Adding Fractions with Models

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Objective

The student will be able to add fractions using models.

Big Idea

Pizza, Pizza!

Opener

15 minutes

In this lesson students will be examining how to add fractions using models.  They will complete a task that requires them to use an area model for adding fractions.  The lesson closes with a strategy discussion for the task and looking at solving the task using a number line model. 

To begin students will estimate sums of benchmark fractions in an activity called More or Less Than One.  This activity and description are taken from activity 13.1 from the second edition of Teaching Student-Centered Mathematics by John Van de Walle. 

Tell students that they are going to estimate a sum or difference of two fractions.  Their job is to decide only whether the exact answer is greater than one or less than one.  Display or project a problem for about 10 seconds, then hide, cover, or remove it.  Ask students to hold up a car (with “More than one” and “Less than one” on either side).  Do several problems.  Have students discuss how they decided on each estimate.  Students with disabilities may need more time and should have number line marked with benchmark fractions available to assist them in visualizing the amounts.

I recommend using whiteboards instead of using a card.  These are the fraction problems I choose to use for this activity.

  • 1/3 + 1/2 
  • 3/10 + 1/5
  • 1/8 + 4/5
  • 9/10 + 7/8
  • 3/5 + 3/4 + 1/8
  • 3/10 + 1/4 + 1/3

I allow my students to use any manipulatives or models they choose to help them solve the problems. 

Practice

30 minutes

In the practice portion of this lesson students will be a working in small groups to complete a task I found in the New York State curriculum called Kelly’s Pizza Shop.  Students will be adding slices of pizza as fractions to determine the total number of pizzas sold in a week.

I give each student a copy of the task and read it over with them.  I tell students I would like them to make sure they have an accurate model that helps them solve the problem.  I also ask them to use circles to represent the fractions.  The circle representation is a version of the area model of fractions and builds off the previous lesson in which area models were introduced to students. 

While students are working in their small groups I circulate the room and listen to conversations.  I am careful not to give guidance as I want them to think through this problem on their own(MP 1).  Up until this point in the unit students have worked hard on learning how to create models of fractions and this task relies on the ability to create a model(MP 4).

Closer

15 minutes

This lesson wraps up with a class discussion about the strategies involved in solving the task.  I have students share their thinking and offer others to build upon their peer’s thoughts.  At the close of the discussion I ensure the correct answer to the task using the circle area models is displayed on the board.

At this point I think it is important to relate the circle area model back to another type of model we have been using; the number line.  I challenge the students to think about we could use a number line to solve this same task. 

What would a number line model for this task look like?  How would we set it up?

Does it change the answer of the total number pizzas sold?  Why not?

Are there any other models we could use to represent the solution to this task?

I continue the class discussion and guide the students to the simple conclusion that there is more than one model to solve problems involving fractions and if done correctly they all lead to the same answer.