Today's "warm up" was geared toward reminding students that they can represent fractions in many ways...so I gave them 5 minutes to make a "mini poster" (literally 4 inches by 4 inches!) to show as many ways to show 1/2 as possible. After they worked, we did a little gallery walk. We came back together and had a discussion about what we saw...different shapes...number lines...fractions of sets...equivalent fractions...
It was a good warm up to our main lesson which worked to help students derive the "computation" method for finding equivalent fractions. (If you missed my post yesterday about building that understanding, CLICK HERE to read that one!). After our explorations, it wasn't that big of a stretch for students to recognize that multiplying or dividing the numerator and denominator by the same number generated new fractions that are equivalent. We proved it with some drawings, some manipulatives, and then moved to bare numbers.
So after working with equivalent fractions for a while, I wanted to put my students to the test to see how WELL they understood the concept! So often we give students a quick exit slip or something like that--a "fill in the blank" worksheet that follows whatever computation rule we have taught. If they fill in the blanks correctly, we assume understanding. It just isn't that simple.
To really get students talking, I asked them to do an activity in my big fraction unit....an activity where they need to first generate equivalent fractions (sometimes I do this activity where they can write fractions, draw fractions, etc like the warm up) but today I simply wanted them to use their new algorithm to make a set of 5-7 equivalent fractions for the "unit fraction" I assigned them. The group below was working to generate a list of fractions equivalent to 1/8.