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Grade 5 Mathematics: Division of Fractions

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Grade 5 Mathematics: Division of Fractions California CCSS.Math.Content.5.NF.7: Apply and extend previous understandings Common Core of division to divide unit fractions by whole numbers and whole numbers State Standards by unit fractions Mathematics CCSS.Math.Content.5.NF.7.B: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CCSS.Math.Content.5.NF.7.C: Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Common Core CCSS.MATH.PRACTICE.MP4 Model with mathematics. Math Practice Standards CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. Specific Learning Students will divide a whole number by a fraction using fraction models. Objectives Students will apply their learning to a real world problem. Materials • Math Journals • Pencil • Different colored pen/pencil Lesson Plan Teacher asks/says/does: Student asks/says/does: Engage 1. Write the expression 8 ÷ 2 1. Students will share their under the ELMO and ask thinking with their partner. Concept/Learning students to discuss with a Goal: partner what the expression 2. Students will volunteer answers means to them and how they to the whole class. Students will would find the answer. activate prior 3. Students will review objective knowledge of 2. Ask students to volunteer their and agenda for the lesson. division. thinking. 3. Draw eight circles. Ask students how they would show 8 ÷ 2 in the picture. 4. Review objective and agenda with students by saying, “Today, you are going to use what you already know about division, fractions, and fraction models in order to divide a fraction by a whole number.” Instructional Partner Share: All students engage with the material when they are Strategies Used required to discuss their thinking with a partner. (with rationale): Modeling: The picture helps connect the concept of division with the numerical expression. Scaffolding: The lesson begins with a simple division problem to help students make the connection between new and previous learning. How is student Partner Share participation ensured? Questions and What does 8 ÷ 2 mean? These questions will help students Levels of recall previous learning and Questioning How many groups of 2 are in 8? demonstrate understanding of the (Blooms) Used: concept of division. How can I show 8 ÷ 2 in a picture? How can I use multiplication to check my answer? Explore 1. Write the expression 1 ÷ ! 1. Students will record their thinking ! in their notebook throughout the under the ELMO. Ask Concept/Learning remaining portion of the lesson. students how they should Goal: interpret this expression 2. Students are selected via volunteers based on their previous Students will or equity sticks to help answer work thinking about 8 ÷ 2. connect division of a questions about the steps to whole number by a ! 2. Ask students how many simplify and explain 1 ÷ . fraction to their ! halves are in one whole. understanding of division of whole 3. Use the ELMO to draw the 3. Students work independently and numbers. fraction model to determine with a partner to simplify and the answer. Note the explain 1 ÷ ! . differences between the ! picture of 8 ÷ 2 and 1 ÷ ! . ! 4. Write 1 ÷ ! on the ELMO. ! Have students think about the problem independently for two minutes before discussing with a partner. Pick students to discuss their reasoning with the class. Instructional Modeling: Students will use fraction models to develop their Strategies Used understanding of a whole number divided by a fraction. (with rationale): Private Think Time: Students are provided an opportunity to attend to the material on their own before hearing ideas from their partner. This increases students’ ability to discuss with their partner. How is student Private Think Time participation Partner Share ensured? Questions and What does ½ mean? Students will demonstrate Levels of understanding of division of a whole Questioning What does 1 ÷ ! mean? number by a fraction. Students will (Blooms) Used: ! apply their learning to a new problem. How many ½ “groups” are in 1? What does ½ look like in my picture? How can I use this same thinking to determine 1 ÷ !? ! How can I use multiplication to check my answer? Explain 1. Discuss with students how 1. Students will write the expression they can extend their in their own notebook. Students strategy for dividing 1 by a will participate in a whole class Concept/Learning fraction to dividing other discussion of how to solve the Goal: whole numbers by a expression, 3 ÷ ! fraction. Ask students to ! Students extend their simplify the expression 2. Have students turn to their neighbor learning to more ! 3 ÷ . to discuss what happened. Use the complex problems. ! timer to allow time for discussion. 2. Draw a fraction model as When timer beeps, select volunteers shown below. or use equity sticks to have students explain their thinking. 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3. To find the quotient of 3 ÷ ! count the number of ! one-halves. (To emphasize this step in the drawing, circle each half as shown below. This may be something that is skipped once students understand the concept). There are 6 halves in three. Therefore, there are 6 one-halves in three- wholes. Three divided by one-half equals 6. 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 Instructional Modeling: Students extend fraction models to more difficult expressions. Strategies Used (with rationale): Summarizing: Students are able to synthesize new material by discussing what they just saw with their partner. How is student Whole Class Discussion participation Partner Share ensured? Questions and How does the problem differ Students will analyze the new problem Levels of from 1 ÷ ! and 1 ÷ !? based on their understanding of the Questioning ! ! previous problems. Students will (Blooms) Used: extend their understanding of a fraction How can we represent this model to solve the new problem. difference in our fraction model? Can you tell your partner what the expression 3 ÷ ! means? ! How do we use our fraction model to determine the answer? Elaborate 1. Provide students with 1. Students will practice the concept additional problems to solve by solving new problems through Concept/Learning in their notebook. Provide private think time and then with a Goal: private think time before partner. asking students to share Students apply their with a partner. 2. Students will extend their thinking learning to real by participating in a whole class world problems. Examples: discussion of a word problem. 2 ÷ ! 5 ÷ ! ! ! 3. Students will work on their own to solve a second world problem 2. Explain that can use division before discussing with the class. of a whole number by a fraction to help solve real- world word problems. Model for students how one can use a fraction model to answer the question below. Example: Josh has 3 candy bars. He cut each candy bar into ! pieces to share with ! his friends. How many pieces does Josh have? 3. Provide students with an additional word problem for them to solve on their own. Bring students back together to discuss as a class. Example: How many 1/3- cup servings are in 2 cups of raisins? Instructional Modeling: Students continue to use fraction models to solve problems. Strategies Used (with rationale): Connecting Concept to Real World Problem: Some students might grasp the concept more with the use of a real life example. How is student Private Think Time participation Partner Share ensured? Whole Class Discussion Questions and How can I represent the word Students must apply their learning to Levels of problem by a fraction model? create a fraction model and write an Questioning expression to represent a word (Blooms) Used: In the word problem, what problem. quantity is the whole number? What fraction am I dividing the whole number by? What mathematical expression represents the word problem? Evaluate 1. Return to the objective. 1. Students will reflect on their Have students give a understanding of the objective. Concept/Learning “thumbs-up” to show if they Goal: understand the objective, a 2. Students will simplify and explain “thumbs-sideways” if they a final problem on their own. Students will think they got it but are not synthesize the sure; or a “thumbs-down” if concepts addressed they don’t get it or feel lost. in this lesson by simplifying a new 2. Provide students with 3x5 expression. index card. Ask them to write to their parent(s)/guardian(s) explaining how to simplify 2 ÷ !. ! Instructional Individual Work Time: Students are able to discuss with a partner Strategies Used throughout the lesson. They will work on this last problem individually so (with rationale): they can summarize their learning. How is student Individual Activity participation ensured? Questions and How would you explain to your This closing question asks students to Levels of parent or another adult how to summarize the key learning in the Questioning simplify 2 ÷ !? lesson. (Blooms) Used: ! .
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