Adding and Subtracting Fractions

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Objective

Students will be able to add and subtract fractions with like denominators.

Big Idea

Understanding that when the total number of parts of a whole are the same, fractions can be added.

Anticipatory Set

7 minutes

I open the lesson with a challenge, writing two fractions on the board and asking students to think about how we can add these fractions together to get a total. 

I do not know what students are going to be able to tell me about adding fractions.  However, I want students to focus on the main concept of this lesson: adding and subtracting fractions. As students respond to the given question, I assess their knowledge and used what they need to know to adjust the complexity of this lesson. Some students want to add the denominator and the numerator, I point out when the denominators are the same you only add the numerators.

 We will use the following Mathematical Practices for this lesson:

MP.2. Reason abstractly and quantitatively.

MP.4. Model with mathematics.

MP.5. Use appropriate tools strategically.

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

Fraction Pad

Modeling

15 minutes

 

My goal here is to build students’ background knowledge on how to add and subtract fractions with the same denominator, and how to determine if fractions are the same or equivalent. 

After I gain a clearer picture of what students need to know, I invite students to the carpet to demonstrate how to add and subtract like fractions.

  First, I discuss how it is much easier to add and subtract fractions that have the same denominator. I use a visual representation of two fractions with the same denominator.  I place them side by side and point to the number above the fraction bar.  I ask students what is the number above the fraction bar called?  (Numerator).  Then, I point to the number below the fraction bar. I ask students what is the name of the number below the fraction bar? (Denominator).  I want to make sure they know the difference between the numerator and the denominator before I move towards my next point. 

After that, I ask students what do you do when you need to add or subtract fractions that D NOT have the same denominator?  We come to the conclusion through group led discussion that we need to create equivalent fractions to the point that each of the fractions we are working with has the same denominator.  (Based on student’s response I decide to demonstrate specific instructions in order to accomplish my intended discussion.) Even though we are not working on changing unlike denominator fractions to like fractions, I want my students to know that something has to occur before adding unlike fractions.

 I introduce student to some math manipulatives. I show students how one half can be equivalent to 2/4, 4/8, and 5/10 by stacking each quantity.  Students need to see that because the lengths are the same we know for sure the fractions are the same or equivalent.  

 Then, I model additional portions that can create equivalent fractions. I repeat this process until students are able to be involved in this problem-solving strategy of creating equivalent fractions that will provide two fractions with like denominators. 

 

After that, I simply demonstrate visually and verbally how to add together fractions with like denominators.

Checking for Understanding/Probing

7 minutes

 I ask students to move into their assigned groups.  I give each student a set of fraction stacks.  To get them started, I guide them by offering one fraction: (1/4).  I ask students to generate at least one equivalent fraction.  If needed I will provide additional examples.  Once students are comfortable creating their own equivalent fractions using the fraction stacks, I move into facilitator mode.  As I circle through the groups, I encourage students to represent two quantities at a time.  Then, I ask them to write an addition problem to solve.  I tell them to solve the addition problem by using the fraction stacks and adding.  As I move around I ask other groups to write and solve their own problems adding or subtracting fraction by using the stacking method. Students seem to understand that only the numerators are added when adding like fractions.

 

Independent Practice/Closing

20 minutes

 In this portion of the lesson I want to see how well students can explain how adding and subtracting like fractions occur. I ask students to move back into their assigned seats.  I ask a couple of volunteers to explain some of the different strategies they used. It is important for students to explain mathematically because it helps them develop their conceptual thinking skills. To extend this lesson a bit, I ask them to write it out in their math journals. This will allow me to keep a running record of their growth. As students are writing in their journals, I circle the room to check for understanding. For instance, I may ask how did you get your answer. Can you show me another way? Did anyone get something else? Explain? Can you illustrate it for me?

 

Extension:

If some students finish early I will have them to solve equations by adding  and subtracting fractions with like denominators. I will use students work samples to determine if they have mastered this particular skill.

Student Sample 1

Student Sample 2