I expect some students to have had trouble with last night's homework who built it. I have noticed that the more words on a page the less likely they are to do the work. Because of this I really want them talking about the homework. This is a way to reengage those students who didn't do it. There were also a few problems in which the ratio was reversed from black:white to white:black and I want some peer instruction to take place to reinforce the fact that the order matters.
The warm up homework check tells students that one person in their homework used pattern A, two used pattern B, and 3 used pattern C. My intention is not to give them a hint, but to start an argument within their group. They are told to make an argument for or against if they disagree. This information helps guide the conversation. As always I circulate to make sure students are using evidence to support their arguments. I may again display the sentence frame we have been using ("for every ___ black there are ___white") and encourage them to use this to help them explain their ideas. (MP3)
Because my students seem to have developed an over reliance on the teacher I sometimes like to present new information or vocabulary in written form instead of direct teaching. This gives them something to refer to other than the teacher and makes them feel a little more self sufficient because they can find the answers to their questions on their own. I like to write the text in as kid friendly terms as possible and I like to include diagrams and questions along the way for them to check their own understanding.
This reading Another kind of ratio.docx is about part to whole ratios, which follows earlier lessons about part:part ratios (which is the blackest? & designing a floor pattern).
20 minutes probably won't be enough time for them to finish all the questions, especially the "check yourself" part on the back, but they can work on it for homework.
I have students work with their math family groups on individual white boards so they can help each other. Being allowed to talk to each other here makes them way less inclined to silently copy and allows for valuable peer instruction. Then I have them all raise their white boards on a count of three so I can see all of their work at once and give feedback.
I show students only one problem at a time and ask them to write a part to whole ratio. The first eight are visual patterns, the first four of which should go pretty quickly, because there is no simplifying. For the next four I may need to ask peers to help each other simplify and then I check in with those students who didn't get it the first time before I do my count down.
The remaining practice problems are written sentences and require more thinking and I expect some common struggles.