Grade Level/Course: Grade 5 Lesson/Unit Plan Name: Multiplying Fractions Rationale/Lesson Abstract: Students will conceptually understand multiplying fractions using an area model. Students will then be able to apply their understanding of multiplying fractions to solve word problems. Timeframe: 3 Days Common Core Standard(s): 5.NF.B.4 – Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.B.6 – Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Instructional Resources/Materials: -‐Scissors -‐Transparencies -‐Fraction Area Models -‐Zip-‐lock bags Page 1 of 11 MCC@WCCUSD 10/06/13 Background/Connecting Prior Knowledge: Utilize students’ prior knowledge on multiplying whole numbers using an array or area model to introduce multiplying fractions. Remind students that we use multiplication to find ‘groups of’ something. 2 x 3 is 2 groups of 3 1 1 2 x is 2 groups of 2 2 1 1 1 1 x is of a group of 4 2 4 2 Activity/Lesson: Multiplying Fraction by a Whole Number 2 2 or 4 of 3 3 Draw It 4• “We will begin by drawing 4 groups of 2 ” 3 “How many thirds do we have out of the four groups?” [8] 2 So 4 • 3 8 = 3 8 8 “Is there another way I can write ?” “What do you know about the fraction ?” 3 3 Take this opportunity to review that an improper fraction tells us that there are whole(s) within the fraction. “We can combine all the thirds and see how many wholes we have.” “How many wholes did we create?” [2] “How many thirds do we have left?” [two thirds] Page 2 of 11 MCC@WCCUSD 10/06/13 ∴ 4 • = 2 3 8 2 or 2 3 3 Write It 4• 2 3 “Do you notice another way we can get the answer 8 ?” [4 times 2 give us 8 and we can keep the 3 3 as the denominator.] 4 ” 1 As you work out the algorithm, point to the picture to show students the connection between the visual and algorithm. “We can multiply like-terms by converting the 4 to a fraction, 2 3 4 2 = • 1 3 4•2 = 1• 3 8 = 3 4• or 2 2 3 We Do (Draw It and Write It) 3 • 5 4 You Try (Draw It and Write It) 2 3 • 6 Page 3 of 11 MCC@WCCUSD 10/06/13 Multiplying Fraction by a Fraction (Build It, Draw It, Write It) Build It and Draw It Make copies of the Fraction Area Models template on to transparencies. Sets can be made for partner share or individual students. Remind students when we create an area model for a multiplication problem, one term is represented by the height and the other term is represented by the base. Since we are multiplying fractions, which is part of a whole, the area of the model/square will always equal to a one. Therefore, the height will equal to one and the base will equal to one. As students build each step to simplify the problem, have them record each step by drawing what they’ve built. Tell students to use a striped Fraction Area Model to represent one term and a dotted Fraction Area Model to represent the other term. Example #1 1 3 • 4 5 Have students pull out the striped Fraction Area Model for and the dotted m odel f or Draw the models. Overlay the on top of the model. The over lapping parts show what is of a group of . The numerator and the denominator is represented by the amount of pieces that creates the whole which is 20. = = *Remember, fraction is out of a whole. To find what is 1 3 3 of we can’t just make fourths out of the , 4 5 5 but we have to make fourths out of the whole. Page 4 of 11 MCC@WCCUSD 10/06/13 “Do you notice another way we can get the answer?” Allow students to discover the rule to multiplying fractions where we can multiply across the numerator and d enominator to get the answer. Example #2 Follow the same process as Example #1. 5 2 • 6 3 Ask students what they notice about the answer. Is this the final answer? Students should point out the fraction is not in simplest form. = = Simplify the fraction. Page 5 of 11 MCC@WCCUSD 10/06/13 Ask students what they notice about the step where we multiply the fractions to where we simplify the fraction. Show students that instead of multiplying our numerator and d enominator together and then decomposing it by its prime factor to simplify, we can prime factor it right away. We Do (Build It, Draw It, Write It) 1 3 • 6 4 You Try (Build It, Draw It, Write It) 1 4 • 2 5 Page 6 of 11 MCC@WCCUSD 10/06/13 Word Problems Emphasize to students that drawing a visual representation of the word problem will help them visualize what they need to find and how they need to solve it. 4 2 Sammy’s play mat is of a meter long and of a meter wide. Find the area of Sammy’s play 5 3 mat. Draw a square to represent the length of Sammy’s play mat. On the same model, create horizontally to represent the width. ∴ The area of Sammy’s play mat is 8 15 We Do 4 There are pounds of dog food in each bag. How many pounds of dog food would be in 3 6 bags? You Try 2 3 Zoe brought of her leftover lasagna to work. She ate of the leftover lasagna at lunch. How 3 4 much lasagna does Zoe have leftover? Page 7 of 11 MCC@WCCUSD 10/06/13 Closing Display a multiplication problem using whole numbers and another problem using fractions, with answers, side-‐by-‐side. Ask students what they notice about the answers to both multiplication problems. Students may tell you that the answers are larger in value than the problem. This is true for multiplying whole numbers. For multiplying fractions, the terms of the fraction do get larger, but a larger denominator means smaller in value for a fraction. Page 8 of 11 MCC@WCCUSD 10/06/13 Fraction Area Models Copy the two pages onto transparency and have students cut them out to model multiplying Page 9 of 11 MCC@WCCUSD 10/06/13 Fraction Area Models Copy the two pages onto transparency and have students cut them out to model multiplying Page 10 of 11 MCC@WCCUSD 10/06/13 Assessment: 2 2 foot of a rope in his garage. He used of it for his tree house. How much rope 5 6 does he have left? Which of the following response are possible solutions? Jack has a) 2•2 2 •3•5 b) 4 11 c) d) 2 3•5 Page 11 of 11 MCC@WCCUSD 10/06/13