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.

Part 1: 
You have 2 gears on your table, one with 8 teeth and one with 12 teeth. Answer the following questions:
1. If you turn the small gear a certain number of times, does the big gear turn more revolutions, fewer, or the same amount? How can you tell?

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Solve for x without using a pencil.

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1) 15 – x =10
2) 6 – x = 8
3) -3 –  x = 5
4) -x = 6
5) 2x – 4 = x + 2
6) -5x + 6 = 2x + 20
7) 2– 3x + 6 = 2x – 12
8) -2( 3x – 4) = -4x – 10

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1. Solve the equation 2(3x+4) = 6x + 9
2. After solving, could you solve it in another way?
3. What would be the relationship between the graphs of each side of the equation?

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1. Solve the equation 2(3x+4) = 6x + 8
2. After solving, could you solve it in another way?
3. What would be the relationship between the graphs of each side of the equation?*

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1. Solve the equation 2x+3=5x−9.
2. After solving, could you solve it in another way?
3. What would be the relationship between the graphs of each side of the equation?

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Missing assessment problem.

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(x+3)2 + 4(x+3) = 45

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Paper Folding Problem (exponential)
Fold this piece of paper in half and then open it up. How many regions were made?
a) Fold the paper in half twice. How many regions? How many regions will be made with three such folds?

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Concert Hall Problem (arithmetic sequence)
The first row of a concert hall has 10 seats. Each row thereafter has 2 more seats than the row in front of it.
a) How many seats are in Row 10? (If student had difficulty, ask how many seats in Rows 2, 3, and 4.)

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