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.

2. If f(1)=5 and f(x+1)=2f(x), find the value of f(3).

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The graph of y=x^2 - 2x is at right. Use this graph and any other lines which you may need to add to it to solve the equations given. Briefly explain your method.
x^2 - 2x = 3
x^2 - 2x = x
(needs image)

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Given is a sketch of the Bet-Shean Temple (BST) restoration (Stern, 1992).
The sketch is drawn on a scale of 1:200.
a) What are the dimensions of the main hall of the BST in reality?

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The Graphs at right represent a function in three subdomains (note that the scales are not the same in the three graphs).
Draw the graph of the function in one coordinate system.

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Imagine water flowing through a pipe into a container. The following equations show how the water level or height of the water (w) in the container was related to the number of minutes (t) when the pipe was opened for 10 minutes.
w = t + 8 for the first four minutes (t = 0 to 4)

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(Need 1-4)
5. Does there exist a function all of whose values are equal to each other?
6. Does there exist a function whose values for integral numbers are non-integral and whose values for non-integral numbers are integral?
7. What is a function, in your opinion?

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A. The first two entries in a table of numbers are given on the right. Write five more numbers in the table to create a linear relationship. Write five more numbers in the table to create an exponential relationship. Write five more numbers in the table to create a quadratic relationship.

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Students are given a worksheet in a dynamic geometry package.  The construction, hidden from the students, is as follows: given two points A and B, construct the line through them.  Take a third point, P, and construct H, the foot of the perpendicular from P to line AB.  Students can drag any of

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The two graphs at right are y= x^2 - kx and y=3.  Use the information given to solve the following equations for x.
x^2 -kx = 3
x^2 - kx = 0

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The “Ovens” Problem: A cook has to cook a large roast as quickly as possible.  The meat is at room temperature.  The cook has a conventional oven and a microwave oven.  In a cooking test it was found that during the cooking time, the temperature of the roast in the conventional oven is always hig

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