Practice Exam 1
1. How many tens are in 7654? How many whole tens are in 7654?
2. In base ten, 3421 is exactly __________ ones, exactly __________ tens, exactly
___________ hundreds, and exactly ___________ thousands; also, 3421 is exactly
___________ tenths and exactly ___________hundredths.
3. A soap factory packs 100 bars of soap in each box for shipment. If the factory makes
15,287 bars of soap, how many full boxes will they have for shipment? Explain.
4. 524 eight = __________
ten
5. 287ten = __________ four
6. 2.31four = ________________ as a mixed number in base ten.
7. If you are counting in base five, what would be the next six numerals after 2314five?
8. Write how many fingers you have in base five. In base two. In base ten.
9. Which is larger?
21four or 21 five? Explain.
10. Base eight pieces, with the small cube (a dot here) as the unit.
11. Write the base b numeral for 2b4 + b2 + 3b + 1.
12. Define your unit and sketch base blocks to represent 32.67 eight.
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13. The base ten decimal 18.5 could be written in base six as
A) 10.5six.
B) 20.3six.
C) 30.3six.
D) 128.5six.
E) None of A–D
14. If 31b = 28ten, then b =
A) 4.
B) 5.
C) 7.
D) 9.
E) This is impossible for any whole number b.
15.
241six
+ 135six
16.
127nine
– 58nine
17.
4.4five
+ 3.3five
18. Use drawings of multibase blocks to illustrate 32 five + 23five.
19. 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?
A) For each given value, write the quantity next to it.
B) Sketch a diagram to show the relevant sums and differences in this situation.
C) Solve the problem. Show all your work here.
20. A first grade teacher always reads subtraction statements such as “7 – 5 = 2” to his class
as “seven take away five is two.” That is, he always reads the minus sign as “take
away.” Comment on why this might not be a good practice.
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21. 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? Explain your
answer. What type of subtraction is this?
22. 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.)
23. A) This is a typical problem from an elementary textbook:
Jasmine works in a book store. Today, three boxes of Harry Potter books arrived.
There are 144 books in each box. Jasmine is told to stack the books in piles in an area
of the book store. She is told to put the books into 16 piles. How many books are in
each pile?
What interpretations of multiplication and division are represented in this problem?
B) What if the question changes to She is told to put 27 books in each pile. How many
piles can she make? What interpretation of division is now represented?
24. Make up a story problem involving quantities of ice cream in an ice cream store, so that
the problem could be solved by the calculations given:
2  18
A) Can be solved by
16 18
B) Can be solved by
3
 24
C) Can be solved by 4
25. Show 3335 ÷ 23 with a scaffolding algorithm and then by the standard algorithm. Show
how each number in the standard algorithm is associated with number in the scaffolding
algorithm.
26. Name two positive and two negative aspects of learning nonstandard algorithms.
27. Draw how one would act out 200 – 62 (take-away view) to support the usual right-left
algorithm, with base ten materials. (Make clear what represents 1.) Make a separate
drawing for each step (add steps if you need them).
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28. Below is a worked-out calculation of 313  42, using the lattice method for
multiplication. Explain why the method does give the correct number in the tens place
(the circled 4). (Note: Some current textbooks use this algorithm to teach
multiplication of whole numbers.)
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