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.

A bag of snack food has 4 vitamins and weighs 228 grams. How many grams of snack food are in 6 bags?

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Write an equation for the following statement: “There are six times as many students as professors at this university.” Use S for the number of students and P for the number of professors.

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Phone Cost Problem
The Jog Phone Company is currently offering a calling plan that charges 10¢ per minute for the first 5 minutes for any phone call. Any additional minutes cost only 6¢ per minute.

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(No assessment provided.)

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The Large Foot Pizza Company sells a large pizza that contains 36 pieces. Your class has purchased two of these pizzas for an upcoming class party. Everyone has agreed that each person will receive the same amount of pizza.

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Square Tiles Task
Tiles are arranged to form pictures like the ones below. Find a formula that enables you to calculate the number of square tiles in Picture “n.” How did you obtain your formula?
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A rental car company charges 100 shekels for a day and an additional 5 shekels per kilometer. The company would like to have a clear description of the price that any client may have to pay when returning a rented car. Suggest such a description.

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(No assessment provided.)

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(No assessment provided.)

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Here are the first two pictures in a growth pattern.
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1. Show two different ways to extend this tile pattern. Draw the third and fourth tile designs on grid paper.

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