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.

If you have “n + 5”
• Can “n” stand for “4”?
• Can “n” stand for “37”?
• Can “n” stand for “3r + 2”? 

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Which is larger, 2n or n + 2?

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Are these two equations equal to each other?
Why or Why not?
• 3x = 5 + 4            
• 3 + x = 5 + 4

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Find the next term:
a) 1, 2, 4, 8, …
b) 1, 3, 6, 10, …
c) 1, 4, 9, 16, …
d) 1, 1, 2, 3, 5, …

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If e + f = 8, what does e + f + g = ?
How do you know?

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ANSWER THE FOLLOWING:
65 + 49 =
58 + 79 =
126 + 199 =
Tell me how you solved this mentally.

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Jason uses a simple method to work out problems like 27 + 15 and 34 + 19 in his head.
                    Jason’s calculation (Picture)
1) Show how to use Jason’s method to work out 298 + 57
2) Show how to use Jason’s method to work out 35.7 + 9.8

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(No assessment provided.)

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Students are asked to interpret slope within the context of a real world situation.  Students are given a road sign from a street in Colorado that says, “7% grade ahead.”
Explain the meaning of the sign.

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Suppose that turtle and rabbit are racing to a pole and back.  Suppose turtle travels at 30 ft./sec. on the way there and 50 ft./sec. on the way back.  How fast would rabbit have to travel [at constant speed] to tie with turtle.

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