# 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.

For the equation 2(x + 1) + 4 = 12, identify all possible steps that could be done next. |
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3( x + 2) = 12 |
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Solve this equation in two different ways: |
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If m is a positive number, which of these is equivalent to (the same as) m + m + m + m? |
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Here are two equations: |
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Question 1a: Write a story problem that can be formulated by the equation: x+5=8. |
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A school with 345 students had a sports day. The students chose between football, swimming, and bike riding. Twice as many students chose basketball as bicycling, and there are 30 fewer students who chose swimming than football. 120 students went swimming. How many students chose football? |
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Problem 1: Grandmother Rachel mixed 20 kilograms of jam containing 15% sugar with 15 kilograms of jam containing 40% sugar. How many kilograms of |
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One of the workers in the jam factory mixed one barrel of jam containing 14% sugar with another barrel of jam containing 30% sugar. The new |
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The Pet Problem: There are 280 animals signed up to be in the pet show. There are four times as many dogs as cats and there are twice as many birds as cats. How many of each animal signed up for the pet show? |
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