Adding Fractions Lesson Plan 236c4s

LESSON PLANNING GUIDE

Lesson Plan: Adding Fractions with Unlike Denominators

Date:

Estimated Time of Lesson Plan: 120 minutes

Grade/Subject: 5th/Math

Organization of Student Learning: Whole class, partner, small group, independent Learning Objectives and Assessment: Objective 1: TSW find equivalent forms for fractions using common denominators. “I Can recognize equivalent forms of the same fraction.”

Objective 2: TSW add fractions using models.

“I Can use fraction tiles to add fractions.”

Objective 3: TSW use equivalent fractions to add fractions with unlike denominators. “I Can add fractions with different denominators.”

Standard: CCSS 4.NF.A.1 1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Standard: CCSS.5 NF.A.2

Assessment: X Formative □Summative Students will be provided a bag full of fraction cards. Each card will have a different fraction on it. All of the fractions will be equivalent to either 1/5, ¼, 1/3,or ½. Students will be told to sort them into groups of equivalent fractions.

Assessment:

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.

Standard: CCSS.5NF.B.1

X Formative □Summative Students will use fraction tiles with their partners to model a given sum and write an equation from their model.

Assessment:

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.)

X Formative □Summative Students will work with a group to find a variety of equations that equal a given sum. Students must use their understanding of common denominators to prove the equations equal the given sum.

Leading Questions:  How can you prove that two fractions are equivalent?  How can you prove that two fractions are equivalent without using models?  How might you use fraction tiles to model a specific sum of two fractions?  Could you model a given sum in more than one way?

Lipscomb College of Education, Fall 2012

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How could we use what we know about equivalent fractions to add two fractions whose denominators are not the same?

Materials and Resources: Teacher - Interactive whiteboard, Glencoe virtual manipulative website, document camera Student- Fraction card sort, iPads or fraction tiles, butcher paper or ½ piece chart paper, Envisions math student workbook. Technology Use: Teacher and students will use the IWB (interactive whiteboard) along with the Glencoe virtual manipulative website. Students may use iPads with k12 Equivalence Tiles app in place of fraction tiles. Teacher will use document camera to share student work with the class. Set: At each table there are baggies full of fractions for you and your elbow buddy. Yesterday we used fraction tiles to model equivalent fractions and then you developed your own rule about how to find equivalent fractions. Today we are going to take what you have learned about equivalent fractions and use it to add fractions whose denominators are different. First, I would like you to sort the fraction cards in your baggies into groups of equivalent fractions. (Give students several minutes to sort while walking around asking students how they determined where to put certain cards.) Instruction:  Tell students that today they are going to begin by practice modeling addition problems using fraction tiles.  Teacher model 5/6 on IWB using virtual manipulatives. Explain while modeling that the first thing you are going to do is model the sum 5/6.  Tell them that now you are going to take other fraction tiles and line them up below 5/6 to come up with an addition problem that would be equivalent to 5/6. (Line up the fraction tiles beneath 5/6. Use (1)1/3 and (8) 1/12 tiles).  Explain that this model shows that 1/3 + 8/12 is equal to 5/6 because they match up exactly.  Tell students to use their iPads or fraction tiles to find a different way to come up with 5/6.  Have 1 or 2 volunteers share their examples using the IWB.  Teacher model a new sum on the board (3/4). Have students work with their elbow buddy to model two fractions with unlike denominators that would equal ¾. (Teacher walks around asking questions and checking progress. Remind students the models must line up perfectly.)  Have elbow buddies share equations while teacher models them on the board.  Teacher point out that there are relationships within the denominators either by factors or multiples.  Teacher asks if there are any questions about modeling sums.  Explain to students that although modeling can be used to prove an answer, it is not always as accurate as mathematics.  Have class look back at original sum 5/6.  The teacher will write the equation 1/3 + 8/12 on the IWB.  Say, if this represented pizza, it would be hard to tell someone exactly how much you had because one pizza is cut into thirds and on is cut into twelfths. Those are extremely different in size. In order to express how much you have, you have to have the same size pieces or denominators.  Remind students that they have rewritten fractions with the same denominator before when they compared fractions and that they would use that same method today.  Remind the students that first we must find the least common multiple for the denominators.  Have the students say the multiples for the denominator 3 as you write them on the board.

Lipscomb College of Education, Fall 2012

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Have the students say the multiples of 12 as you write them on the board. Ask the students to identify the least common multiple and circle it. (12) Beneath the original equation on the board write the new equation with the denominators of 12 but blank numerators. 1/3 + 8/12 /12 + /12 Explain how you would find what factor you would multiply the original denominator by to equal the new denominator. (3 x ____ = 12) Multiply the numerator by the same number to get the new fraction. 1/3 + 8/12

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4/12 + 8/12 Explain that 1/3 would be 4/12 and 8/12 would stay the same because the denominator is already 12. Now have students look at the equations that they found to equal ¾. Have students look at the equation 2/8 + 6/12. Ask them to find the common denominator, which is the least common multiple between 8 and 12 with their elbow buddies. Tell them the LCM is 24. Have them give thumbs up or down for their answers. Follow the same process modeling the math on the board. 2/8 + 6/12 /24 + /24 Have students rewrite equivalent fractions with elbow buddy (6/24 + 12/24). Have students add fractions and simplify. (18/24 = 3/4) Now give students a sum to try to write a problem for themselves using their iPad fraction tiles. (7/8) Walk around and check modeling to avoid incorrect equations. Then have them attempt to prove it using math. Share some correct students work under the document camera. Tell students they will now try to find 5 different equations that will have the sum 1 1/4 with their table groups. Remind them to trace/sketch their models on paper and to prove that their equations equal 1 ¼ using math. Give each group chart paper for their final answers. (Walk around room having students explain strategies and check models for accuracy.) Students should post completed work around the room.

Closure: Today our goal was to be able to model math equations and use common denominators to add fractions. I would like each group to stand by their poster and explain how you proved your equations were equal to 1 ¼. Cross-curriculum Connections: Students are currently using fractions in art class to complete projects. Differentiated Instruction: Students have the opportunity to use manipulatives both virtual and physical. They have the opportunity to use math equations to prove their understanding. They have the opportunity to explain their understanding. They have the opportunity to work with partners, groups, and independently. ELL Modifications: N/A

Lipscomb College of Education, Fall 2012

SPED Modifications: These students will receive more guided practice over each skill before being asked to combine them to achieve the task. The culminating task of this lesson will not be completed in groups but with partners and with teacher guidance through each step. Assignment: Students will complete workbook page 165 independently.

Lipscomb College of Education, Fall 2012