Grade 7 Number Sense 1'3

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Grade 7 Number Sense 1.3

• Convert fractions to decimals and percents and
  use these representations in estimations,
  computations, and applications.

• At a recent school play, 504 of the 840 seats
  were filled. What percent of the seats were
  empty?
• A. 33.65 B. 40 C. 50.4 D. 60

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Answer to NS 1.3
You have to write 504 of the 840 seats as a
fraction
You then convert it to a percent. This will give
the percent of the seats that are filled, 60.
But the question is asking for the percent of the
seats that are empty. Therefore the correct
response is 100 60 40.
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Grade 7 Number Sense 1.6

• Calculate the percentage of increases and
  decreases of a quantity.
• Between 600am and noon, the temperature went
  from 45 degrees to 90 degrees. By what
  percentage did the temperature increase between
  600 A.M. and noon?
• A) 45 B) 50 C) 55 D) 100

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Answer to NS 1.6
The percentage of increase is the ratio of the
amount of change to the original, written as a
percent. Therefore, the increase, 45 degrees,
divided by the original temperature, 45 degrees,
equals 1 or 100.
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Grade 7 Number Sense 1.7
Solve problems that involve discounts, markups,
commissions, and profit and compute simple and
compound interest.
Mr. Yee invested 2,000 in a savings account that
pays an annual interest rate of 4 compounded
twice a year. If Mr. Yee does not deposit or
withdraw any money, how much will he have in the
bank after one year? A) 2,080.00 B)
2,080.80 C) 2,160.00D) 2,163.20
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Answer to NS 1.7
If the interest is computed twice a year then the
0.4 rate must be divided by 2. Also, after the
interest is calculated, it must be added on to
the deposit, becoming the principal for the next
compounding period. Therefore, 2000(.02)
40 2000 40 2040, after 6 months. Now
2040 (0.2) 40.80 2040 40.80 2080.80.
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Grade 7 Number Sense 2.1
Understand negative whole-number exponents.
Multiply and divide expressions involving
exponents with a common base.
A) 3 B) C) D) 3
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Answer to NS 2.1
Simplify each expression Or
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Grade 7 Number Sense 2.2
Add and subtract fractions by using factoring to
find common denominators.
Which of the following can be used to compute
A) C) B) D)
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Answer to NS 2.2
Factored form of the common denominator and then
multiply each fraction by one, ie.,
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Grade 7 Algebra and Functions 2.1
Interpret positive whole-number powers as
repeated multiplication and negative whole-number
powers as repeated division or multiplication by
the multiplicative inverse. Simplify and
evaluate expressions that include exponents.
Simplify the expression A) B)
C) D)
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Answer to AF 2.1
The base is a variable and the exponent does not
apply to the 2. To make the negative exponent
positive, it goes below the fraction bar
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Grade 7 Algebra and Functions 4.1
Solve two-step linear equations and inequalities
in one variable over the rational numbers,
interpret the solution or solutions in the
context from which they arose, and verify the
reasonableness of the results.

• Before each game, the Harbor High Mudcats
  sell programs for 1.00 per program. To print
  the programs, the printer charges 60 plus 0.20
  per program. How many programs does the team
  have to sell to make a profit of 200?
• 250 programs B) 300 programs
• C) 325 programs D) 350 programs

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Answer to AF 4.1
One equation that you could use to solve this
problem is 200 1x 0.2x 60 To solve the
problem, you add 60 200 260 and then divide
by 0.8 to get 325 programs.
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Grade 7 Algebra and Functions 4.2
Solve multi-step problems involving rate, average
speed, distance, and time or a direct variation.
A person drove for 6 hours at an average speed of
45 miles per hour (mph) and for 9 hours at an
average speed 0f 55 mph. Find the average speed
for the entire trip. A) 50 mph B) 51 mph C) 52
mph D) 53 mph
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Answer to AF 4.2
The average speed is for the entire trip. The
total miles must be divided by the total time. 6
hours _at_ 45 mph 270 miles and 9 hours _at_ 55 mph
495 for a total of 765 miles. The total time is 6
9 15 hours. Therefore, the average speed for
the entire trip is 765 miles 15 hours
51 mph.
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Grade 7 Statistics, Data Analysis, and
Probability 1.3
Understand the meaning of, and be able to compute
the minimum, the lower quartile, the median, the
upper quartile, and the maximum of a data set.

• Twenty students took a math test. The upper
  quartile value of the test scores is the median
  of the
• Top four scores
• Top five scores
• Top ten scores
• Middle five scores

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Answer to SDAP 1.3
Since 20 students took the math test, the median
divides the data into two sets of ten each. The
upper quartile value is the median of the upper
half of the data, which in this item is the
median of the top ten scores.
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Grade 7 Measurement and Geometry 1.1
Compare weights, capacities, geometric measures,
times, and temperatures within and between
measurement systems (e.g., miles per hour and
feet per second, cubic inches to cubic
centimeters)

• Order the following three speeds from fastest to
  slowest
• 3,100 yd/hr, 160 ft/min, 9,200 ft/ht
• 9,200 ft/hr 3,100 yd/hr 160 ft/min
• 9,200 ft/hr 160 ft/min 3,100 yd/hr
• 160 ft/min 9,200 ft/hr 3,100 yd/hr
• 160 ft/min 3,100 yd/hr 9,200 ft/hr

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Grade 7 Measurement and Geometry 2.3
Compute the length of the perimeter, the surface
area of the faces, and the volume of a
three-dimensional object built from rectangular
solids. Understand that when the lengths of all
dimensions are multiplied by a scale factor, the
surface area is multiplied by the square of the
scale factor and the volume is multiplied by the
cube of the scale factor.
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In the figure above, an edge of the larger cube
is 3 times the edge of the smaller cube. What is
the ratio of the surface area of the smaller cube
to that of the larger cube?
A) 1 3 B) 1 9 C) 1 12 D) 1 27
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Answer to MG 2.3
The ratio of the surface areas is the square of
the ratio of the lengths. Therefore, since the
ratio of the lengths is the ratio of the surface
areas is .
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Grade Measurement and Geometry 2.4
Relate the changes in measurement with a change
of scale to the units used (e.g., square inches,
cubic feet and to conversions between units (1
square foot 144 square inches or 1ft2 144
in2, 1 cubic inch is approximately 16.38 cubic
centimeters or 1 in3 16.38cm3.
How many square feet are in 5 square yards? A)
15 B) 25 C) 45 D) 60
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Answer to MG 2.4
Changing from square yards to square feet is
different than converting yards to feet. Each
square yard is equal to 9 square feet, 5 (9) 45
square feet.
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Grade 7 Mathematical Reasoning 2.4
Make and test conjectures by using both inductive
and deductive reasoning.
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• While preparing for the local marathon, Angela
  made the following statements
• If I do not stretch before the race, I will get
  muscle cramps.
• If I get muscle cramps, it will be too painful
  to run.
• If it is too painful to run, I will not finish
  the race.
• Based on Angelas statements, what can be
  concluded
• If she finishes the race, Angela stretched before
  the race.
• If she did not finish the race, Angela had
  painful muscle cramps.
• If she stretches before the race, Angela will
  finish the race.
• If she has muscle cramps, Angela did not stretch
  before the race.

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Answer to MR 2.4
Using logic, you know that if Angela does not
stretch before the race, then she will not finish
the race. Therefore, if she finishes the race
then she must have stretched before the race.
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Grade 7 Number Sense 1.1

• Write each number in scientific notation.
• 62,000 ______________
• 2. 0.000000824 ______________

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Answer to NS 1.1

• 62,000 6.2 x 104
• 2. 0.000000824 8.24 x 10-7

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Grade 7 Number Sense 1.1
Rewrite the scientific notation numbers below in
standard decimal notation. 1. 4.385 x 10-3
______________ 2. 1.8 x 105 ______________
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Answer to Grade 7 NS 1.1

• Rewrite the scientific notation numbers below in
  standard decimal notation.
• 4.385 x 10-3 .004385
• 2. 1.8 x 105 180,000

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Grade 7 Number Sense 1.2

• Between which 2 whole numbers does the square
  root lie?
• A. 60 B. 12 C.
  115

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Answer to Grade 7 NS 1.2