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* *Reflection: Routines and Procedures
Writing arguments - Section 2: Warm up

This discussion was really hard for my students. Explaining and justifying is not something they are used to doing. They are used to the teacher verifying all their answers for them, so the only convincing they have needed is the teacher's confirmation. Many of my students think that math doesn't have to make sense, it just has to be remembered. **They are used to just believing something because the teacher said it. **So, when I ask them to convince someone they don't always know how to make connections to prior knowledge and explain **why** something is true.

Some questions that help them critique and improve these arguments were:

**"What do we know about this that someone else might not?"****"What would someone need to know in order to understand this?"****"How would we explain to someone what it means to be proportional here?"****"What else do we know that might help someone believe this?"****"What else could we show or explain if someone still wasn't convinced?"****"How would we explain this to a second grader?"**

Something else that would have been really helpful for this discussion would have been changing out the old table top sentence starters they have on their desks for some that would help them more specifically to clarify & critique. Students have become accustomed to using them as a way to conduct productive mathematical discussion, but once they become proficient in the beginning sentence starters it might be time to switch them out for new ones.** In addition to helping them have more productive talk they also help them ask important questions about the math.** I would explicitly point them out and let them know this is a different kind of discussion than they might be used to having and that the new sentences should make it easier.

*Routines and Procedures: Facilitating collaborative discussions*

# Writing arguments

Lesson 6 of 10

## Objective: SWBAT make an argument supported by evidence to explain proportionality.

*54 minutes*

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.

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#### Warm up

*15 min*

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.**

#### Resources

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#### Writing arguments

*30 min*

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.

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#### Wrap up

*9 min*

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.

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- UNIT 1: Order of operations & Number properties
- UNIT 2: Writing expressions
- UNIT 3: Equivalent Expressions
- UNIT 4: Operations with Integers
- UNIT 5: Writing and comparing ratios
- UNIT 6: Proportionality on a graph
- UNIT 7: Percent proportions
- UNIT 8: Exploring Rational Numbers
- UNIT 9: Exploring Surface Area
- UNIT 10: Exploring Area & Perimeter

- LESSON 1: Patterns in the graph
- LESSON 2: What is it trying to tell us?
- LESSON 3: Keep it in proportion
- LESSON 4: Recognizing proportional relationships in a graph
- LESSON 5: Are they proportional?
- LESSON 6: Writing arguments
- LESSON 7: Clarify & Correct arguments
- LESSON 8: Which is blackest the sequel
- LESSON 9: Scaling up, scaling down, scaling all around
- LESSON 10: Ratio assessment day