SWBAT make connections between different representations of rational numbers and the concept of proportion.

Students discuss similarities and differences between different representations.

When beginning to work with percents it is important for students to make connections to and between prior knowledge and equally important for the teacher to assess gaps and misconceptions in prior knowledge. Math Graffiti is a good way to surface what students know and what incorrect or incomplete understanding needs to be clarified or taught. It is an especially good activity after coming back from a vacation or when a topic such as this relies on a broad spectrum of prior knowledge. I have done this type of activity before, but when I saw one of my Master Teacher colleagues, Tim Marley (grade 12 math), calling it "math graffiti" I had to use the name! It gives students a greater sense of freedom to just write in any direction, make corrections, ask questions, and respond to input of others, which is the whole point. I want students to read and respond to input of others like they would on the bathroom walls.

15 minutes

This warm up Graffiti warm up.docx is a "brain dump" or brainstorm where I ask students to take 3 "silent minutes" to write down everything they know, think they know, or wonder about ratio, percent, fraction, decimal, and proportion. I encourage them to include pictures, vocabulary, examples, definitions, and phrases. Students are so used to being asked for complete sentences they may need to be told that disorganized lists and sentence fragments are fine. This is not going to be used for an essay. This type of activity is really helpful for ELL students, because everyone is using sentence fragments and they don't need to worry so much about the language coming out right. The use of pictures and examples with labels is also really helpful for ELL students in concept and academic vocabulary development.

As I circulate I am doing two things. I am encouraging students to keep their pencil moving. I may suggest a diagram, vocabulary, label parts of examples, etc. I am also looking for common questions and answers. For example I notice in today's lesson that several students have questions or are uncertain about proportions. I look for students who may have more ideas written down for those topics and make sure to start their group at that poster. For example, as you can see in Mei Lin's warm up (sample 3) she has some good ideas for proportion, which others had questions about. I make sure that Mei Lin's group starts at the Proportion poster so that other groups will all see her input.

After the three minutes I ask them to share each of their ideas with their math family group after which they will be given one more silent minute to write down any additional ideas they got from their families. I expect they will continue to write as they listen to other's share as well.

35 minutes

During the exploration I have 5 - 6 posters around the room. The posters are labeled Proportions, Percents, Ratios, Decimals, Fractions, & 10%. In retrospect I might eliminate the 10% poster and have students work in larger groups so they have more time at each of the other posters. Students start by transferring their ideas from their "brain dump" warm up onto the posters. Students move in groups of 4-6 writing and responding to the graffiti on each poster. I tell them to pay special attention to the topics they were most uncertain about.

As I circulate I make sure that students write any questions they have on the posters so that students can respond to them. If I notice groups are off task I will suggest they write some examples or label examples already on the poster, or write down vocabulary, etc. As I circulate I am also looking for mistakes that need correction and I may draw these to the attention of the group to have them make corrections to it.

If students do not get a chance to get through all the stations I ask them to either return to the poster where they started and see how others added to it or to go to the poster on the topic they have the most uncertainty (if they didn't get a chance to see what others wrote). This lesson might be better with two days to allow students to digest all the comments. If you only devote one day I would hang up the posters around the room so students can see them.

If you teach more than one class you may want to extend the lesson to another day so that each class can respond to the "graffiti" of another class. This lesson could be done the next day or could be done later after some clarifying lessons.

4 minutes

Before students leave I want the to explain how some of the topics (fractions, percents, proportions, etc) relate to one another Percent graffiti exit ticket.docx. I also want to see what questions they still have after looking at the "graffiti". I want to use the input from the exit ticket Math graffiti student inquiry to explore.docx to see what ideas need to be clarified along the way in the next few lessons. I am also always on the lookout for student questions that may be worthy of further investigation by the whole class. These ideas are sometimes hard to recognize so it is important to really look and listen for conceptual content in student questions. They don't always use the same vocabulary we do to describe things, so the content is sometimes lost on us if we don't really try to understand their meaning. Their questions and input can also point out for us when we have completely bypassed a certain type of example like "5.0 can't be made into a percent". This is a reminder to me that I have not given them any examples greater than 100% and I had better do that at some point so they don't continue with this misconception.