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.

Accepted Answer

The answer of My sister can walk from school to...

Question 15

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? 
A) List three quantities associated with this problem. If possible, give the associated value.
B) Draw a diagram to represent the quantities in this problem.
C) This diagram was provided by a fifth-grader. Tell why it is not helpful.
  
D) Solve the problem and explain your solution process.

Accepted Answer

The answer of The big dog weighs five times as...

Question 16

The label on a can of chicken broth claims that its weight is 1.4 kg. Use your metric knowledge to tell how many milligrams this would be.

Accepted Answer

The answer of The label on a can of chicken...

Question 17

The larger the unit of measure used to express the value of a specific quantity, the larger its numeric value will be.

Accepted Answer

Using a larger unit of measure to express a specific quantity results in a smaller numeric value because fewer units are needed to represent the same quantity.

Question 18

Give an estimate of the following and explain how you did it.
The length of this line in metric units: ____________________________

Accepted Answer

The answer of Give an estimate of the following and...

Question 19

List the following measurements in order from greatest to least:
8 m, 359 cm, 66 m, 3912 mm, 5198 cm, 7 m

Accepted Answer

The answer of List the following measurements in order from...

Question 20

How many grams are there in centigrams? A) 1 × 10^-2 B) 100 C) 0.001 D) 1 × 10²

Accepted Answer

There are 100 centigrams in a gram, which is mathematically represented as 1 × 10^-2 grams.

Quiz 1: Reasoning About Quantities