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 don't specifically tell them to use simplifying and this was a purposeful choice on my part. 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 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! 



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Part to whole ratio

Unit 5: Writing and comparing ratios
Lesson 4 of 14

Objective: SWBAT write and simplify part to whole ratios.

Big Idea: Different ratios can be written to represent the same scenario.

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3 teachers like this lesson
Math, Number Sense and Operations, simplifying, ratios, part to whole, pattern
  54 minutes
defining terms
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