Download Answer Key for Practice Exam 1

Answer Key for Practice Exam 1
1. 765.4, 765
2. In base ten, 3421 is exactly 3421 ones, exactly 342.1tens, exactly 34.21 hundreds, and
exactly 3.421 thousands; also, 3421 is exactly 34210 tenths and exactly 342100
hundredths.
3. 152, because there are 152 hundreds in 15,287.
4. 340 ten
5. 10133 four
13
6. 2 16
ten
7. 2320, 2321, 2322, 2323, 2324, and 2330
8. 20five. 1010two. 10ten.
9. When a numeral has more than one digit, it will vary in value if written in different
bases because the place values will differ. 21 four = 9 ten and 21 five = 11ten. Here,
without converting, you can argue that the two groups of five will be more that the two
groups of four.
10. 1220ten
11. 20131b
12. Using the flat = 1, 3 large cubes, 2 flats, 6 longs, 7 small cubes.
13. C
14. D
15. 420six
16. 58nine
17. 13.2 five
18. The small square is being used as the unit.
The five small squares can be traded for a five (long) leaving 0 ones. There are now six
longs. Five would be traded for a flat of 25, leaving one five (long). The answer is
therefore 110five.
19. A) 46 students, total number of students in C and D
6 students, difference in numbers of students in A and D
2 students, difference in numbers of students in B and C
B) (sample drawing)
46
2
C
D
6
B
A
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20.
21.
22.
23.
24.
C) (46 – 2) + 6 = 50 students for Sections A and B together
Reading “–” only as “take away” ignores the fact that other situations—comparison and
missing addend—might also involve subtraction.
A) Four
B) 12, because there are the two separate amounts; this situation involves an additive
comparison.
(3 + 2)  3  4 = 60, or possibly (3  3  4) + (2  3  4) = 36 + 24 = 60.
A) There are 432 books, from a repeated-addition multiplication. She could do this
problem by putting one book down 16 times, then a second book on top 16 times, etc.
This is the partitive or equal sharing interpretation of division.
B) This time Jasmine would put 27 books in a pile, then 27 in another pile, etc. She is
“taking-away” 27 books at a time, and she can do this 16 times. This is the quotitive or
measurement or repeated subtraction interpretation of division.
(Admittedly, if Jasmine is working in a bookstore, she probably knows enough to
simply divided 432 by 27 or by 16. But to do that, she must have some ideas about
division that she learned in school, doing problems of both types.)
A) How many 1/8 quart servings can you get from 2 quarts?
B) The store puts 1/8 pint on each cone. How many pints would they use for 16 cones?
C) The store stocks 24 different kinds of ice cream. Three-fourths of them are changed
every month. How many kinds are changed every month?
25.
In the second algorithm, the 23 actually is 2300, yielding 100 in the quotient. The 103 is
actually 1030, from which 920 (that is 23  40, which 460 twice, making the first
division easier) is subtracted, leaving 115 in both algorithms. In the first algorithm, 115
÷ 23 is done in two steps, and in one step in the second algorithm, both times yielding 5.
The first scaffolding algorithm could be done in multiple ways yielding the same result.
26. Positives—Practice reasoning about the operations and place values; if
student-generated, they can make sense to them; encourages a “make sense” view of
mathematics; can be more efficient in selected calculations. Negatives—Time away
from conventional algorithms, which always work; students who attempt to just
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memorize the techniques without understanding them will likely garble them.
27. Initially, with the small cube representing one, two flats. Second, trade a flat for ten
longs. Third, trade a long for ten small cubes, giving one flat, nine longs, and ten small
cubes. Fourth, take away (x-out, say) two small cubes and then six longs, leaving one
flat, three longs, and eight small cubes.
28. The circle 4 comes from the diagonal 2 + 0 + 2. The top 2 comes from 3  4(0) = 12(0)
so that 2 is describing a number of tens in the product. The 0 comes from 3  2 = 06
and shows that that partial product does not contribute a whole number of tens to the
product. The bottom 2 comes from 1(0)  2 = 2(0), showing that it is counting the
number of tens from that partial product.
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