advertisement

2.2 Unit Fractions of a Whole ? Essential Question What do the top and bottom numbers of a fraction tell? Texas Essential Knowledge and Skills Number and Operations—3.3.C Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number. What do the top and bot tom numbers of a fraction tell ? Also 3.3.A MATHEMATICAL PROCESSES 3.1.C Select tools, technology, and techniques 3.1.F Analyze mathematical relationships Are You Ready? Access Prior Knowledge Use the Are You Ready? 2.2 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson. Lesson Opener Making Connections Invite students to talk about kites. Ask them the following questions. Vocabulary fraction, unit fraction Go to Multimedia eGlossary at thinkcentral.com Have you ever flown a kite? How many kites have you ever seen in the sky at the same time? What did the most interesting kite you have ever seen look like? Using the Digital Lesson You can use the lesson opener to explain to students parts of a whole. Point out, or ask students to identify, one group of objects in the sky in the lesson opener. Ask students what objects on the ceiling and walls of the classroom could be grouped together. Point out to students one group of objects on the ground in the lesson opener. Ask students what objects on the tables, counters, and floor of the classroom could be grouped together. Ask students what one kite or one gopher hole represents. Resources Learning Task Direct students’ attention to the group of kites in the sky. • How many kites does Doc see flying? (4) • What is the whole in this problem? (the number of kites) • How would you tell someone that 1 of the kites is blue using the word fourth? (One fourth of the kites is blue.) Literacy and Mathematics You may choose the following activity. Invite students to draw a picture of the kites. Have them color or label the kites to show how many are red, blue, and green. Alternately, have students use connecting cubes to represent the kites in the problem: 1 green, 1 blue, and 2 red. For the student For the teacher Interactive Student Edition provides students with an interactive learning environment! Digital Management Center organizes program resources by TEKS! eTeacher Edition Math on the Spot Video Tutor Online Assessment System iTools Virtual Manipulatives Soar to Success Math Online Intervention Lesson 2.2 43A Name Unlock the Problem 2.2 Hands On ? How can you use numbers to show a part of a whole? Solve the problem to find out. Number and Operations—3.3.C Also 3.3.A MATHEMATICAL PROCESSES 3.1.C, 3.1.F Unit Fractions of a Whole Essential Question What do the top and bottom numbers of a fraction tell? A fraction is a number that names part of a whole or part of a group. In a fraction, the top number tells how many equal parts are being counted. Example 1 1 _ 6 Find part of a whole. The bottom number tells how many equal parts are in the whole or in the group. Read the information with students. Point out that the “Read” part is in word form and the “Write” part is in number form. A unit fraction names 1 equal part of a whole. It has 1 as its top number. 1 _ is a unit fraction. 6 • What does the top number of the unit fraction 1_6 tell you? the number of pieces of pie that Luke ate Example 1 Find part of a whole. • What does the bottom number tell you? the total Luke’s family picked strawberries to make a strawberry pie. They cut the pie into 6 equal pieces. Luke ate 1 piece. What fraction of the strawberry pie did he eat? number of equal pieces in the whole pie Shade 1 of the 6 equal parts. Example 2 Read: one sixth Find part of a group. 6 So, Luke ate _ of the strawberry pie. Example 2 Find part of a group. Jake has a collection of marbles. What fraction of his collection is yellow? There is 1 yellow marble out of a group of 8 marbles. • What number represents the total number of marbles to write as the bottom number? 8 • What number represents the total number of yellow marbles to write as the top number? 1 English Language Learners Leveled Activities ELPS Beginning: Activity 20 1.A.1, 3.G.2, 4.C.3 Intermediate: Activity 3 2.D.2, 2.E.3, 3.F.2 Advanced: Activity 41 4.F.3, 4.F.8 Advanced High: Activity 48 4.F.1, 4.F.2, 4.G.2 thinkcentral.com for the ELL Activity Guide containing these leveled activities. Module 2 © Houghton Mifflin Harcourt Publishing Company Have students look at Jake’s marbles first and guide them through the text. • What is the relationship between the number of yellow marbles and the total number of marbles? Write: 1_6 1 _ Tell students that they have learned how to find the fractional part of a whole. Now they will learn how to describe a fraction of a group. 43 Hands On Unlock Unlock the the Problem Problem number of yellow marbles → 1 ___ total number → 8 of marbles Read: one eighth or one out of eight Write: 1_8 1 _ 8 of Jake’s collection is yellow. So, _ ELL Language Support Module 2 43 Verbal / Linguistic Small Group ELPS 1.A.1, 2.E.3 Strategy: Identify Patterns • Students identify patterns in language to help communicate about fractions. • Help students find patterns between cardinal numbers, which tell about quantity, and unit fractions. • As students work through problems, prompt them to identify these patterns: four/fourth; six/sixth; eight/eighth, etc. • Point out that these numbers don’t follow the pattern: two/half, three/third. Math Talk Share Share and and Show Show Mathematical Processes 1 _ 3 1. What fraction names the shaded part? _ Explain how you knew what number to write as the bottom number of the fraction in Exercise 1. Think: 1 out of 3 equal parts is shaded. Share and Show The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. I counted the total number of equal parts in the whole. Since there Write the number of equal parts in the whole. are 3 equal parts, I wrote 3 as the Then write the fraction that names the shaded part. bottom number. 2. 3. Math Talk 4. Mathematical Processes Use Math Talk to reinforce that the denominator tells how many equal parts there are in the whole. 3 equal parts _ 4 equal parts _ 8 equal parts _ 1 _ 3 _ 1 _ 4 _ 8 _ Guide students in completing Exercises 2–4. 1 _ • For which part of the fraction do you write the number of equal parts? the bottom number in the Write a fraction to name the yellow part of each group. 5. fraction 6. Use the checked exercises for Quick Check. 1 _ 1 _ 4 _ 3 _ 7. 3 8. 1 _ 4 _ 2 1 _ 5 _ Quick Check 1 IF Problem Problem Solving Solving Draw a picture of the whole. Check students’ drawings. THEN 1 10. _ is 6 Possible drawing: 44 © Houghton Mifflin Harcourt Publishing Company 1 9. _ is 2 a student misses the checked exercises Differentiate Instruction with RtI Tier 1 Lesson 8 In Exercises 5–8, students write the fraction that names part of a group. Remind them to count the total number of objects in the group for the bottom number in the fraction. Problem Solving Problems 9–10 require students to visualize and draw a picture of the whole given a part of it. Guide students to think about how many of the parts shown make up a whole. Enrich Kinesthetic Individual Go Deeper Materials: pattern blocks • Give students a set of pattern blocks. Explain that the yellow hexagon represents 1 whole. • Have students find what fraction of the yellow hexagon is represented by other blocks. For example, 2 red trapezoids together completely cover the yellow hexagon. So, a red trapezoid is 1_2 of a yellow hexagon. whole one half one third Go to Go to thinkcentral.com for additional enrichment activities in the Enrich Activity Guide. To extend students’ thinking, have them draw more than one possible whole for Problems 9–10. Then ask them to draw other pictures showing part of a whole, exchange with a classmate, and draw a picture of the whole. one sixth Lesson 2.2 44 Name Problem Problem Solving Solving Problem Solving Use the pictures for 11–13. Students use the pictures in the chart to solve Problems 11–13. If students have difficulty with Problem 13, have them find a lunch item that relates to the fraction 1_4 . 11. 1 _ 8 Give students the opportunity to share and discuss their explanations for Problem 14. 12. Problem What fraction of the cookie did Kylie eat? Write the fraction in numbers and in words. 1 _ 2 Problem 15 is a multi-step problem that requires students to reason about equal parts and the number of parts that equal 1 whole. Kylie’s Lunch Dylan’s Lunch sandwich pizza cookie fruit bar Use Diagrams The missing parts of the pictures show what Kylie and Dylan ate for lunch. What fraction of the pizza did Dylan eat? one half Write Math 13. What’s the Question? The answer is 1_4 . Possible question: What fraction of the fruit bar did Dylan eat? COMMON ERRORS C 14. E Error Students might count only the unshaded parts as the denominator. Example When writing the fraction that names the shaded part, students might write the answer 1 _ instead of 1_ . 5 6 M Math on the Spot Video Tutor V Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment. No; possible explanation: the square is not divided into six equal parts, so he did not shade _16 . 15. © Houghton Mifflin Harcourt Publishing Company Springboard to Learning Remind students that the bottom number should tell the total number of equal parts in the whole or in the group. Diego drew lines to divide the square into 6 pieces as shown. Then he shaded part of the square. Diego says he shaded 1_6 of the square. Is he correct? Explain how you know. Multi-Step Riley and Chad each have a granola bar broken into equal pieces. They each eat one piece, or 1_4 , of their granola bar. How many more pieces altogether do Riley and Chad need to eat to finish both granola bars? Draw a picture below to justify your answer. 6 more pieces Check students’ drawings. Possible drawing: Module 2 • Lesson 2 45 3 RtI Tier 1 Lesson 8 2 1 Enrich 7 Name Name Unit Fractions of a Whole LESSON 8 Enrich 7 1 3.3.C OBJECTIVE Use a fraction to name one part of a whole that is divided into equal parts. Whole Lot of Fractions! Draw lines and shade each shape to show the fraction. Math on the Spot videos are in the Interactive Student Edition and at thinkcentral.com. A fraction is a number. It names part of a whole or part of a group. 1 1. __ The top number tells how many equal parts are being counted. The bottom number tells how many equal parts are in the whole. A unit fraction names 1 equal part of a whole. It always has 1 as its top number. Possible answers are shown. 1 2. __ 2 4 How much is 1 part of a fruit bar that is cut into 8 equal parts? Step 1 Use fraction strips. Make a strip showing 8 equal parts, or eighths. 1 3. __ 1 4. __ 1 5. __ 1 6. __ 4 8 Step 2 Shade 1 of the parts and name it. 3 © Houghton Mifflin Harcourt Publishing Company __. This fraction is called 1 8 1. So, 1 part of a fruit bar that can be divided into 8 equal parts is __ 8 Write the number of equal parts in the whole. Then write the fraction that names the shaded part. 1. 2. 4 1 __ 4 45 Module 2 2 equal parts Number and Operations 3. 3 1 __ 3 equal parts 7. 6 1 __ 6 Stretch Your Thinking What unit fraction of the figure is shaded? Explain your answer. _1 ; 6 equal parts possible answer: I can divide the shape into 6 equal triangles, and 1 out of 6 equal parts is shaded. 15 Enrich © Houghton Mifflin Harcourt Publishing Company E7 Mathematical Processes Model ¥ Reason ¥ Communicate Daily Daily Assessment Assessment Task Task 3 Fill in the bubble for the correct answer choice. 16. 17. Daily Assessment Task There are 2 red cubes, 3 yellow cubes, and 1 blue cube in a bag. What fraction of the cubes are blue? A 1 _ 4 C 1 _ 6 B 1 _ 3 D 1 _ 2 2 1 Can students explain what the top and bottom numbers of a fraction tell? THEN IF Representations Brandon shared a large burrito with two of his friends. The missing part of the picture shows what Brandon ate. What fraction of the burrito did Brandon eat? NO • Soar to Success Math Warm-Up 5.08, 5.10 YES • • Enrich 7 Homework and Practice Lesson 2.2 A 18. 1 _ 4 B 1 _ 3 1 _ 2 C D 1 _ 6 TEXAS Test Prep Coach Multi-Step For an art project, Tonya and Sahil each have a piece of fabric cut into equal pieces. They each used one piece, or 1_3 , of their fabric. How many more pieces altogether do Tonya and Sahil have left to use? Test Prep Coach helps teachers to identify common errors that students can make. A 2 C 4 In the Test Prep exercise, if students selected: B 6 D 5 A They switched the numerator and the denominator. C They miscounted the number of equal parts. TEXAS Test Prep Mary shaded part of a rectangle. What fraction names the part she shaded? A 3_ 1 B 1 _ 3 C 1 _ 4 D 1 _ 2 © Houghton Mifflin Harcourt Publishing Company 19. 46 D They counted the number of unshaded parts instead of the total number of parts. ? Essential Question Write Math What do the top and bottom numbers of a fraction tell? The top number tells how many equal parts are being counted. The bottom number tells how many equal parts are in the whole. Differentiated Centers Kit Literature Pizza Parts! Students read about how to find equal parts to write fractions. Activities Fish for Fractions Students complete orange Activity Card 11 by playing a Go Fish game in which they match fraction symbols, words, and pictures. Lesson 2.2 46 5 Number and Operations—3.3.C Also 3.3.A MATHEMATICAL PROCESSES 3.1.C, 3.1.F Ho mewo rk and Practice 2.2 Fill in the bubble completely to show your answer. Unit Fractions of a Whole 7. Write the number of equal parts in the whole. Then write the fraction that names the shaded part. The drawing below shows what the moon looks like tonight. What fraction names the shaded part? 2 equal parts 6 equal parts 1 _ 1 _ 6 2 3. B 9. 4. 8 equal parts 4 equal parts 1 _ 8 1 _ 4 Problem Problem Solving Solving © Houghton Mifflin Harcourt Publishing Company Mike divided a piece of paper into 4 equal parts. He shaded one of the parts. What fraction of the piece of paper did Mike shade? 2. A Toni’s fruit bar is divided into three equal pieces. Toni ate one piece. What fraction of the fruit bar did Toni eat? Draw a picture to show your answer. 10. 6. The missing part of the picture shows what Kylie ate for lunch. What fraction of the sandwich did Kylie eat? 2 __ 1 1__ 3 C D 1 __ 2 1__ 6 A B 1 _ 1 _ 2 3 Module 2 • Lesson 2 Use the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson. Module 2 47 48 1 __ 2 1__ 4 C D 1 __ 8 4 __ 1 What is __1 of this rectangle? 3 A C B D Multi-Step Two brothers each have a sandwich divided into 4 equal pieces. Each brother eats one part, or 1_4 , of his sandwich. How many parts of the sandwiches are left altogether? Check students’ drawings. Homework and Practice 47-48 8. 11. Multi-Step Taylor has a yellow block of cheese and an orange block of cheese. He cuts each block into eight equal parts and takes one part, or 1_8 , of each block. How many parts of the blocks of cheese are left altogether? A 1 part C 6 parts A 6 parts C 8 parts B 4 parts D 8 parts B 14 parts D 12 parts © Houghton Mifflin Harcourt Publishing Company 1. 5. TEXAS Test Prep Lesson Lesson Check Check Name