Lesson LESSON 23 Overview Understand Division with Unit Fractions CCSS Focus Lesson Objectives Prerequisite Skills Domain Content Objectives • Multiply and divide whole numbers. • Multiply whole numbers by unit Number and Operations—Fractions • Identify situations that involve dividing a fractions. Cluster unit fraction by a whole number. • Multiply unit fractions by unit fractions. B. Apply and extend previous • Identify situations that involve dividing a a 1 understandings of multiplication and • Understand that 5 a 4 b 5 a 3 . whole number by a unit fraction. ··b ··b division to multiply and divide fractions. • Use a visual fraction model to find the quotient of a unit fraction divided by a Lesson Vocabulary Standards whole number or the quotient of a 5.NF.B.7 Apply and extend previous whole number divided by a unit fraction. There is no new vocabulary. Review the understandings of division to divide unit following key term. fractions by whole numbers and whole • For a given division equation with a unit • unit fraction a fraction with a numbers by unit fractions. fraction and a whole number, write a numerator of 1. Other fractions are built a. In terpret division of a unit fraction by a multiplication equation that also can be used to find the quotient. from unit fractions. non-zero whole number, and compute such quotients. For example, create a Language Objectives 1 story context for 4 4, and use a ··3 • Draw a visual model to illustrate dividing visual fraction model to show the a unit fraction by a whole number. quotient. Use the relationship • Draw a model to illustrate using between multiplication and division multiplication to find the quotient of a 1 1 to explain that 4 4 5 3 12 unit fraction and whole number. 1 ·· 1 ·· because 3 4 5 . ··12 ··3 • Draw a visual model to illustrate dividing b. Interpret division of a whole a whole number a by unit fraction. number by a unit fraction, and • Draw a model to illustrate using compute such quotients. For example, 1 multiplication to find the quotient of a create a story context for 4 4 , and ··5 whole number and a unit fraction. use a visual fraction model to show the quotient. Use the relationship between multiplication and division 1 to explain that 4 4 5 20 because 5 1 ·· 20 3 5 4. Learning Progression ··5 Since Grade 3 students have used visual fractions to gain a conceptual Standards for Mathematical models such as arrays and area models to understanding of dividing with unit Practice (SMP) build foundational understanding of fractions. They divide whole numbers by SMPs 1, 2, 3, 4, 5, and 6 are multiplication and division of whole unit fractions and divide unit fractions by integrated in every lesson through the numbers. Students have multiplied with whole numbers, using area models, bar Try-Discuss-Connect routine.* fractions in Grade 4 and in previous models, fraction bars, number lines, and In addition, this lesson particularly Grade 5 lessons. Students have developed pictures to represent the division. emphasizes the following SMPs: an understanding of fractions as quotients In the next lesson students will apply 2 Reason abstractly and and learned that dividing a whole number their understanding of the concepts in this quantitatively. by a whole number is equivalent to lesson when they divide with unit 7 Look for and make use of structure. multiplying a whole number by a unit fractions in order to solve word problems. 8 Look for and express regularity in fraction. In Grade 6 students solve mathematical repeated reasoning. In this lesson students use their and real-world problems involving understanding of division with whole division of fractions by fractions. * See page 305m to see how every numbers and multiplication with unit lesson includes these SMPs. 457a Lesson 23 Understand Division with Unit Fractions ©Curriculum Associates, LLC Copying is not permitted. Lesson Pacing Guide Teacher Toolbox Whole Class Instruction Small Group Differentiation SESSION 1 Division with Unit Fractions Additional Practice PREPARE Explore • Start 5 min Lesson pages 461–462 • Model It 10 min Ready Prerequisite Lesson 45–60 min • Discuss It 5 min Grade 4 • Model It 10 min • Lesson 23 Understand Fraction Multiplication • Discuss It 10 min • Close: Exit Ticket 5 min RETEACH SESSION 2 Understanding of Division with Unit Additional Practice Tools for Instruction Fractions Lesson pages 465–466 Develop Grade 4 • Start 5 min • Lesson 23 Understand Fraction Multiplication 45–60 min • Model It: Area Models 5 min Fluency • Discuss It 5 min Understanding of Grade 5 Division with Unit • Model It: Number Lines 5 min • Lesson 23 Dividing with Unit Fractions Fractions • Discuss It 5 min • Connect It 15 min REINFORCE • Close: Exit Ticket 5 min Math Center Activity SESSION 3 Ideas About Division with Unit Lesson Quiz Grade 5 • Lesson 23 Quotients—Greater Than 1 or Refine Fractions or Digital • Start 5 min Comprehension Check Less Than 1? 45–60 min • Apply It 35 min • Close: Exit Ticket 5 min EXTEND Enrichment Activity Lesson Materials Grade 5 Lesson none • Lesson 23 Mystery Equation (Required) Activities Per student: 1 set of fraction circles or tiles Per pair: 2 sets of fraction circles or tiles Digital Math Fraction Models Independent Learning Tool PERSONALIZE i-Ready Lesson* Grade 5 • Understand Division with Unit Fractions * We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson. ©Curriculum Associates, LLC Copying is not permitted. Lesson 23 Understand Division with Unit Fractions 457b LESSON 23 Connect to Family, Community, and Language Development The following activities and instructional supports provide opportunities to foster school, family, and community involvement and partnerships. Connect to Family Use the Family Letter—which provides background information, math vocabulary, and an activity— to keep families apprised of what their child is learning and to encourage family involvement. Available in Spanish Teacher Toolbox Understand Division with Unit Fractions ACTIVITY DIVIDING w Un FrNs Dear Family, 23 Do this activity with your child to understand division with unit fractions. Work together with your child to solve real-life problems involving division with This week your child is exploring division with unit fractions. unit fractions. • Together with your child, use the picture to solve the problem below. 1. Suppose we want to give each person in our family half of a sandwich. A unit fraction is a fraction that has 1 as the numerator. 1 and 1 are examples of ··6 ··4 The sandwiches are shown below. How many people can we feed with these unit fractions. To learn about division with unit fractions, your child might see a 4 sandwiches? Do we have enough for our family, too many, or too few? problem like the one below. A butcher wants to divide 3 pounds of meat into packages that will each contain 1 pound of meat. How many packages can she make? ··2 1 This problem can be solved by fi nding 3 4 . It can be helpful to use a number line ··2 model to understand the problem. 1 1 1 1 1 1 2 lb 2 lb 2 lb 2 lb 2 lb 2 lb 0 1 2 3 1 The model shows that 3 4 5 6. The butcher can make 6 packages that each ··2 1 contain pound of meat. ··2 Another way to say this is that the butcher can make 2 packages of meat per pound. An equation that shows this is 3 3 2 5 6. 1 • Look for similar situations in everyday life that involve dividing with a So, 3 4 5 6, and 3 3 2 5 6. Your child is learning that division and multiplication ··2 unit fraction. Below are some examples of problems you could solve. with fractions are related, just like division and multiplication with whole numbers are related. 2. If you divide 2 hours of piano practice into sessions of 1 hour each, how many ··2 sessions do you have to practice? Invite your child to share what he or she knows about division with unit fractions by doing the following activity together. 1 3. One lap around the track is mile. How many laps do you need to do to run ··4 3 miles? Answers: 1 1 1 1. 4 4 __ 5 8; You can feed 8 people with the four sandwiches; 2. 2 4 __ 5 4 sessions; 3. 3 4 __ 5 12 laps 457 458 2 2 4 ©Curriculum Associates, LLC Copying is not permitted. Lesson 23 Understand Division with Unit Fractions 457 458 Lesson 23 Understand Division with Unit Fractions ©Curriculum Associates, LLC Copying is not permitted. Goal Math Talk at Home The goal of the Family Letter is to provide opportunities for families Use the examples in the activity as a model to come up with other to help students develop an understanding of division with unit real-world problems involving dividing with unit fractions. Using fractions. food items and number of friends or family members might be a scenario that most family members can relate to. Activity Conversation Starters Below are additional conversation starters Encourage students to solve real-life problems involving division students can write in their Family Letter or math journal to engage with unit fractions. Look at the Dividing with Unit Fractions activity family members: and modify it if necessary to connect with your students. • What are some examples of whole objects that you might want to divide equally? • How many parts will you divide or split the object into? Why? 457–458 Lesson 23 Understand Division with Unit Fractions ©Curriculum Associates, LLC Copying is not permitted.