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Initial Assessment
1) What is 1 / 2 - 1 / 3 ? 3/6 - 2/6 = 1/6
2) What is 2 / 3 of 1 / 4 ? 2/3 x 1/4 = 1/6
3) What is 5% of 80? 5/100 x 80 = 4
4) If a # b = 2 times b - a, what is 4 # 7? 2 x 7 - 4 = 10
5) What is 6 * 5 * 4 * 3 * 2 where (a * b = a times b)? 30 x 12 x 2 = 720
6) What is -6 divided by 2 ? -3
7) What is 5.2 - 8.71 ? -3.51
8) If Joe is 3 years less than twice Sally's age, and Sally will be 5 one year from today, how old is Joe? 2 (5 - 1) - 3 = 5 years old
9) List all the factors of 36.
1, 2, 3, 4, 6, 9, 12, 18, 36 (make a factor tree, or find pairs)
10) Which of the numbers in this set are prime? {5, 6, 7, 9, 10, 21, 23, 27}
answer: 5, 7, 23 (primes have only 1 and themselves as factors)
11) What is the average of 4, 6, and 12? (4 + 6 + 12 ) / 3 = 7 1/3
12) What is the average of 4, 6, and -7? (4 + 6 - 7) / 3 = 1
13) If my car gets 40 miles per gallon, how many gallons will I burn if I drive 125 miles?
You can drive 40 miles with 1 gallon, 120 miles with 3. answer is 3 1/8 gallons.
14) What is 3^5 (this was printed correctly on the actual test) ?
3 * 3* 3* 3* 3 = 9 * 9 * 3 = 81 * 3 = 243
15) If f(x) = 7x + 5, what is f(4) ?
f(4) = 7 times 4 + 5 = 33
16) What is 100,000 times 500 divided by 10,000?
100,000/10,000 = 10, so 10 * 500 = 5,000
17) What is x if 17x + 3 = 51 + x ?
16x = 48, so x = 3
18) What is the area of a right triangle with length 18 inches and height 6 inches? (include units)
Draw a rectangle with length 18 and height 6, then half its area to get 54 square inches.
19) What is (4 - 4) / (2 + 1) ?
4 - 4 is 0, so the answer is 0 no matter what the denominator is.
20) Estimate how many pieces of pasta are in the jar at the front of the room.
There were exactly 430 pieces.
full credit for any gues that was in the range 300-600 inclusive.
1/2 credit if within 200-900.
Interesting to note that the average of all the students guesses was 410.
What are some ways we could quickly determine how many pieces of pasta are in the jar without counting each one? Suppose it was a large barrel instead of a jar.
- We could acvcurately weigh 100 pieces, then weigh the barrel with the pasta and subtract the weight of just the barrel. 100 * The weight of the pasta/(weight of 100 pieces) = number of pieces in the barrel.
- I could pour out a cup of pasta for each person in the room to count - then sum the totals from each person. This uses students like parallel processors.
2) What is 2 / 3 of 1 / 4 ? 2/3 x 1/4 = 1/6
3) What is 5% of 80? 5/100 x 80 = 4
4) If a # b = 2 times b - a, what is 4 # 7? 2 x 7 - 4 = 10
5) What is 6 * 5 * 4 * 3 * 2 where (a * b = a times b)? 30 x 12 x 2 = 720
6) What is -6 divided by 2 ? -3
7) What is 5.2 - 8.71 ? -3.51
8) If Joe is 3 years less than twice Sally's age, and Sally will be 5 one year from today, how old is Joe? 2 (5 - 1) - 3 = 5 years old
9) List all the factors of 36.
1, 2, 3, 4, 6, 9, 12, 18, 36 (make a factor tree, or find pairs)
10) Which of the numbers in this set are prime? {5, 6, 7, 9, 10, 21, 23, 27}
answer: 5, 7, 23 (primes have only 1 and themselves as factors)
11) What is the average of 4, 6, and 12? (4 + 6 + 12 ) / 3 = 7 1/3
12) What is the average of 4, 6, and -7? (4 + 6 - 7) / 3 = 1
13) If my car gets 40 miles per gallon, how many gallons will I burn if I drive 125 miles?
You can drive 40 miles with 1 gallon, 120 miles with 3. answer is 3 1/8 gallons.
14) What is 3^5 (this was printed correctly on the actual test) ?
3 * 3* 3* 3* 3 = 9 * 9 * 3 = 81 * 3 = 243
15) If f(x) = 7x + 5, what is f(4) ?
f(4) = 7 times 4 + 5 = 33
16) What is 100,000 times 500 divided by 10,000?
100,000/10,000 = 10, so 10 * 500 = 5,000
17) What is x if 17x + 3 = 51 + x ?
16x = 48, so x = 3
18) What is the area of a right triangle with length 18 inches and height 6 inches? (include units)
Draw a rectangle with length 18 and height 6, then half its area to get 54 square inches.
19) What is (4 - 4) / (2 + 1) ?
4 - 4 is 0, so the answer is 0 no matter what the denominator is.
20) Estimate how many pieces of pasta are in the jar at the front of the room.
There were exactly 430 pieces.
full credit for any gues that was in the range 300-600 inclusive.
1/2 credit if within 200-900.
Interesting to note that the average of all the students guesses was 410.
What are some ways we could quickly determine how many pieces of pasta are in the jar without counting each one? Suppose it was a large barrel instead of a jar.
- We could acvcurately weigh 100 pieces, then weigh the barrel with the pasta and subtract the weight of just the barrel. 100 * The weight of the pasta/(weight of 100 pieces) = number of pieces in the barrel.
- I could pour out a cup of pasta for each person in the room to count - then sum the totals from each person. This uses students like parallel processors.