Download pt - key - ps num add subtract

PRACTICE TEST – Problem Solving, Numeration, Add & Subtract
ANSWER KEY
1.
Steps from Private Eye:
o
Information summary.
o
Identify the question.
o
Investigate strategies.
o
Implement a strategy.
o
Improvement.
Strategies:
o
Make a drawing or diagram.
o
Guess and check.
o
Make a table / chart.
o
Use a model.
o
Work backwards.
o
Find a pattern.
o
Use algebra.
o
Choose an operation.
o
Make it simpler.
o
Identify a subgoal.
2.
4
8
6
3
9
2
7
1
5
2. Nine has to be on the second row since 3 is above it and 2 is
below it. It has to be in the very center since 7 is to the right
of 3. This leaves 6 and 4. 4 can’t be next to 2, so 4 is in the
upper left, leaving 6 in the lower left.
3. 5 + 7 – 3 = 9
4. 3 + 11 = 14. 14 is four less than the number, so the number is 18.
5. Let the girls be A, B, C, D, E. One round would consist of AB, AC, AD, AE, BC, BD, BE, CD, CE, DE ->
10 games. So double this: total of 20 games.
6. 765
7. Sum of two digits = 10 implies the following pairs: 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5. Difference = 4 implies
3 and 7. Dividing by 10 leaves a remainder less than 5 implies 73 (remainder 3), not 37 (remainder 7).
8. There may be more, but here are the ones I found: ABF, ABE, ABG, ABD, AFE, AGD, ACE, ACD, BHE,
BDE, CFE, CGH, CHD, CGD, CED, DHE.
9. Greens cannot have a green house or a brown one (bc Browns can’t have a brown car). Therefore, the
Greens’ house is white, so the Browns’ car is white and the Greens’ car is brown and the Browns’ house
is green. This leaves the Whites with a brown house and a green car.
10. The fifth figure is a stack (top to bottom) 1, 3, 5, 7, 9 squares for a total of 25 squares. The 6 th figure is a
stack (from top to bottom) 1, 3, 5, 7, 9, 11 squares for a total of 36 squares.
Figure
Total
1
1
2
4
3
9
4
16
5
25
6
36
10th
100
Nth
N2
11. Make four columns with the digits 0 through 9. Cross out all odds. The 1st digit is 8 (8000 is the only
possibility > 7000) This sets the tens digit as 2 (sum of thousands and tens = 10). This leaves 4 and 6
for the hundreds and ones digits. To be divisible by 4, the last two digits must be divisible by 4. Looking
at 24 or 26, the choice is 24, so the ones digit is 4, leaving the hundreds digit as 6. ANSWER: 8624
12. Under ABCDE, list the digits 0 through 9 in columns. Under ABC, mark out all evens; under DE, mark
out all odds. Under B, mark out 1 and under C, mark out 9, since B > C. The only square numbers under
A and B are 1 and 9. The only prime numbers under C are 3, 5, 7. The only prime number under D and
E is 2, so both D and E are 2. Since A – C = 2, then A is 9 and C is 7. B > C leaves B as 9 also. The zip
code is 99722.
13. a. {4, 5}
b. {1, 2, 3, 4, 5, 6, 7, 8}
c. {6, 7, 8, 9, 0}
d. (9, 0}
e. {6, 7, 8}
14.
Little John
R L R L
|---|---|---|---|---|---|---|---|---|
Friar Tuck R L R L R L R L R
15. a. L = 4, G = 2, C = 2
4 steps
6 steps
b. L = 5, G = 2, C = 3
16.
17. Complete the table:
Cubes in tail
Cubes in all
1
10
2
11
3
12
10
19
100
109
N
9+N
18. Since 5/8 have less than 5 years experience, 3/8 have 5 or more years. So 15 teachers represent 3/8 of the
faculty. This means that 5 teachers represent 1/8 so 40 teachers represent 8/8 or the entire faculty.
NUMERATION
19. Number: SIX
Numeral: 6
Set:

20. A. 5 ten-thousands = 50,000 B. 5 ones = 5 C. 5 millions = 5,000,000
D. 5 hundreds = 500
21. A. ■■■■■││●●● B. five hundred twenty-three
C. 5 hundreds + 2 tens + 3 ones
22. A. 1,234,568,000
B. 1,235,000,000
C. 1,234,567,900
D. 1,234,570,000
23. 13510 = 20134 The place values for base 4, from right to left, are ones, fours, sixteens (4 sets of 4), sixty-fours (4
sets of 16). There are two sets of 64 (2 x 64 = 128) in 135, leaving 7 left. There are no sets of 16 and one set of 4
with 3 left over.
24. 26710 = 11236 The place values for base six, from right to left, are ones, six, thirty-six (6 sets of 6), two hundred
sixteen (6 sets of 36). There is one set of 216 in 267, leaving 51 left. There is one set of 36 in 51, leaving 15. There
are two sets of 6 in 15, with 3 left (ones).
25. 76
The place values for base 7, from right to left, are ones, sevens, forty-nines (7 sets of 7). 1367 means there
is 1 forty-nine, 3 sevens, and 6 ones or 1x49 + 3 x 7 + 6 x 1 (expanded form, base 7) = 49 + 21 + 6 = 76 base 10.
26.
578 The place values for base 3, from right to left, are ones, threes, nines (3 sets of 3),
twenty-sevens (3 sets of 9), eighty-ones (3 sets of 27), and two-hundred-forty-threes (3 sets of
81). 210102 base 3 means 2 groups of two-hundred-forty-threes, one group of eighty-ones, no
groups of twenty-sevens, one group of nine, no groups of threes, and two ones or 2 x 243 + 1 x
81 + 0 x 27 + 1 x 9 + 0 x 3 + 2 x 1 (expanded form, base 3) = 486 + 81 + 9 + 2 = 578 base 10
27. One-to-one correspondence: The matching of a quantity objects with the correct number concept.
Cardinal number is a numeral used to indicate a quantity, i.e. answer to “how many” or “how much.”
Nominal number is a numeral used to identify (name) an object, i.e. a house number.
Ordinal number is a numeral used to place an item in order, i.e., first, second, twenty-third.
Addends: number being added
Sum: the answer in addition
Difference: the answer in subtraction
29.
30.
1
512
+ 278
790
 | 
  | | | | | | |         exchange for |
7 hundreds + 9 tens + 0 ones
10
4 0 12
512
     |  
-278
 exchange for          
234
Exchange for | | | | | | | | | |
2 hundreds + 3 tens + 4 ones
31. 5 + ? = 12 → 12 – 5 = 7
1 2 3 4 5 6 7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
There is a difference of 7 between 12 and 5.
32. - 35. See Textbook Chapter 7 Meaning of Operations or the handout from class for examples.