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December 2015 Vol. 23. No. 3 Focus on Standardized Tests

Theme articles

Can you solve these 6th-grade math questions?

By the Notebook on Dec 1, 2015 02:45 PM

The following multiple-choice questions are from a selection of sample test items provided by the Pennsylvania Department of Education for the 6th-grade PSSA exam in math. Calculator use is permitted. The exam also includes open-ended questions where students are expected to explain their answers.


1. Emily is making bows using ribbon. She has two pieces of ribbon to use. One is 23 yards long. The other is 4 1/4 yards long. She needs 1 5/6 yards of ribbon to make each bow. What is the greatest number of bows Emily can make?

A. 12

B. 14

C. 15

D. 19


2. Gracie is rewriting the expression (24 + 40) as an integer times the sum of two integers. By factoring out a 2, she knows she can rewrite the expression as 2 times the sum of two integers. What are all the other numbers greater than 2 that Gracie can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers?

A. 4, 8

B. 4, 6, 8

C. 3, 5, 6, 10, 12, 20

D. 3, 4, 5, 6, 8, 10, 12, 20


3. Quincy and Ray keep track of their scores in a game. The person with the greater score is winning the game. Quincy has a score of –70, and Ray has a score of –60. Which statement best explains who is winning and how many points away from 0 that person is?

A. Ray is winning and needs to lose 60 points to get to 0.

B. Ray is winning and needs to gain 60 points to get to 0.

C. Quincy is winning and needs to lose 70 points to get to 0.

D. Quincy is winning and needs to gain 70 points to get to 0.


4. At a factory, a machine tests 1 out of every 75 items produced for quality. The machine requires a safety check after testing 450 items. The factory produces 303,750 items each month. How many safety checks does the machine require each month?

A. 6

B. 9

C. 50

D. 54


5. When a farmer harvests chicken eggs, he expects 2% of the eggs to be cracked. How many eggs would the farmer expect to be cracked when harvesting 350 eggs?

A. 3

B. 7

C. 18

D. 70


6. Alex and Payton each have a favorite pancake recipe.

• Alex’s recipe uses 7 1/2 cups of flour for 5 batches.

• Payton’s recipe uses 3/4 cup of flour more per batch than Alex’s recipe uses per batch.

Which expression can be used to determine the number of cups of flour used to make x batches of Payton’s pancake recipe?

A. 2 1/4 x

B. 8 1/4 x

C. 1 1/2 x + 3/4

D. 7 1/2 x + 3/4  


7. This soccer season, Gavin scored 9 fewer than 3 times the number of goals that Rico scored. Rico scored 12 goals. The value of which expression is equivalent to the number of goals Gavin scored this soccer season?

A. 3(4 – 3)

B. 3(12 – 9)

C. 9(4 – 1)

D. 9(36 – 1)


8. Which expression uses exactly three terms and is equivalent to 6(2 + x + x + y)?

A. 8 + 8x + 7y

B. 12 + 12x + 6y

C. 8 + 6x + 6x + 6y

D. 12 + 6x + 6x + 6y


9. Michael has $68. Craig has $24 less than Michael has. Michael spends $20 on a new hat. The solution of which equation represents the amount of money (x), in dollars, Craig has after Michael buys the hat?


A. x + 4 = 48

B. x + 4 = 68

C. x + 20 = 44

D. x + 24 = 48


10. The heights, rounded to the nearest foot, of the trees in a park are listed below.

23 13 8 52 26 42 48 52

What is the median of the tree heights?

A. 33 feet

B. 34 feet

C. 39 feet

D. 44 feet





1. B;  2. A;  3. B;  4. B;  5. B;  6. A;  7. C;  8. B;  9. A;  10. B





Comments (23)

Submitted by Anonymous (not verified) on December 1, 2015 4:50 pm

No, I could not solve most of the problems. The thinking required to solve them is way above the reasoning ability of an 11 year old. This test was not constructed by an educator who knows the abilities of sixth graders. It was designed to make sure that our students fail it.


Submitted by Differential equations (not verified) on December 2, 2015 5:46 am

I HOPE you can figure out what is 2% of 350.  Or if you add 60 to a -60 then the answer is zero.  Or how to get a median from a group of numbers.   And if these questions are way beyond the thinking of an 11-yr old they better hit the books and study before they get themselves into massive debt on a student loan to go to college.  They better understand interest rates and repayment schedules and the fact that you can't declare bankruptcy on a student loan.

Submitted by Anonymous (not verified) on December 1, 2015 7:31 pm

I was a 6th grade teacher for many years and had to get the kids ready for this testing. The problem is a manifold issue as I see it. One, most kids are not doing math at this level and therefore would not be successful. Two, the social promotion policies and curriculum force teachers to teach mist of the content to the below basic kids. If many have been promoted without mastering even 3rd or 4th grade math, how does anyone expect them to pass this? Thirdly, there is not even teacher professional development and chances for mastery of subject material before being forced to try to teach this to the students. If administrators, lawmakers, policy makers, union bashers, and parents took this test then they would be more understanding and hear the voices of those who work the closest to the kids: the teachers!!! Lastly, depending on where I live, ie come from, especially if it's poverty, who the hell cares about any of these problems???? Not one of my kids did!!! And yes I failed it ( I cheated by looking at the answers) and I gave a Masters degree!

Submitted by Taxpayer (not verified) on December 1, 2015 8:54 pm

I got 100%. Any "teacher" who couldn't pass that shouldn't be teaching.

Submitted by Anonymous (not verified) on December 1, 2015 8:30 pm

You are a big fat liar if you say that you got 100%.  Again, if you think you can teach better than the professionals have a go at it.

Submitted by Anonymous (not verified) on December 1, 2015 8:37 pm

Give  this test to your own eleven old child, then post the results. If he gets all the answers right,  forget  seventh grade through high school and skip him right on to college.

Submitted by Differential equations (not verified) on December 2, 2015 5:30 am

Um, right.  Shouldn't he be learning quadratic equations, inequalities, x and y graphing, and polynomials before he starts college?   These questions aren't exactly higher math.  

Submitted by Dan Fitzsimmons (not verified) on December 2, 2015 7:55 am

Seriously? You did that in sixth grade? I don't remember doing that until, at least, 8th grade, and I went to Masterman (for middle and high school). So you really think they should be ready to do high school and college level math in sixth grade and understand how the economy works? Did you? You're missing the point in your arguments. These are tests being given to sixth graders, not high schoolers. They're 11/12 years old. People are not saying that students shouldn't ever know how to do these problems, they're saying that it's too much for a kid in sixth grade. If you can't see that, then you live in some fantasy dream world.

Why not use your name when you post? Are you afraid of something?

Submitted by Anonymous (not verified) on December 2, 2015 8:52 am

Yes he should before college, but in ALGEBRA class, in high school, not in 6th grade. 

Submitted by Differential equations (not verified) on December 2, 2015 6:40 am

I can certainly understand why teachers insist their pensions are affordable.  If they can't do these problems then they probably don't get concepts like the present value of money or how much money is needed to create a stream of payments over a given number of years (ie. a retirement annuity)  or why PSERS' assumption of 8% returns is equivalent to cooking the books.  Check out that story in the NY TImes about that 48-yr old teacher who is $400,000 in debt.  She must have flunked sixth grade math.  ("Student Debt in America, Lend with a smile, collect with a fist")

Submitted by Differential equations (not verified) on December 2, 2015 5:51 am

Yes these are slightly challenging problems where it's important to READ the problem carefully and ignore information that doesn't affect the answer, or to remember facts that are plainly stated.  For instance in #9 you can ignore what Michael spends on the hat, and remember that Craig has $44.  So the only possible answer is A.   I have no idea how a test like this could be part of a "Batman" plot to privatize schools.  

There would be no pension crisis if lawmakers and union bosses  understood what numbers you can and cannot ignore.  For instance if the average gain in the stock market over the last 100 years is 6%, you can't change that number and assume Madoff 8% gains in the pension fund investments.    If 10% gains occurred during the dot-com boom, you have to  ignore that because that was only a bubble (that later blew up).   Of course some people always think they can beat the odds, whether it's playing slots at Foxwoods, betting on horses, or cooking the PSERS books.  Big mistake.  

Submitted by Anonymous (not verified) on December 2, 2015 8:17 am

Don't attribute adult problem solving ability to an eleven year olds's brain. At eleven, kids are mastering the basics of math and developing math problem solving skills. The context of these problems are not familiar in their lives. This test is three to four grade levels above 6th grade.

None of the adults responding to this article were required to take a test like this in the 6th grade.

Submitted by Anonymous (not verified) on December 2, 2015 9:19 am

Consider a learning support student, who is reading below grade level.  Even with accommodations, they look at these tests and give up. They are destined to fail even before they begin.

Submitted by Anonymous (not verified) on December 2, 2015 1:16 pm

The same can be said for ELLs.  

Submitted by Umroh Murah (not verified) on March 6, 2017 4:24 am

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Submitted by sâm hàn quốc (not verified) on September 10, 2017 9:45 pm

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