Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
These tasks are to be used after students have explored and discovered patterns with fractions. I believe students should use manipulatives to discover rules for themselves before being given the opportunity to apply this knowledge in different situations. Before completing these tasks, we explore comparing fractions using benchmark numbers, common denominators, and common numerators. One task also encourages students to use their knowledge of fractions to compare what is not included. For example 97/100 is greater than 22/25. Hopefully students will notice that both are 3 parts less than one whole, so they can make determinations based on the size of each part. This will be challenging for many students, but I included it for discussion and/or differentiation. Students will be able to use all of these strategies in the following tasks.
Some of the tasks are “Show What You Know”, which allows discussion with a group and requires students to prove their solution. They work in small groups to discuss and complete this task, and then one group proves, to the entire class, that their answer is correct. We discuss multiple ways to find the solution. The other tasks are application problems.
I have found these discussions help students to be more successful when solving the application problems independently. They are better able to write about their thinking when we have modeled it together.
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