Modeling with Box Diagrams on the iPad (day 2 of 2)

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Objective

SWBAT model and solve word problems involving fractions and percents of whole numbers using a box diagram.

Big Idea

Students represent the percent as a fraction in order to set up a box diagram.

Intro & Rationale

This is a great way to give students access to technology in the classroom. This is the second day we are working with this iPad app, Thinking Blocks. I decided to have a second day for several reasons. Some of my students have several years worth of gaps in their fraction sense and this app provides a non threatening way to give them a better feel for what the numerator and denominator represent and more practice modeling fractions of numbers. Often when teachers have to intervene several grade levels below the students feel bad about it and their level of engagement is low, but this keeps their attention and enthusiasm. When they work with fractions and percents it is a real stumbling block when they don't understand the basic concept of numerator and denominator. In addition, their are multiple levels as well as related apps that allow for differentiation. Most of my students have very deficient fraction sense, but are also intimidated by word problems, which is also addressed by this app. Modeling how to solve word problems with box diagrams is a really nice visual scaffold for ELL students.

Warm up

15 minutes

The warm up Warm up 12 kittens.docx tells students that Jessica found a litter of 12 abandoned kittens. She found homes for 3/4 of them and kept the rest. Students are asked how many Jessica gave away and how many she kept. Some students will use the box diagram and some will scale the fraction up to a total of 12. I ask students to model the method they used for the class. I want to see if the ipads are helping students figure out how many sections to divide the box diagram into. Prior to using them I would have seen just as many students dividing it into thirds and fourths and I am looking to see if they are getting better at recognizing that it is the denominator that tells how many equal parts to divide it into. Because students have had trouble identifying what the numbers in a fraction represent I also want to remind them that 3/4 means that 3 kittens out of every 4 is given away.

In the spirit of remediation we have also been doing decimal placement. Students were not clearly understanding that the decimal point marks the end of the whole part of a number. I put 5 or 6 numbers on the board, some whole, some with decimals, and ask students to place decimal points in them without changing the value. We take time as a class to discuss why they may be right or wrong. It only takes a couple of minutes and it is well worth it. If they persist in this misunderstanding they have difficulty with percent applications.

Exploration

30 minutes

Students have used this app before in the previous lesson (day 1) so they don't need any more orienteering. I do remind them to choose a level that is an appropriate challenge for them and I show them that there are two more "Thinking Blocks" apps to choose from. Students stay really engaged as long as the technology is novel in the classroom. They know they are doing math, but the graphics and sounds make them feel like they're playing a game. I love it when I hear them say they are going to download this app on their phones when they get home!

Exit ticket

9 minutes

The exit ticket Exit ticket box diagram for percent.docx tells them that Jose made 60 cowboy cupcakes and he brought 75% of them to share at school. Students are asked how many he brought to school. This is the same ratio as the warm up, but I want to see how many of them are now thinking of a percent as a ratio. I noticed in their homework that they were dividing the box diagrams correctly, but few were still stuck when asked to use the model for a percent problem. I was actually surprised how few were still making this mistake as the ipad app did not specifically ask any questions about percent.  I am hoping that having access to peer instruction for their exit ticket will help those few make the connection from percent to fraction. They are used to setting up and simplifying a percent to a fraction and now that they are used to using a box diagram to model the fraction problems I think they will make the last connection more easily.