##
* *Reflection: Discourse and Questioning
Ratio soup assessment day - Section 2: Warm up

I was really happy with the way this warm up went. I was afraid students would try to compare one fraction at a time using a whole variety of ratios when I really wanted them to focus on the simplified part to total ratios. Normally I am happy with multiple methods, but here I really just wanted to focus on using common denominators. **It worked out really well because three of the ratios I had given them simplify to a common denominator and only one that didn't.** Most of them immediately recognized that the three were easy to put in order because of the common denominator. They got stuck exactly where I had anticipated and didn't know where the last one fit.

When my students asked for help I asked them to explain their thinking to me first. Then I had my questions ready for them. **Sometimes it helps just to revoice their thinking in mathematical terms.**

**What made the first three so much easier to compare?****So, it would be easier if this last one had the same denominator too?**

As I watched my "peer instructors" working with their groups I noticed that the information they were relying on most was the visual "scaling".** I took my cue from them** and asked students to focus on the designs when answering my questions:

**"Show me in the picture where we see the (2/9 or 4/9) in the designs?"****"What does the 9 represent in the picture?"****"Do we see that in the other designs?"****"So, these three (A,B,C) are all the same size, but this last one isn't?"****"So, it's easier when you can scale the design to '9 squares'?"**

**My role also included helping students listen to and understand each other's thinking**. One student in the group might explain their thinking visually, but another student in the group might need to see how it relates to the math.

*Discourse and Questioning: Teacher's role during student discourse*

# Ratio soup assessment day

Lesson 7 of 14

## Objective: SWBAT explain the concept of "building up" a ratio pattern as a model for making equivalent fractions in order to make common denominators.

## Big Idea: Repeating the same pattern over and over is a concrete model for understanding the abstract process of multiplying the numerator and denominator by a common factor.

*54 minutes*

#### Warm up

*20 min*

Have students discuss their responses to the reflection questions at the bottom of their homework from last night. Have them also work on coming to agreement on the correct order for the figures.

As I circulate I am listening for areas of struggle. I really want students to use common denominators to compare the designs. I expect students to have trouble with floor D, which simplifies to 1/3. All the other ratios simplify to ninths. When I begin to hear this I ask that each group send me one person from their math family to come meet with me for some targeted instruction which they will bring back to the group. This instruction is meant to give them an initial taste of scaling ratios up and also to see that comparing ratios is easier with common denominators. I don't choose any specific students, I leave that to the group. If a student has trouble bringing the ideas back to their group they can ask one of the other "teachers" to help them. I'm experimenting here with using direct instruction with just a small group and having them instruct their peers because I want to encourage students to view one another as resources. The student "learners" in a team are much more likely to ask clarifying questions if they know that the "teacher" is bringing back specific information.

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#### white boards

*10 min*

Just a little practice before the test. My students have been working a lot with tile patterns, but may need a little more practice with the verbal scenarios. I have students work together and help each other on one problem at a time then hold up their work on white boards on a count of three. That way I can see everyone's answer at once and can give quick feedback when needed.

This is a set of practice problems in which students are supposed to write part:whole and part:part ratios:

**Jonathon bought 6 candy bars at the store. 2 of them contained almonds.****There are 12 girls and 8 boys on the team.**

Simplifying is a key skill to look for here. The main mistake I expect from kids is not paying enough attention to what the numbers represent. Asking students to take the time to define what each number is counting should help them identify what the parts are and what the whole is. I might also ask:

**"For which problem was the part:part easier to write? Why?"****"For which problem was the part:whole easier to write? Why?"****"What did you have to do in order to figure out the part or whole?"**

White board practice notes contain more suggestions.

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#### Assessment

*20 min*

I have students turn over their tests Writing ratios assessment.docx when they are done and I bring them their homework to start on. This does two things: it reduces the chances of copying and it also keeps students from being intimidated or rushed when others are getting up and turning in their tests.

I constantly circulate and look for errors. I like all my tests to be formative, so if I see students making mistakes I will try to circle the directions or a word in the problem that will focus their attention on their mistake. For example, if they are not simplifying I will circle "simplest form", or if they are writing a part:part instead of part:whole I will circle the word "whole", etc. I want students to feel like the classroom is a learning environment vs. a testing environment. I want them to feel that their learning is supported rather than judged.

ELL students take the same test. I circulate during the test and they know they can raise their hand and ask if they are not sure what a question is asking. I know enough Spanish math words to help prompt them like "simplifica por favor" or "que es egual?" They love it when I try to speak Spanish, especially when I mess it up and they have to correct me. I always circle or underline the part of the directions I am clarifying so they connect it to the English words. I expect them to have trouble when there is more than one direction like "write a ratio AND simplify" so I look for ratios that aren't simplified on their tests. I also think they will have trouble when they are asked which ones are equal. When I can predict the areas where they will have trouble I can either get my Spanish ready or just ask one of their bilingual peers how to say it. They love being my teacher!

#### Resources

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#### homework

*4 min*

My students begin their homework as soon as they finish their test. We have worked on a growth pattern before in an earlier unit. I bring it back here because it helps students understand the idea of scaling up ratios and ties in really well with the tile designs we have been working with.

#### Resources

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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