Exam 3: Understanding Whole Number Operations

Rita is given this problem: Zetta has $39, but she needs $78 to buy a jacket she wants. How much more does she need? Rita's replies, "79 minus 40 is 39, so she needs $39." Explain Rita's reasoning. What is your reaction to this method of doing the problem?

Label each word problem with the type of division being depicted. A) The big bag has 48 plastic cars, to be put into bags holding six cars each. How many bags of cars will there be? B) The big bag has 48 plastic cars, to be split fairly among six youngsters. How many cars will each youngster get?

Two basketball coaches, A and B, are talking. A says to B: "Your tallest player is 6 inches taller than my tallest player!" B says to A: "Yes, but your second-tallest player is 8 inches taller than my second tallest player." A says to B: "Hmm. My second-tallest player is 4 inches shorter than my tallest player." Make a drawing, and tell the difference in heights of Coach B's two tallest players.

Consider the following work of a student: 84 20 400 160 900

A) Make sketches for 3 × 6 and 6 × 3 and contrast them. B) Make sketches of 1/2 × 6 and 6 × 1/2.

Write a word problem for 37 ÷ 5 for which the answer would be 7.

For A, B, and C below, state: 1) the operation you would use to answer the question, 2) the situation in which the problem fits, and 3) an expression that yields the answer. A) Susan has $175. She wants to go on a ski trip that costs $250. How much more money does she need? B) John is 6 ft 1 in tall and Steve is 5 ft 9 in tall. How much taller than Steve is John? C) Karen has four fish in her aquarium. She puts three more in. How many fish are in the aquarium now?

A local community college has two sections of Math 210 (Sections A and B) and two sections of Math 211 (Sections C and D). Together, Sections C and D have 46 students. Section A has six more students than Section D. Section B has two fewer students than Section C. How many students are there in Section A and Section B altogether?

Perform the following subtraction using the "equal additions" method. 432 -287

Antonio asks, "When I multiply [e.g., 49 × 23, shown below], why do I have to put in the 0 [points to the zero in 980]?" What would you say to Antonio? 49 147 1127

Suppose you are using toothpicks to act out the following story problem: Jack had eight candy bars. Bill had four. A) How many more candy bars did Jack have than Bill? B) How many toothpicks would you need to act the problem out? C) What type of subtraction is this?

A designer of women's "mix and match" clothing designs three styles of skirts, two pairs of pants, three types of tops, and four styles of jackets. How many different outfits could be purchased if each outfit has a skirt OR pants, a top, and a jacket? (Assume that a woman will not wear a skirt and a pair of pants at the same time.)

Using a circle to represent 1, make drawings to illustrate each of the following. A) 3 × 4, array B) 1/3 × 6, fractional part of an amount

Consider this problem situation, which would involve dividing by 3: You are putting books on three empty shelves in your classroom. To make them look neat, you put the same number of books on each shelf. How many books will be on each shelf? Write another problem situation about the books so that your problem involves another way of thinking about division by 3.

Marge bought several types of candy for Halloween: Milky Ways, Tootsie Rolls, Reese's Cups, and Hershey Bars. The Milky Ways and Tootsie Rolls together were six more than the Reese's Cups. There were four fewer Reese's Cups than Hershey Bars. There were 12 Milky Ways and 28 Hershey Bars. How many Tootsie Rolls did Marge buy? A) List five quantities involved in this problem. B) Sketch a diagram to show the relevant sums and differences in this situation. C) Solve the problem.

The work of two students is shown below. Each student "invented" the method used; that is, it was not taught to the student. Figure out what each student was thinking while doing the problem. Then work the second problem (i) using the same method as the student, and (ii) comment on the student's method in terms of the "number sense" exhibited. A) 732 (i) 8341 513 B) 19 × 35. Well, 20 × 35 is like 10 × 35 two times, so that's 350 two times, which is 700. But that's twenty 35s and I only want nineteen 35s. So 700 minus 30 is 670 minus 5 is 665. (i) 21 × 43

For each story problem, 26 - 12 can be used to solve the problem. Label each of the story problems as comparison subtraction, take-away subtraction, or missing-addend subtraction. A) Laresa had $26 when she went into the store, and her friend Tisha had $12. How much more did Laresa have than Tisha? B) Laresa had $26 when she went into the store. She bought a wallet for $12. How much did she have left? C) Laresa had $26 when she went into the store because she had $12 already and then received cash for babysitting. How much did she earn babysitting?

Write a word problem for 37 ÷ 5 for which the answer would be 2.

Which way of thinking about subtraction is involved in each story problem? Write the equation you would write for the problem. (Hint: How would you act it out?) A) University X wants to enroll 5000 new freshmen. It currently has enrolled 4275 new freshmen. How many more freshmen does University X need to enroll? B) This year's budget is $1.6 million. Last year's budget was $1.135 million. How much larger is this year's budget than last year's?

In each story problem, the calculation 6 - 2.5 can be used to solve the problem. Which story problem involves the "missing-addend" situation and which involves "comparison"? A) Two joggers decided to run at the beach. They usually run for 6 miles. How much farther do they have to run if they have already run 2.5 miles? B) Two joggers decided to run at the beach. One runs 6 miles and the other runs 2.5 miles. How much farther than the second jogger does the first jogger run?