5.NF-FrAcTiOn fUn – Add and subtract fractions with unlike denominators

                     

FuN wItH fRaCtIoNs  by Mike Prelesnik & John Broin

Target Grade: 5th grade

CCSS:  5.NF.A.1   Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

CCSS:  5.NF.A.2   Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. for example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Mathematical Practices:

Make sense of problems and persevere in solving them–This is achieved when the project is started with the explanation of what the whole is and how a fraction is breaking the whole into “pieces”  and then adding  “pieces” together from different wholes in order to get an equivalent sum.

Reason abstractly and quantitatively–When  introducing  fractions with different denominators and show the students that they still equal the same whole, the students then start to look more abstractly at the task and start putting together that 3/3 is the same as 2/2  and also finding it incorrect to add 1/3  and 1/2 unless the pieces are converted into the same size piece and they see this visually.

Model with mathematics–This is accomplished throughout the entire project starting with the teacher modeling right up front about what our whole number is and continues through the students modeling the actual addition of fractions using the tools provided (which also covers the Practice of  “Use appropriate tools strategically”)

Attend to precision–This practice comes in different forms for this project.  Each strip is broken down into smaller and smaller pieces (sizes) and it requires extreme precision to make sure that 5/6 and 7/8 aren’t mistaken as the same size.

Materials and Equipment:

There is no technology needed for this modeling activity.  All that is needed is precut strips of paper of equal size and shape, colored pencils, white board, and the worksheet.  You can also purchase plastic folding strips from a teachers supply store if budget permits.

Modeling Activity:

This activity helps teach the mathematical concept of adding fractions by using strips of paper to represent the whole and then folding the strips to help represent how many pieces the whole is split up into.  This is a hands on activity that will give the students a visual representation of the value of each fractions

In reaching the CCSS of 5.NF.A.1 (which is replacing given fractions with equivalent fractions in order to produce an equivalent sum)  the students will each have several strips of paper, all of equal shape and size.  Each student will then be asked to represent the value of 3/5 by folding the strip into 5 equal parts and then shading 3 of these parts with a colored pencil.  The students will then use a different strip to represent the value ¾ using the same procedure.   The student will then use these 2 strips and discuss in groups of 4 how they can add the pieces together.   The teacher will walk around the classroom during this part of the activity and ask leading questions to help the students discover, on their own, the conclusion that if you break each piece into the size of piece from the other strip, that they will become equivalent size pieces on both strips, and then they can count the shaded parts and add those together.   Once the teacher is satisfied that the groups have a clear understanding, a representative from each group should stand up at the white board and show, graphically, how they added their 2 fractions.

See video for visual reference:  http://www.youtube.com/watch?v=lidrNnp2ga0

 

Addressing CCSS: 5.NF.A.2  is done through the worksheet that is sent home with the students for a more summative assessment.  This worksheet will have the Title picture above to give the student a visual representation of a whole broken down into different size pieces.  Then,  a set of story problems for each student to work out on their own will involve real world application like using recipes and having  to adjust them to meet different scenarios.  I.E.

1. You give 1/3 of a pan of brownies to Susan and 1/6 of the pan of brownies to Patrick. How much of the pan of brownies did you give away?

 

2. You go out for a long walk. You walk 3/4 mile and then sit down to take a rest. Then you walk 3/8 of a mile. How far did you walk altogether?

 

Adaptations:

For students who are having a hard time understanding the procedure of breaking each piece of one strip into the size of piece from the other strip, the teacher can simplify the problems by using larger fractions like ½ and 1/3.  Also, you could draw the activity on a full size sheet of paper representing each fraction as a bar that is broken into its respective pieces and then have the students write down what they see on the paper.

 

Discussion Questions:

1.   What’s the top number of a fraction represent?

2.  What’s the bottom number of a fraction represent?

3.  Why can you add the top numbers if they are different but you can’t add the bottom number if they are different?

4.  Can the top number be larger than the bottom number?  If so, what does this represent?

5.  Is it possible to have 2 different denominators and have the fractions be equivalent?

6.  Where would you use these skills in the world outside of the classroom?

 

Leave a Reply

Your email address will not be published. Required fields are marked *