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 I get 8 miles per gallon out of my car during the first leg of a journey but for some reason only get 4 miles per gallon during the second leg, what is my car’s performance over the entire trip?

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The Smith family's whole holiday is shown on the graph at right. The vertical axis shows the distance (in kilometers) away from home and the horizontal axis shows the time (in days) since the start of their trip.

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Graph the equation y=x+4.
Jimmi said that this line would go through the axis at (4,0) because in the equation you add 4 to x. Do you think that Jimmi was right?

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Graph the equation y = x and then change it to the equation y = x+3.  Predict how the graph would change.

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What are some of the possible values for the slope of a line that lies in the shaded region?  How do you know?

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1. Graph y = 2x+1.  Explain your thinking as you create the graph.
2.  What would happen if you change the 1 to a 7?  What would happen to the graph? Why do you think that? 

3. Graph y = 2x+7.
4. Write the equation of a new line halfway between the lines you drew.

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Marna and Peter are two students who are standing one meter apart.  They start walking in a straight line one behind the other.  Marna is walking behind Peter carrying a calculator and CBR to measure the distance between them.  They walk for 7 seconds.  Interpret the graph at right.

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Sarah, Rivka, Rachel and Leah discussed the question of whether or not their success on tests is related to the amount of time that they prepare for tests.

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Consider the starburst pattern on the right.  Using a graphing utility (such as grapher or a graphing calculator), recreate the starburst pattern.

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Which of the graphs to the right represent journeys? Describe what happens in each case. Why do you think that?

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