Exam 1: Reasoning About Quantities

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

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

Name a metric unit that is analogous to a yard. Which is LARGER?

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

Size 1 Pampers fit babies who weigh 4 to 6 kg. Maggie weighs 11 pounds. Will size 1 Pampers fit her? Justify your answer and use a sketch or diagram to show the relationship between kilograms and pounds. (A kilogram is about 2.2 pounds.)

Use a diagram to solve the following problem: Dylan lives 8 miles from campus. Connor lives 2 miles farther away from campus than Dylan does. If each drives a car to campus, how many miles altogether do Dylan and Connor drive to and from campus?

Haley and Tyler are solving the following story problem: "One kind of candy costs $3.50 per pound. How much will 0.42 pound cost?" Haley thinks you should subtract, and Tyler thinks you should divide. A) What are these children likely to be thinking? B) Is either correct? Explain your reasoning.

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.

Use a diagram to solve the following problem: Jesse collects stamps. He now has 444 stamps. He has three times as many stamps from European countries as he does from Asian countries. How many of his stamps are from European countries?

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

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

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.

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

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.