Ratio soup assessment day

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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.

Intro & Rationale

Warm up

20 minutes

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.

white boards

10 minutes

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.

Assessment

20 minutes

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!

homework

4 minutes

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.