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* *Reflection: Debate
Part to whole ratio - Section 2: Warm up

In my common core journey to engage students in the Math Practices I have noticed several "shifts" in my instructional practice. This lesson highlights one in particular. **I want my students to interact with the math in a more meaningful way.** Because of this I find myself giving different information to and asking different questions of my students.

This causes me to look at the standards a little differently as I plan a lesson. **I look for ways to tell them less, give less direct instruction, and make them figure out more.** I think this helps my students learn to use the math rather than just do the math, find connections between related ideas. In this warm up my students are given scenarios in which** simplifying can be used as a tool to help them figure something out**. This is very different from giving them direct instruction to "simplify the following ratios".

*I knew that several students would simplify and that some may not fully understand the process. The task gives them freedom to choose their own tools all of which, through reflection, can help them better understand simplifying. My job is to listen for and share their ideas with the class.*

**I don't specifically tell them to use simplifying and this was a purposeful choice on my part.****I look for areas of complexity in the math and try to anticipate student responses.** These are areas that might give rise to confusion or misconception and dissagreement. **Dissagreements and confusion are the perfect opportunities for students to use evidence, construct arguments, and critique the arguments of others (mp3)**. This is also where much of the differentiation happens naturally.

I knew my students would make mistakes on their homework, but I wanted to capitalize on them. I have come to believe that pointing out and correcting another person's mistakes is not an effective way to change their mind or instill longterm learning. In this lesson I set them up to defend, argue, and change their minds in a non threatening way. **My job was to circulate and help them articulate their thinking, listen to each other, and question each other.** As always, their Table top sentence starters help them navigate the argument process.

My students never cease to amaze me with new ways of articulating mathematical ideas. When they engage in these group discussions the room gets a little noisy, but there is much **more differentiated instruction happening than I as a single teacher could accomplish in the same amount of time!**

*Debate: Start an argument!*

# Part to whole ratio

Lesson 4 of 14

## Objective: SWBAT write and simplify part to whole ratios.

*54 minutes*

#### Warm up

*15 min*

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)

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#### Purposeful Reading

*20 min*

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.

#### Resources

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#### White boards

*19 min*

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.

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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: Which is the blackest?
- LESSON 2: Designing the floor pattern
- LESSON 3: Breaking down the design
- LESSON 4: Part to whole ratio
- LESSON 5: The secret side of ratios
- LESSON 6: Comparing ratios
- LESSON 7: Ratio soup assessment day
- LESSON 8: Scaling up ratios
- LESSON 9: Terminology for scaling ratios
- LESSON 10: There's an ap for that!
- LESSON 11: Let's get organized!
- LESSON 12: Navigating a data table
- LESSON 13: Mistakes & Peer Instruction
- LESSON 14: Mickey Mouse Proportions