This collection of 150 problems asks students in Grades 4 and 5 to perform calculations to make a comparison and come to a decision. The Dare to Compare format recasts more traditional math problems from a single calculation to two or more calculations to come to a final conclusion. Rather than compute a single sale price, the student computes two sale prices to determine which sale is a better deal. Instead of calculating the number of fat calories in a single food item, the student calculates the number of fat calories in two separate food items to determine which has the least amount of fat calories.
The problems are intended to be non-routine but accessible. The solution process is open-ended, allowing students to create mathematical reasoning and to decide how to quantify in order to formulate a conclusion. Comparisons are especially suited for problems involving fractions, rates, ratios, and proportional thinking. However, they can serve as a backdrop for any mathematical topic – geometry, graphing, patterns, elementary algebraic reasoning, probability, counting, measurement, number operations, and logic. So the comparisons are rich in both mathematical content and critical thinking. Each problem is accompanied by one or more hints and a complete solution.
Which fence is longer? Whose heart beats faster? Which food is less expensive? Who travels the furthest? Which collection of coins is worth more? Which shape has a larger area? Which sale is a better deal? Which fraction is larger? Which jar holds more water when full? Which food has less fat calories? Who makes the greater profit? Which event lasted longer? Comparisons provide a motivating backdrop to perform mathematical calculations in a wide range of contexts.
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