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 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
sugar should be added to the new mixture in order to obtain jam that contains 35% sugar?

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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
mixture weighs 80 kilograms and contains 20% sugar. How much jam was in the first barrel? How much was in the second barrel?

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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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Miss Dean’s moped went 48 miles on 3/8 gallon of gas. How many miles would the moped go on one gallon of gas?

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A carpenter has a board 200 inches long and 12 inches wide. He makes 4 identical shelves and still has a piece of board 36 inches long leftover. How long is each shelf?

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In grandmother Rachel’s jam factory, jam is made out of sugar and fruit. Grandmother Rachel mixed 300 kilograms of jam containing 30% of sugar
with 700 kilograms of jam containing 20% of sugar. What percentage of sugar does the new mixture contain?

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372 people are working in a large store. There are 4 times as many stock people as checkers, and 18 more checkers than managers. How many stock people are in the company? How many checkers? How many managers?

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In grandmother Rachel’s jam factory, jam is made out of sugar and fruit. Grandmother Rachel mixed 300 kilograms of jam containing 30% sugar
with 700 kilograms of jam containing 20% sugar. What percentage of sugar does the new mixture contain?

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Candy Bar Problem: There were three kinds of candy bars being sold at the concession stand during the Friday dance. There were 22 more Peanut bars sold than Wafer bars and there were 32 more Peanut Butter Bars sold than Wafer bars. There were 306 candy bars sold in all.

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