SWBAT identify a constant ratio by modeling a proportional relationship on the ipad.

Students find different ways of representing the same ratio.

Students will be using an ipad app called MAT-P in this lesson. The app provides a visual way for students to really explore the idea of ratio and helps students learn to use the ipads as a tool for that exploration. I have found that the first time using the ipads can be a little crazy and exciting for students. Many of them have never used them before and I want to give them a chance to explore on their own for a while. As I check out a device to each student I allow them to explore the apps that are loaded and allow them to take selfies with the photobooth app. Reminding them that I will see each photo helps keep them school appropriate. Each ipad has a number and each student is assigned a certain number. If one of them gets locked with a password I know who to go to.

This app is great for engaging ELL students in free exploration of the concept of ratios.

10 minutes

Students are given a partial ratio table and are asked to fill in the blanks, describe the pattern with words, and describe the pattern mathematically. What ratio is being maintained between x and y? Because we will be using ipads for the first time in class I want to set up the expectation that the math will be the focus. With this ap students will be completing a ratio table and this warm up highlights that and helps them view it as a tool to discover the ratio.

It is important to show the pattern they describe with words mathematically. If they say that each number (x) is multiplied by 4 I show that multiplication in order to help them see the pattern. "If x is 4 then y would be...." (5x4) I write 5x4 under the 20 and continue this pattern with the other y values so students can see that each y is equal to x multiplied by 4. Seeing this helps them generalize the pattern for any value of x when I put in a variable.

Some students will know right away that the ratio is 1:4. Others will know that every x is multiplied by 4, but will have trouble writing the ratio. The table can be used to scaffold by putting a 4 in for y and asking for x.

25 minutes

The MAT-P app requires students to turn two bars green by maintaining a constant ratio. There are multiple ways to do it and several scaffolding tools for students, which they mostly find on their own. Before they begin their exploration I do a quick overview on the projector. I show them how to switch between the 4 challenges, how to switch from a blank background screen (A) to one with grids to choose from (B), to one with numbered grids to choose from (C), to one with a ratio table with markers (D). I show them how their worksheet is broken down so they can use the worksheet record their work. Most of the worksheet works with challenge number 1 to give them a feel for how to find the ratio. I also tell students to set the difficulty level to high. It doesn't make their job harder, but it makes it easier for them to find accurate numbers for the heights of each bar.

As I circulate and make sure students are recording their work into the worksheets I may help students find some scaffolding tools for themselves. In level D the ipad ap has a play/pause button that will help them see the green bars at several different levels. They can also drag the markers until they turn green to help them find the numbers that work.

Most student won't go to the settings which allows them not only to see the ratio settings, but to change them. It's not a completely terrible thing if they do, because they still need to find additional numbers at which to place the markers. **What I am really interested in is just giving them a chance to explore how two values can change proportionally to one another.**

5 minutes

Before I collect the ipads, which takes about 2 minutes, I want to go over how they used the ipads ratio table in screen D to find the ratio. I display that screen on the projector and ask students to read me different sets of numbers that turned their markers green. I fill them in on the ipad and then ask them what constant ratio is being maintained between the heights of the bars or what ratio best describes how their heights keep changing together.