SWBAT make an argument supported by evidence to explain proportionality.

Students will see that there are multiple methods for showing proportionality.

Students often balk at writing in math class. This lesson allows them time in class and in their math family groups to work together to write or strengthen their arguments. Students have a tendency to ask the teacher "is this ok?", "is this good enough?", etc. The teachers role is to ask students if their argument is convincing enough and clear enough for everyone in the group. I ask if there is any other evidence they could explain that would make their argument better. Each member of the group should read through it and add to it. This is a good way to introduce students to the skill of critiquing an argument. It is also really helpful for ELL students to do this type of work in a group, because they can work together to find the right words.

15 minutes

This warm up gives students two arguments and are asked which one is stronger.

**Luis and Alfonso used the same proportion of black and white tiles in their designs because the ratios remain constant.****Luis and Alfonso used the same proportion of black and white tiles in their designs because the ratios remain constant. When the ratios are simplified they are the same. Luis used a ratio of 16:20 black to white tiles and Alfonso used a ratio of 12: 15 black to white tiles. Both simplify to 4:5.**

Students then figure out what kinds of things made the one argument stronger than the other. I ask which is more convincing and why. Why does one leave room for doubt? **Then I have them decide together what additional evidence could be included with the stronger argument if someone still was not convinced.** I ask them what they could tell, show, or describe.

**This is so different from just writing the final answer and circling it. I want them to understand that an solution is only valid if you can convince others that it is right.**

30 minutes

This activity follows the homework homework proportion argumentation.docx and Who has proportional designs.docx from the previous lesson (Are they proportional?) in which students wrote arguments to explain which tile floor designs used the same proportions of black and white tiles. Students work together in their math family groups to critique and revise the arguments made in the homework. They are given some questions to help them evaluate the arguments and the evidence and also helpful vocabulary and sentence structure. revising arguments.docx

I expect a lot of students may have made some conclusions about which designs were proportional, but may not have written the arguments. They are not used to writing for math class, which is why they do this portion in class. I remind students that if they or some of their partners did not complete the writing part that they still have a lot to offer their team mates. They can find evidence in the graphs or ratio tables, offer conclusions, or help evaluate any conclusions or arguments.

One problem with group work is that some students end up doing all the work and others do nothing. I like to circulate and ask groups which argument is being worked on and suggest that the others can start looking for evidence to support the next argument or can start describing or showing the data in a graph.

9 minutes

With about 10 minutes to go I usually stop them and tell them that I would prefer 3 strong complete arguments to 5 incomplete weak arguments. They are asked to finish up whichever argument they are currently working on and then turn them over to the rest of the team to decide if there is more explanation needed of the evidence (remember to leave no room for doubt) or if more evidence would make the arguments more convincing. This is another way to make sure all the members are involved.