Modeling with Box Diagrams on the iPad (day 1 of 2)

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SWBAT solve word problems and calculate the fraction of a whole number using a box diagram.

Big Idea

Students need to understand that a denominator shows the number of equal parts the whole is divided into.

Intro & Rationale

In the previous lesson (The Cup Half Full day 1) we ran into some trouble because of student's lack of fraction sense. They had trouble understanding that the denominator tells how many equal parts the whole is divided into. This lead to some difficulty setting up a box diagram. Specifically, students didn't know how many sections to divide the box into and didn't know how to figure it out. For this lesson I borrowed a class set of iPad minis from the U.C. Davis department of education and had students use an app called Thinking blocks for fractions, which helps students model word problems with fractions using box diagrams. Because the technology is still pretty novel, especially in the classroom, there is a high level of engagement. If I had just done this lesson with worksheets I think the level of engagement would have been dramatically lower. Because they were so engaged students ended up doing a lot more work than they might otherwise have done. Another great thing about this app is that it has several levels as well as a couple of related apps that help differentiate the level of challenge. This is great for ELL students and special education students because it allows them several check points along the way.

Warm up

10 minutes

In this warm up Warm up 35 donuts.docx students are asked how many donuts were eaten in class and how many I took home if I brought 35 and the class ate 3/5 of them. I ask students to come up and model their solution for the class. Some may try to use the box diagram provided while others will scale up the fraction to a total of 35. I expect mistakes when trying to use the diagram and I want to bring them to the surface and identify for them exactly where they are running into trouble. The main mistake (not knowing how many sections to divide the whole amount into) is caused by weak fraction sense, when students don't realize that a denominator indicates the number of equal parts the whole is divided into. Having fraction circles handy is always a good idea when you suspect the need for scaffolding fraction sense will arise. Any time you use concrete manipulatives and diagrams it helps ELL students bridge their language and concept development.


35 minutes

Before I assign iPads to each student I do a quick demo of the app. The Thinking Blocks app is pretty self explanatory and I expect students to find even more as they explore, but I want to show them how to drag the blocks and the labels into the box diagram. As I drag the blocks I count them just to emphasize the relationship between the denominators in the fractions and the number of blocks that are provided. I also show them how to check at each point with the "check" button, so they can recognize the sound they will hear when they are right or wrong.

As students are working out some of the first problems I circulate mostly to see which students may need more of a challenge and show them how to move to different levels if they choose. Students sometimes choose to pair up if they have trouble reading the problems. It is nice for ELL students to be given this option. Sometimes they want their own iPad, but just work together on two separate problems.

Using the iPads makes students feel like they are playing a game which changes the way they respond to frustration and difficulty. Getting problems right feels like winning, but there is less stigma connected to wrong responses. As I circulate students are not at all hesitant to ask questions when they need help.

Wrap up

9 minutes

As I collect the iPads students begin their exit ticket Exit ticket box diagram for fractions.docx which tells them that Nathalie thinks 6/10 of 30 is 24 and Priscilla thinks that 3/5 of 30 is 24 and asks them to model both methods with box diagrams to show who is right. When they finish their exit ticket they leave it on the edge of their desk and start their homework homework box diagrams.docx. As I circulate to look at their tickets I am looking to see if they divided each box into the correct number of sections. Some students may have divided both boxes into 5 equal parts if they simplified 6/10. If I don't see the simplification on their paper I will ask them to explain their reasoning. It should also be very clear to me which students are still not relating the denominators to the number of sections.