Modeling Addition of Fractions

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Objective

Students will be able to use models to add fractions with like denominators.

Big Idea

Given a set of models students will be able to use them to add two or more fractions.

Anticipatory

10 minutes

  I open today’s lesson by reflecting on what we already know about fractions.  I say, “You know how to model fractions with fraction strips, today we will learn all about how to use fraction strips to add fractions."  This brings students deeper into the learning process, since both of these skills will be used to master this lesson.  If some students have forgotten the purpose of fraction strips, I remind them by illustrating and explaining the purpose of using them when problem-solving. 

 I place a bell ringer on the board.  A bell ringer is a morning question, which usually relates to the math lesson of the day.  I ask students to think of different ways to model 3/5.  I want to see if students can illustrate models that represent the given fraction.  Using models is an essential skill to obtain in order to learn how to add fractions. 

In this lesson we will be focusing on the following Mathematical Practices:

 MP.1. Make sense of problems and persevere in solving them. 

MP.2. Reason abstractly and quantitatively. 

MP.4. Model with mathematics. 

MP.5. Use appropriate tools strategically. 

MP.6. Attend to precision. 

MP.7. Look for and make use of structure.

MP.8. Look for and express regularity in repeated reasoning

Fraction Pad

Modeling

20 minutes

In this section of the lesson, I want students to develop an understanding of fraction equivalence and addition of fractions with like denominators.

To start,  I pose a quick problem just to see what they know already about using models to add fractions. 

Question:

Pam is working on a family blanket.  She sews 3/8 of her blanket with green trim and 4/8 of her blanket with pink trim.  How much of the blanket has she sewn so far? 

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I ask students to use their fraction strips to model and solve the given problem.  I allow them about five minutes or so.  After that, I ask volunteers to share how they found their answers.  

Some students are comfortable explaining, however, they are not using mathematical terms as they should.

 Explanation:

I explain to my students that they should always focus on the how and why, instead of just the computational part of adding fractions. This will help them to develop their conceptual thinking. 

I draw a fraction strip on the board that represents 1 or the whole blanket.  There are two fractions in the problem that have eight as the denominator, how can I represent the numerators? How can I represent the denominators? If students do not seem to understand you can color the numerators red and the denominator purple so that the students can visually see the difference.  After that, I ask them how many parts did I color red. and how many parts did I color purple? 

I point out that when you are adding denominators that are alike the number stays the same, however, the numerators should be added to get a total.  Then, I ask students to add the numerators together, and leave the denominator the same.  The students'  response should be 7/8. 

  I repeat this method with other problems until a level of understanding is reached.

 

Guided Practice

20 minutes

In this portion of the lesson, I allow students to work with models to learn the concept of adding fractions with like denominators.

Reminders:

When adding fractions with like denominators, you should only add the numerators!

 Materials:  crayons, fraction strips, and guided Practice

I ask students to move into their assigned groups.  I give each group a set of fractions to add with like denominators.  I tell them to use the fraction strips to model each fraction as they begin to add them.  I give them about 15 minutes to complete this task.  As students are working, I circle the room to check for understanding.  I ask students to explain how they are using the fraction strips to find their answers. Can you think of other ways to solve the given set of problems?  Do you have to change the denominators if they are alike?

Response:

Most students notice that the shaded parts represent the numerator, and this helps them determine the total number.

 Repeat this given task until a level of understanding is reached; however, you can use students' response to questions to see where they are in their learning.

Independent Closing

15 minutes

Shapes: triangles, squares, and pentagons.

 In this portion of the lesson, I want students to use shapes as visual models. They use models to help them determine the total of two fractions.

By now, students should be able to explain how to add fractions by using any model they choose.  So I ask them to return to their assigned seats to illustrate their favorite shapes.  Then I have them to write the fractions of the given shapes, and find the fraction of the shapes that have four or five sides by adding the two factions together.  This is a fun and creative way to assess student’s knowledge of how to take what they have learned so far and create something totally new with it.  As students are working I ask some probing questions. Can you explain what you have done so far? What did you notice?  How can you be sure?

 Students explain how models can be used to help them determine the total amount of two fractions with like denominators. They explain that they added the shaded part of the illustrated fraction shapes.

Student Sample