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.

Compare the functions in the family ga(x)=xn+ax for several fixed values of n.

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Consider the sequence of W-patterns.
[Figure from Rivera/Becker reference below, p. 68.]
A. How many dots are there in pattern 6?  Explain.
B. How many dots are there in pattern 37?  Explain.

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1. (a) If y is increased by t, find an expression for 3y2+2y.
(b) Given f(x) = -2x2+3x, find f(x+h).

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2) 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 3: Grandmother Rachel mixed 20 kilograms of jam containing 15% of sugar with 15 kilograms of jam containing 40% of sugar. How many kilograms of
sugar should be added to the new mixture in order to obtain jam that contains 35%
of sugar?

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Problem 2: One of the workers in the jam factory mixed one barrel of jam containing 14% of sugar with another barrel of jam containing 30% of sugar. The new
mixture weighs 80 kilograms and contains 20% of sugar. How much jam was in the first barrel? How much was in the second barrel?

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

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For Groups Q and R:
10. Sarah argues that if 3k 2+2k-1=0 and 3+k-2k 2=0  then it is true that
3k 2+k-1=3+k-2k 2 . Is she right? Explain your answer.

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Group R:For first year university students
6. Explain what an equation is. [read question 3 below before answering]
7. Give an example(s) of an equation.
8. What is an equation for?
9. Look at the following list. Decide which ones you consider are equations

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Group Q: For upper secondary school (age 16-18 years)
3. Explain what an equation is. [read question 3 below before answering]
4. Give an example(s) of an equation.
5. Look at the following list. Decide which ones you consider are equations

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