PSSA

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PSSA

• OPEN-ENDED MATH QUESTIONS

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DIRECTIONS

• To get full credit, you must do the following

1. Show or describe each step of your
work, even if you did it in your head
(mental math) or used a calculator.

• 2. Write an explanation stating the mathematical
  reason(s) why you chose each of your steps.

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DIRECTIONS

• Make two columns

• Put work on the left side

• Put explanation on the right side

• Show and number each step of the work

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• WORK

• EXPLANATION

Make sure ALL steps are explained using
This section is where you would show or describe
your work using
WORDS ONLY
NUMBERS
Use in the explanation.
MAGIC WORDS

• and

OPERATIONS
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USE MAGIC WORDS TO EXPLAIN YOUR WORK.
To figure out
To see
Because
To get

• To find

Therefore.
To show
Since
To determine
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Directions

• You must show your work and explain all your
  steps to get full credit.

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Sample 6th grade question

• Sarah wants to buy a radio that costs 120.00.
  It is on sale for 15 off. What will the discount
  be? What will the sale price of the radio be?
  If Sarah has 100 will she have enough?
• SHOW YOUR WORK and EXPLAIN YOUR REASONING.

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SOLUTION
1) I multiplied the cost of the radio by the
discount percent TO GET the discount amount.
1) 120.00 x .15 18.00
2) I subtracted the discount amount from the
original cost of the radio TO FIND the sale price
of the radio.
2) 120.00 18.00 102.00
3) I then compared the amount of money Sarah has
to the sale price TO FIGURE OUT if she has enough
money to buy the radio.
3) 102 gt 100
4) The discount amount of the radio will be
18.00. The sale price for the radio will be
102.00. Sarah does not have enough money
BECAUSE the sale price is greater than 100.
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Sample 7th grade question

• Mrs. Cunninghams class took a test on fractions
  and received the following results 82, 85, 92,
  97, 98, 86, 90, 72, 88, and 98.
• A. Construct a stem-and-leaf plot for these
  grades.
• B. Find the range in grades. Show all work.
• C. Find the mode of the scores.
• D. Find the score that is the median of the
  set of scores. Show all work.
• E. What is the AVERAGE test score on Mrs.
  Cunninghams fraction test? Show your work
  and EXPLAIN.

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SOLUTION
A)
B) Range 98 72 26
C) Mode 98
D) Median 88 90 2 89
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SOLUTION
1) I added the test scores TO FIND total of all
the scores on the fraction test
E) Average Mean

• 72 82 85 86 88 90 92 97 98 98
• 888

2) I divided the total of the scores by the
number of results in the set of scores TO
DETERMINE the average score for the class..
888 10 88.8
4) The average test score in the set of scores in
Mrs. Cunninghams Math class was 88.8 which
rounds to 89.
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Sample 8th grade question

• Four members of the Brown family took a trip from
  Pittsburgh to Harrisburg, a distance of 221
  miles. It took them 4 hours and 15 minutes to
  make the trip. The car required 13 gallons of
  gasoline at 3.10 per gallon. The turnpike toll
  was 11.00, and they spent 27.56 for food. What
  was the average cost per mile based on the total
  expenses of gas, food, and tolls for this trip?

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SOLUTION

• 1) I multiplied the price of gas and the number
  of gallons TO GET the total cost of gas.

• 1) 3.10 X 13 gal
• 40.30

2) I added the cost of gas, food and tolls
together TO FIND the total cost of the trip.
2) 40.30 27.56 11.00
78.86
3) I divided the total cost of the trip by the
number of miles and I FOUND the cost per mile.
3) 78.86 ? 221 miles ?
.3568325
4) SINCE I had many decimal places, I rounded to
the hundredth BECAUSE I wanted money.
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DESCRIBE
EXPLAIN
VS

• DESCRIPTION - I multiplied 3.10 and 13 and got
  40.30.

• EXPLANATION - I multiplied the price of gas
  per gallon and the number of gallons to get the
  total price for the gas.