If your students are anything like mine they are completely intimidated by fractions or any vocabulary associated with them! Their math identities are very fragile and they tend to shut down at the mere mention of a denominator! Their knowledge gaps are all over the place in terms of equivalent fractions. Some students have the process down, some have the algorithms and vocabulary hopelessly mixed up, very few truly believe that 1/2 is truly equal to 10/12. This is the perfect time for peer instruction and context! In order for peer instruction to truly work students need to be able to make their thinking visible to each other. I do a lot of thinking aloud so they can hear all the stuff that usually goes on inside our heads and stays invisible to others.
This was their first homework assignment where they were comparing fractions and ratios out of context. I expect a lot of difficulty and concern and I like to give them time to work together with a little guidance. The warm up Warm up homework check denominators.docx simply tells them to check their homework homework comparing ratios 2.docx and be sure to show the ratios with the same denominators that were used to compare. I remind them that, like the tile floor designs, it is easiest to compare when the floors have the same number of total tiles. The context helps them make sense of the denominators. As I circulate I listen for and share student ideas, questions, and strategies that may help the class. Some of those ideas may make connections between prior knowledge or context, some might be questions.
I go over this homework a little more slowly than usual, because I want to pretend to be a student doing the homework in order to make my "self talk" visible homework comparing ratios 2 notes.docx. This helps to validate any difficulties or questions that may have come up for them, helps them learn how to pay attention to their thinking as they work, and hopefully helps develop their confidence and perseverence.
Students practice comparing fractions and ratios together in their math family groups. I give them a single set of fraction/ratios group work and peer instruction.docx at a time to compare and then we go over as many possible methods as we can. The key is for students to understand that they can scale up or down or in combination in order to make equivalent fractions with the same denominators. group work and peer instruction notes.docx
I know that my students don't really understand the concept that equivalent fractions are really equivalent. Most accept the idea because the teacher says so, and some may have worked with fraction manipulatives at some point in elementary school. But when they see 2:5 and 10:25, they see larger numbers and can't understand that they could be the same. I like to take a few minutes while groups are working together and work with a small group. I ask the math family groups to send me one person from their group who will meet with me and bring some ideas back to them. I don't choose the students. After I have met with them Are they really equal peer instruction.docx and given them some notes Are they really equal peer instruction notes.docx to take with them I send them back to their math families and say "here come your teachers". If one of them has trouble showing their group they can ask one of the other "teachers" to come over and help.
As I circulate I am looking for groups that aren't sharing their ideas. I am also looking for students who have shown something different than their peers. For example if several students scaled ratios up, but one scaled them down I want them to discuss the similarities in the methods. Sometimes students with less confidence, including ELL students will have done something no one else did, but won't share it. When I see this happening I check in with the group and ask who has shared some ideas. "Have you taken a look at what Karla has on her paper? She has something different from you. Ask her to show you." Then I stick around and make sure they ask. If Karla starts showing them without them first asking I will ask her to wait and make them ask. Helping ELL students integrate into group discussions is as much training other students to invite them as it is encouraging them to participate.
The last few minutes of class are to get them started on their homework homework up, down, all around.docx. They are more likely to do their homework if they get started on it in class. Plus, they have access to their peers and to me if they run in to trouble.