8th Grade Math Prompt

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8th Grade Math Prompt4
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Problem No. 1

• Members of the Youth National Geographic Society
  spent 150 for a trip to Mammoth Cave. They paid
  10 for each member plus 15 for (1) adult
  chaperone.
• On the line below, write an equation that can be
  used to find the number of students who went to
  Mammoth Cave.
• SOLUTION
• Since you know that the total amount spent is
  150, that number has to go on the right hand
  side of the equation.
• You also know that only (1) adult came.

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• You do not know how many members came. Let X be
  the amount of members who came. But you do know
  how much each member had to pay. Your equation
  can now be written as follows
• 10X 15 150
• Now you must solve for X
• This is a two - step equation.

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• First you must get rid of the constant term so
  you subtract 15 from both sides of the equation.
• 10X 15 - 15 150 - 15
• 10X 135
• Second, you must eliminate the coefficient in
  front of the variable by dividing by 10,
• 10X/10 135/10
• Finally, you have X 13.5

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• Scoring was as follows
• 2 points Correct equation process to solve
• 1 point Correct equation OR process
• 0 point No correct answer or process

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Problem No. 2

• For the expression below, use the order of
  operations to solve the problem.
• 9 - 2 x 3(-2)
• SOLUTION
• It is helpful to remember the slogan Please
  Excuse My Dear Aunt Sally. Take the first letter
  of each word and P stands for parenthesis, E
  stands for exponents,

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• M stands for multiplication, D stands for
  division, A stands for addition, and S stands
  for subtraction. This the order that must be
  followed. So
• (-2)(3) -6
• so now the expression reduces to 9 - 6(-2)

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• (-6)(-2) 3
• Finally, you have 9 3 12

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• Scoring was as follows
• 2 points Correct process answer
• 1 point Correct process or answer
• 0 point No correct answer or process

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Problem No. 3

• A garden is in the shape of a rectangle with
  measurements of 20meters by 35 meters.
• If a gardener wants to put a fence around the
  perimeter of the garden, how many meters of
  fencing will be needed?
• SOLUTION

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• It is helpful to draw a picture with the
  dimensions.

35m
20m
20m
35m
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• The perimeter is the distance around the garden
  or the rectangle. So,
• (20 35)(2) (55)(2) 110 meters of fencing

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• Scoring was as follows
• 2 points Correct process answer
• 1 point Correct process or answer
• 0 point No correct answer or process

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Problem No. 4

• Juan is using 1 square foot tiles to cover the
  living room. The living room is 12 feet by 22
  feet. Estimate the number of tiles he will need
  to cover the living room floor.
• SOLUTION

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• Since we are dealing with area, we should first
  find the total area that needs to be covered.
• (12)(22) 264 square feet.
• Juan will need exactly 264 tiles since his tiles
  are 1 square foot. Since the problem asks you to
  estimate the amount tiles needed, you could have
  calculated the total area as (12)(20)

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• which comes out to 240 square feet. So Juan will
  need approximately 240 tiles.
• Other similar answers were accepted.

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• Scoring was as follows
• 2 points Correct process answer
• 1 point Correct process or answer
• 0 point No correct answer or process

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Problem No. 5

• The distance a unicycle travels during (1)
  revolution is equal to the circumference of the
  wheel. If a unicycle has a diameter of 70cm, how
  many centimeters will the unicycle travel during
  one revolution of the wheel?
• SOLUTION

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• From the formula sheet, we see the equation C
  2pr, but 2r is equal to the diameter, so C pd.
• Using the approximate value for p to be 3.14, C
  (3.14)(70), which comes out to be 219.8cm is the
  distance the unicycle will travel in one
  revolution.

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• Scoring was as follows
• 2 points Correct process answer
• 1 point Correct process or answer
• 0 point No correct answer or process

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Problem No. 6

• A man walks 50 meters heading north out of his
  house. At that point he turns east for 30 meters.
  He then remembers that he forgot some important
  papers at his house. He decides to save some time
  by running straight back to his house, the
  shortest distance possible, a straight line.
• Find the distance he ran back to his house to the
  nearest tenth of a meter.

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• SOLUTION
• First you should draw a picture of what is
  occurring.

N
30m
50m
House
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• Now that you have drawn a picture, you recognize
  that this is a problem using the PYTHAGOREAN
  THEOREM.
• First, write the equation a2 b2 c2.
• Assign a to be 30 and b to be 50
• Second, substitute the values for a and b
• 302 502 c2.

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• Third, expand out,
• 2500 900 c2.
• Fourth, perform the arithmetic,
• 3400 c2,
• Fifth, take the square root of both sides,
• SQRT(3400) c.
• Since the problem asks you to give an approximate
  answer to the nearest tenth,

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• you must find out between what two numbers the
  square root of 3400 is.
• You know that 502 2500, 602 3600. You know
  that your answer is between 50 and 60. Your
  estimate will be closer to 60 than 50 because you
  are only 200 away from 3600, while you are 900
  away from 2500.
• Try (58)(58) and you get 3364. Now try 592, and
  you find that comes out to be 3481.

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• You recognize that you are between 58 and 59.
  Again you are closer to 3381 because the
  difference is 19, while you are 81 from 3481. You
  guess that 58.3 will be the answer. So 58.32
  3398.89. This is very close to 3400. Your
  estimate is 58.3 meters, which is the shortest
  distance the man ran back to his house.

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• Scoring was as follows
• 2 points Correct process answer
• 1 point Correct process or answer
• 0 point No correct answer or process

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Problem No. 7

• Here are (2) points with coordinates (3,6) and
  (-2,1). On the graph below, graph the line that
  passes through these two points.
• SOLUTION

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y
.
6
5
4
3
2
.
x
1
6
5
4
3
2
1
0
-5
-4
-3
-2
-1
-6
-1
-2
-3
-4
-5
-6
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• Now that you have sketched the line that passes
  through the (2) points, we must determine the
  slope. The slope can be found by finding the rise
  over the run or can be found by the formula (Y2 -
  Y1)/(X2 - X1). Using the formula, we get (6 -
  1)/(3 - - 2), which is equal to (5)/(5) or 1.
  So the slope is equal to 1. To find the y -
  intercept, look back to the graph and see where
  the

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• line crosses the Y axis. You can see that this
  point is (0,3) or just plain 3.

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• Scoring was as follows
• 3 points Correct graph, slope y-intercept
• 2 points two of above
• 1 point one of above
• 0 point none of above