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Fourth graders in New York State answered this question about multiply whole numbers on their math exams this spring.

Along with this year’s test scores — lower than in the past, if you haven’t heard — the State Education Department also released test questions today.

The items posted on the department’s educator resource website, EngageNY, represent a quarter of the questions that students faced when they sat down to take Common Core-aligned exams this spring. Usually the state keeps test questions under wraps, but this year it decided to publish some of them because of the new, tougher standards.

Critics of the state’s testing practices say transparency can’t be achieved if the entire test isn’t released, and we don’t know how well students did on each of the questions that have been released. Still, they offer a view into the skills and practices that students were asked to demonstrate, and a discussion of test scores without a discussion of what counted is thin indeed.

That’s why we’ve collected a sample of the questions asked at each grade level on the state’s math exams. (EngageNY has more questions, in-depth explanations about how to solve and teach each problem, and, for questions that asked students to show their work, examples of student responses.) We’re hoping to spur a conversation about the questions that’s even better than the one that already happened on Twitter today.

Check out the test questions below, then let us know in the comments what your favorite and least favorite is and why. We’ll be highlighting insightful responses on Thursday.

In third grade, 33.1 percent of city students tested proficient in math.

This problem is about representing fractions on a number line:

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This is a two-step word problem using addition and subtraction:

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This problem is about whole-number quotients.

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In fourth grade, 35.2 percent of city students met the state’s proficiency standard in math.

This is an equivalent fraction problem using visual models.

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This problem asks students to compare fractions:

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This problem asks students to multiply two-digit whole numbers:
Screen shot 2013-08-07 at 11.53.36 AMIn fifth grade, 29.6 percent of city students met the state’s math proficiency standard.

This problem is about adding and subtracting fractions with unlike denominators.

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This problem is about understanding multi-digit numbers:

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 This problem is about expanding a base-ten numeral:

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In sixth grade, 28.8 percent of city students hit the state’s proficiency standard.

This problem is about equivalent ratios:

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 This problem is about inequalities represented on a number line:

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 This problem is about equivalent expressions:

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This problem is about absolute value and coordinates:

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 This is a word problem that involves dividing fractions:

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In seventh grade, 25.7 percent of city students were proficient in math.

This is a problem about probability:

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This is a word problem that uses equations:

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This is a word problem involving unit rates:

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This is a problem involving proportional relationships:

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In eighth grade, 29.6 percent of students were proficient in math.

This is a linear equation problem:

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This a problem that involves understanding how to graph the function of x:

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This is a problem about integer exponents:

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 This word problem involves measuring the volume of a cylinder:

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This problem is about finding relative frequencies using data:

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