Formative Assessments

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Studies on algebraic thinking typically include assessment problems that are used by researchers to elicit a range of students' understanding and misconceptions. These problems are collected here and can be useful tools for teachers' formative assessment of students' comprehension of algebraic concepts.

Given 5a = b + 5, which is larger: a or b?

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Is there a value for x that will make the following statement true?

(6x – 8 – 15x) + 12 > (6x – 8 – 15x) + 6 

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Is there a value for x that will make (2x – 6)(x – 3) < 0 true? 

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p and q are odd integers between 20 and 50.

For these values, is 5p–q>2p+15 always true, sometimes true or never true? 

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For the equation 2(x + 1) + 4 = 12, identify all possible steps that could be done next.

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3( x + 2) = 12
x + 2 = 4
a) What step did the student use to get from the first line to the second line?
b)  Do you think that this way of starting this problem is (a) a very good way; (b) OK to do, but not a very good way; (c) not OK to do?

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Solve this equation in two different ways:
4(x + 2) = 12

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If m is a positive number, which of these is equivalent to (the same as) m + m + m + m?
a) 4m     b) m4     c) 4(m + 1)     d) m + 4

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Here are two equations:
213x + 476 = 984
213x + 476 + 4 = 984 + 4
•Without solving either equation, what can you say about the answers to these equations?
a) Both answers are the same   b) Both answers are different     c) I can’t tell without doing the math

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Question 1a: Write a story problem that can be formulated by the equation: x+5=8.
Question 1b: Reword your story problem so that it can be formulated by the equation 2x+5=8.
Question 1c: Reword your story problem so that it can be formulated by the equation 2x-5=8.

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