Objective To add and subtract mixed numbers with like denominators. 1 materials Teaching the Lesson Key Activities Students practice adding and subtracting mixed numbers that have fractions with like denominators. Щ— Math Journal 1, pp. 132 and 133 Щ— Student Reference Book, pp. 84вЂ“86 Щ— Study Link 4 3 бњ Key Concepts and Skills вЂў Convert between fractions and mixed numbers. [Number and Numeration Goal 5] вЂў Use multiplication and division facts to find equivalent fractions and to simplify fractions. [Operations and Computation Goal 2] вЂў Add and subtract mixed numbers with like denominators. [Operations and Computation Goal 3] Щ— Teaching Master (Math Masters, p. 117) Щ— scissors See Advance Preparation Key Vocabulary mixed number вЂў proper fraction вЂў improper fraction вЂў simplest form Ongoing Assessment: Recognizing Student Achievement Use journal page 133. [Operations and Computation Goal 3] 2 materials Ongoing Learning & Practice Students practice estimating sums of fractions by playing Fraction Action, Fraction Friction. Students practice and maintain skills through Math Boxes and Study Link activities. 3 materials Differentiation Options READINESS Students use a calculator to practice counting by fractions and converting between improper fractions and mixed numbers. ENRICHMENT Students read a poem about fractions. EXTRA PRACTICE Students use bills and coins to model and simplify mixed numbers. Additional Information Advance Preparation For the Math Message in Part 1, make one copy of Math Masters, page 117 for every two students. 272 Unit 4 Rational Number Uses and Operations Щ— Math Journal 1, p. 134 Щ— Student Reference Book, p. 317 Щ— Study Link Master (Math Masters, p. 118) Щ— Game Master (Math Masters, p. 446) Щ— Geometry Template; calculator Щ— Teaching Master (Math Masters, p. 119) Щ— Math Talk: Mathematical Ideas in Poems for Two Voices Щ— calculator; coins and bills of various denominations Technology Assessment Management System Journal page 133, Problems 9, 12, 14, and 15 See the iTLG. Getting Started Mental Math and Reflexes Math Message Students rename improper fractions as mixed numbers. Suggestions: Complete a copy of the Math Message problem. 3 1 бЋЏбЋЏ 1бЋЏбЋЏ 2 2 5 2 бЋЏбЋЏ 1бЋЏбЋЏ 3 3 75 3 бЋЏбЋЏ 18бЋЏбЋЏ 4 4 5 1 бЋЏбЋЏ 1бЋЏбЋЏ 4 4 13 1 бЋЏбЋЏ 2бЋЏбЋЏ 6 6 108 3 бЋЏбЋЏ 21бЋЏбЋЏ 5 5 Study Link 4 3 Follow-Up бњ Go over the answers. 1 Teaching the Lesson б¤ Math Message Follow-Up WHOLE-CLASS DISCUSSION NOTE If students are fairly skilled at finding (Math Masters, p. 117) sums and differences of fractions, this lesson may take less than one day. Ask a volunteer to demonstrate and explain how to use the paper ruler to measure the line segment. Sample answer: Line up the right end of A а·†B а·† with the mark for 4 in. on the ruler. The left end 5 of а·† AB а·† is aligned with the mark for бЋЏ16бЋЏ in. The total length of A а·†B а·† is 5 5 бЋЏ бЋЏ бЋЏ бЋЏ 4 in. П© 16 in., or 4 16 in. This ruler shows the two parts of a mixed number: the whole number and the fraction. A mixed number can be viewed as the sum of a whole number and a fraction. Discuss why fractions greater than 1 are easier to interpret when 3 written as mixed numbers. For example, 2бЋЏ4бЋЏ clearly represents a number greater than 2 but less than 3. This is not as obvious 3 11 when 2бЋЏ4бЋЏ is written as the improper fraction бЋЏ4бЋЏ. б¤ Writing Mixed Numbers Teaching Master Name WHOLE-CLASS DISCUSSION in Simplest Form Date LESSON Time Math Message 4 4 бњ Cut out the ruler below. Use it to measure line segment AB to the 1 nearest бЋЏбЋЏ inch. 16 A Review the meanings of proper fraction, improper fraction, and simplest form with the class. B вЂ” length of AB П бџ A fraction in which the numerator is less than the denominator is called a proper fraction. A proper fraction names a number that is less than 1. 3 9 5 бЋЏбЋЏ 16 4 in. 0 1 2 3 4 5 inches 0 Examples: бЋЏ8бЋЏ, бЋЏ10бЋЏ, бЋЏ4бЋЏ бџ A fraction in which the numerator is equal to or greater than the denominator is called an improper fraction. An improper fraction names a number that is greater than or equal to 1. 5 7 9 Examples: бЋЏ5бЋЏ, бЋЏ2бЋЏ, бЋЏ3бЋЏ Name Date LESSON Time Math Message 4 4 бњ Cut out the ruler below. Use it to measure line segment AB to the 1 nearest бЋЏбЋЏ inch. 16 A B вЂ” length of AB П 0 1 2 3 4 5 inches Math Masters, p. 117 Lesson 4 4 бњ 273 Student Page Date Time LESSON бџ A mixed number is in simplest form if the fraction part is a proper fraction in simplest form. Adding and Subtracting Mixed Numbers 4 4 бњ 2 5 4 5 Example 1: 1бЋЏбЋЏ П© 2бЋЏбЋЏ П ? 84вЂ“86 Step 1 Add the fractions. Then add the whole numbers. 6 3 бЋЏ65бЋЏ П 3 П© бЋЏ5бЋЏ 2 1бЋЏ5бЋЏ П© 5 1 П 3 П© бЋЏ5бЋЏ П© бЋЏ5бЋЏ 4 2 бЋЏ5бЋЏ 1 П 3 П© 1 П© бЋЏ5бЋЏ 1 П 4 бЋЏ5бЋЏ 6 3 бЋЏ5бЋЏ Add. Write your answers in simplest form. 1 4 бЋЏ5бЋЏ 1. 2 1бЋЏ4бЋЏ 2. 2 П© 3 бЋЏ5бЋЏ 3 П© 1 бЋЏ4бЋЏ 4бЋЏ14бЋЏ 7 7бЋЏ35бЋЏ 5 4 бЋЏ8бЋЏ Example 2: ПЄ 1 2 бЋЏ8бЋЏ 1 5 бЋЏ4бЋЏ 3. 3 П© 2 бЋЏ4бЋЏ 2 Step 2 If necessary, rename the difference. 5 4 бЋЏ8бЋЏ 5 4 бЋЏ8бЋЏ ПЄ 1 ПЄ 2 бЋЏ8бЋЏ 1 2 бЋЏ8бЋЏ 4 4 Example 3: ПЄ 2 1бЋЏ3бЋЏ 1 2 бЋЏ8бЋЏ П 2 бЋЏ2бЋЏ 2 бЋЏ8бЋЏ 1 5 бЋЏ3бЋЏ 9 be written using proper fractions, the fraction part is not required to be in simplest form. Students should know how to name fractions in simplest form for standardized tests. However, they may often find it helpful to work with fractions or mixed numbers that are not in simplest form when they are computing with fractions. 2 П© 1бЋЏ8бЋЏ 3 бЋЏбЋЏ 4 П? Step 1 Subtract the fractions. Then subtract the whole numbers. 8 NOTE While Everyday Mathematics requests that mixed-number answers 4 1бЋЏ8бЋЏ 4. 4 Examples: 2бЋЏ7бЋЏ is in simplest form. 4бЋЏ5бЋЏ and 3бЋЏ9бЋЏ are not in simplest form because they contain an improper fraction. 4 4 3бЋЏ8бЋЏ is not in simplest form because бЋЏ8бЋЏ is not in simplest form. Step 2 If necessary, rename the sum. 5 Write 3бЋЏ4бЋЏ on the board and ask a volunteer to rename it in simplest form. Use pictures similar to those below to show the procedure. П? Notice that the fraction in the first mixed number is less than the fraction in the second 2 1 1 mixed number. Because you canвЂ™t subtract бЋЏ3бЋЏ from бЋЏ3бЋЏ, you need to rename 5 бЋЏ3бЋЏ. Step 1 Rename the first mixed number. 1 1 5 бЋЏ3бЋЏ П 4 П© 1 П© бЋЏ3бЋЏ 3 Step 2 Subtract the fractions. Then subtract the whole numbers. 1 П 4 П© бЋЏ3бЋЏ П© бЋЏ3бЋЏ 4 5 бЋЏ3бЋЏ 1 4 бЋЏ3бЋЏ 2 ПЄ 1бЋЏ3бЋЏ 1 4 4 1 2 ПЄ 1бЋЏ3бЋЏ 4 П 4 П© бЋЏ3бЋЏ П 4 бЋЏ3бЋЏ 1 1 1 4 1 4 1 4 1 4 2 3 бЋЏ3бЋЏ 132 Math Journal 1, p. 132 5 34 П 1 1 П 1 1 Time 4 4 5 П 7 П© бЋЏ88бЋЏ 7 бЋЏ8бЋЏ 5 ПЄ 3 бЋЏ8бЋЏ а¬™ 6. 1 4 бЋЏ5бЋЏ ПЄ 2 бЋЏ4бЋЏ 3 ПЄ 2 бЋЏ5бЋЏ 1 бЋЏбЋЏ 2 4 бЋЏбЋЏ 5 5 7. 2 10. 1 2 1 3 бЋЏ5бЋЏ 5 11. ПЄ 1 бЋЏ5бЋЏ 3 ПЄ 1бЋЏ4бЋЏ 3 1 бЋЏбЋЏ 3 3 бЋЏбЋЏ 5 1 бЋЏбЋЏ 4 3 1 а¬™ 3 7 6 бЋЏ8бЋЏ 1 5 4бЋЏ2бЋЏ 5бЋЏ2бЋЏ 2 9 2бЋЏ3бЋЏ 3бЋЏ3бЋЏ 10 A U D I T O R Y 1 бЋЏбЋЏ 4 7 бЋЏ12бЋЏ inches 14. Mr. Ventrelli is making bread. He adds cups 1 of white flour and 1бЋЏ4бЋЏ cups of wheat flour. The recipe calls for the same number of cups of water as cups of flour. How much water should he add? 2 бЋЏ12бЋЏ cups of water 15. EvelynвЂ™s house is between RobertвЂ™s and ElizabethвЂ™s. How far is RobertвЂ™s house from ElizabethвЂ™s? 1 бЋЏбЋЏ 2 3 4 mi 3 1 4 mi 2 miles RobertвЂ™s EvelynвЂ™s 1 1бЋЏ6бЋЏ 2бЋЏ2бЋЏ ELL 3 П© 3 бЋЏ8бЋЏ 1 1бЋЏ4бЋЏ ElizabethвЂ™s 133 Math Journal 1, p. 133 274 1 П44 Have students model mixed numbers using bills and quarters. To 5 model 3бЋЏ4бЋЏ, use $3 and 5 quarters. Five quarters is equal to $1 and 1 quarter. Therefore, $3 and 5 quarters П $4 and 1 quarter. 1 ПЄ 3 бЋЏ4бЋЏ 3 бЋЏбЋЏ 4 12. П© 2 бЋЏ6бЋЏ 6 7 8. 3 13. Joe has a board that is 8 бЋЏ4бЋЏ inches long. He cuts 1 off 1бЋЏ4бЋЏ inches. How long is the remaining piece? а¬™ а¬™ 1 4 Adjusting the Activity 2 ПЄ 2 бЋЏ3бЋЏ 1 бЋЏбЋЏ 3 1 1 П© 3 Add or subtract. 4 бЋЏ6бЋЏ 1 4 5 4 бЋЏ8бЋЏ 9. 1 4 8 8 ПЄ 3 бЋЏ8бЋЏ 8 П 7 бЋЏ8бЋЏ 3 7бЋЏ5бЋЏ 8 Step 2 Subtract the fractions. Then subtract the whole numbers. 8П7П©1 1 П© 84вЂ“86 Step 1 Rename the whole number. 3 бЋЏ4бЋЏ П1 1 4 Write several such mixed numbers on the board. Have students rename them in simplest form. Suggestions: 5 Example 4: 8 ПЄ 3 бЋЏ8бЋЏ П ? 5. 4 4 1 4 3бЋЏ54бЋЏ can be renamed as 4бЋЏ14бЋЏ. Adding and Subtracting Mixed Numbers cont. бњ 1 4 1 4 Student Page LESSON 1 4 П© П Date 1 4 1 3 1 5 4 П© 3 Unit 4 Rational Number Uses and Operations бњ K I N E S T H E T I C бњ T A C T I L E бњ V I S U A L Student Page б¤ Adding Mixed Numbers INDEPENDENT ACTIVITY with Like Denominators Fractions Addition of Mixed Numbers One way to add mixed numbers is to add the fractions and the whole numbers separately. This may require renaming the sum. (Math Journal 1, p. 132; Student Reference Book, p. 84) 5 Example 7 Find 4бЋЏ8бЋЏ П© 2бЋЏ8бЋЏ. Step 1: Add the fractions. Step 2: Add the whole Step 3: Rename the sum. numbers. 2 4 Write the following problem on the board: 1бЋЏ5бЋЏ П© 2бЋЏ5бЋЏ П ? Ask students to solve and then share their strategies. Go over the steps on journal page 132 before having students complete Problems 1вЂ“4 on their own. Bring the class together to share solutions. If necessary, provide more practice, particularly with problems that require renaming. Refer students to page 84 in the Student Reference Book. 5 4 5 бЋЏбЋЏ 8 4 П©2 7 бЋЏбЋЏ 8 12 бЋЏбЋЏ 8 П©2 7 5 бЋЏбЋЏ 8 6 12 бЋЏбЋЏ 8 7 бЋЏбЋЏ 8 12 6 бЋЏ8бЋЏ П6П© 8 бЋЏбЋЏ 8 П© П6П©1П© 4 бЋЏбЋЏ 8 1 бЋЏбЋЏ 2 П7 П7 1 4бЋЏ8бЋЏ П© 2бЋЏ8бЋЏ П 7бЋЏ2бЋЏ 4 бЋЏбЋЏ 8 4 бЋЏбЋЏ 8 If the fractions do not have the same denominator, first rename the fractions so they have a common denominator. 3 Example 2 Find 3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ. Step 1: Rename and add П©5 3 3 бЋЏбЋЏ 4 2 бЋЏбЋЏ 3 П 3 ПП© 5 2 Step 3: Rename the sum. Step 2: Add the whole numbers. the fractions. 3 9 бЋЏбЋЏ 12 8 бЋЏбЋЏ 12 17 бЋЏбЋЏ 12 3 П©5 8 9 бЋЏбЋЏ 12 8 бЋЏбЋЏ 12 17 бЋЏбЋЏ 12 8 17 бЋЏбЋЏ 12 П 8 П© 12 бЋЏбЋЏ 12 П© П 8 П© 1 П© П 9 5 бЋЏбЋЏ 12 5 бЋЏбЋЏ 12 5 бЋЏбЋЏ 12 5 3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ П 9бЋЏ12бЋЏ б¤ Subtracting Mixed Numbers PARTNER ACTIVITY Some calculators have special keys for entering mixed numbers. 3 Example 2 Solve 3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ on a calculator. On Calculator A: Key in 3 with Like Denominators Unit On Calculator B: Key in 3 (Math Journal 1, pp. 132 and 133; Student Reference Book, p. 85) 3 3 4 n d 4 5 + 5 Unit 2 2 n 3 Enter = d 3 Check Your Understanding Solve Problems 1вЂ“3 without a calculator. Solve Problem 4 with a calculator. 1 Go over the three subtraction examples on journal pages 132 and 133 (Examples 2вЂ“4). Ask students to solve Problem 5. If successful, they should continue and complete the page. You may need to provide additional practice before continuing or refer students to page 85 in the Student Reference Book. Ongoing Assessment: Recognizing Student Achievement 7 4 1. 2бЋЏ8бЋЏ П© 7бЋЏ8бЋЏ 1 2 2. 3бЋЏ5бЋЏ П© 2бЋЏ2бЋЏ 3 4 3. 6бЋЏ3бЋЏ П© 3бЋЏ4бЋЏ Ch k 6 4. 14бЋЏ9бЋЏ П© 8бЋЏ7бЋЏ 417 Student Reference Book, p. 84 Journal Page 133 Problems 9, 12, 14, and 15 а¬™ Use journal page 133, Problems 9, 12, 14, and 15 to assess studentsвЂ™ ability to add mixed numbers with like denominators. Students are making adequate progress if they can calculate the sums in Problems 9, 12, 14, and 15. Some students may be able to calculate the differences in Problems 5вЂ“8, 10, 11, and 13. [Operations and Computation Goal 3] Student Page Fractions Subtraction of Mixed Numbers If the fractions do not have the same denominator, first rename them as fractions with a common denominator. 7 3 Find 3бЋЏ8бЋЏ ПЄ 1бЋЏ4бЋЏ. Example Step 1: Rename the fractions. 3 бЋЏ7бЋЏ 8 ПЄ1 бЋЏ3бЋЏ 4 7 8 ПЄ1 бЋЏ6бЋЏ 8 П 3 Step 2: Subtract the Step 3: Subtract the whole fractions. 3 бЋЏ7бЋЏ П 1 3бЋЏ8бЋЏ ПЄ 1бЋЏ4бЋЏ П 2бЋЏ8бЋЏ numbers. 3 бЋЏ8бЋЏ 7 3 бЋЏ7бЋЏ ПЄ1 бЋЏ6бЋЏ ПЄ1 бЋЏ6бЋЏ 8 8 1 бЋЏбЋЏ 8 8 2 бЋЏ1бЋЏ 8 To subtract a mixed number from a whole number, first rename the whole number as the sum of a whole number and a fraction that is equivalent to 1. 2 Find 5 ПЄ 2бЋЏ3бЋЏ. Example Step 1: Rename the whole number. ПЄ2 бЋЏ2бЋЏ 3 2 3 ПЄ2 бЋЏ2бЋЏ 3 П Step 3: Subtract the whole fractions. 4 бЋЏ3бЋЏ П 5 Step 2: Subtract the 1 5 ПЄ 2бЋЏ3бЋЏ П 2бЋЏ3бЋЏ numbers. 4 бЋЏ3бЋЏ 4 бЋЏ3бЋЏ 3 ПЄ 2 бЋЏ2бЋЏ 3 1 бЋЏбЋЏ 3 3 ПЄ 2 бЋЏ2бЋЏ 3 1 3 2 бЋЏбЋЏ When subtracting mixed numbers, rename the larger mixed number if it contains a fraction that is less than the fraction in the smaller mixed number. Example 1 3 Find 7бЋЏ5бЋЏ ПЄ 3бЋЏ5бЋЏ. Step 1: Rename the larger mixed number. 7 бЋЏ1бЋЏ 5 ПЄ 3 бЋЏ3бЋЏ 5 1 3 Step 2: Subtract the Step 3: Subtract the whole fractions. numbers. 6 бЋЏ6бЋЏ 5 6 бЋЏ6бЋЏ 5 6 бЋЏ6бЋЏ П ПЄ3 бЋЏ3бЋЏ ПЄ 3 бЋЏ3бЋЏ ПЄ 3 бЋЏ3бЋЏ П 5 3 7бЋЏ5бЋЏ ПЄ 3бЋЏ5бЋЏ П 3бЋЏ5бЋЏ 5 5 3 бЋЏбЋЏ 5 5 3 бЋЏ3бЋЏ 5 Student Reference Book, p. 85 Lesson 4 4 бњ 275 Game Master Name Date Time Fraction Action, Fraction Friction Card Deck 1 2 1 3 2 3 1 2 4 3 2 Ongoing Learning & Practice 1 4 б¤ Playing Fraction Action, PARTNER ACTIVITY Fraction Friction 3 4 1 6 1 6 5 6 1 12 1 12 5 12 5 12 7 12 7 12 11 12 11 12 (Student Reference Book, p. 317; Math Masters, p. 446) Distribute one set of 16 Fraction Action, Fraction Friction cards and one or more calculators to each group of two or three players. Review game directions on page 317 of the Student Reference Book. Play a few practice rounds with the class. б¤ Math Boxes 4 4 INDEPENDENT ACTIVITY бњ (Math Journal 1, p. 134) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-2. The skill in Problem 5 previews Unit 5 content. Students will need the Percent Circle on the Geometry Template to complete Problem 5. Math Masters, p. 446 б¤ Study Link 4 4 INDEPENDENT ACTIVITY бњ (Math Masters, p. 118) Home Connection Students practice addition and subtraction of mixed numbers. Study Link Master Student Page Date Time LESSON Name 4 4 18 бЋЏ a. бЋЏ 45 П 2 бЋЏбЋЏ 5 26 b. бЋЏбЋЏ П 39 2 бЋЏбЋЏ 3 1 3 a. бЋЏбЋЏ П© бЋЏбЋЏ П 10 5 7 бЋЏбЋЏ 10 56 c. бЋЏбЋЏ П 80 7 бЋЏбЋЏ 10 25 d. бЋЏбЋЏ П 625 1 бЋЏбЋЏ 25 5 1 b. бЋЏбЋЏ П© бЋЏбЋЏ П 12 3 3 бЋЏбЋЏ 4 7 4 c. бЋЏбЋЏ ПЄ бЋЏбЋЏ П 9 9 1 бЋЏбЋЏ 3 6 d. бЋЏбЋЏ 8 0 9 4 Write 2 fractions equivalent to бЋЏбЋЏ. e. 27 бЋЏбЋЏ 12 18 бЋЏбЋЏ 8 ПЄ 3 бЋЏбЋЏ 4 П In a national test, eighth-grade students answered the problem shown in the top of the table at the right. Also shown are the 5 possible answers they were given and the percent of students who chose each answer. Sample answers: a. 4. Thomas Jefferson was born in 1743. George Washington was born m years earlier. In what year was Washington born? Choose the best answer. following set of numbers. 1.5, 2.8, 3.4, 4.5, 2.2, 8.4 3.1 b. mean 3.8 m ПЄ 1743 The mean would double. 1743 ПЄ m 240 5. The table below shows the results of a survey in which people were asked which winter Olympic sport they most enjoyed watching. Use a Percent Circle to make a circle graph of the results. Favorite Sport Percent of People Surveyed Luge 35% Ice hockey 15% Figure skating 40% Other 10% Winter Olympic Sports Preferences 28% D. 21 27% 14% 1 бЋЏбЋЏ 4 1 inches (unit) 3 Add or subtract. Write your answers as mixed numbers in simplest form. Show your work on the back of the page. Use number sense to check whether each answer is reasonable. 1 3 1 бЋЏбЋЏ бЋЏбЋЏ бЋЏбЋЏ 1 1 1 2 2 2 4 3 4. 3бЋЏбЋЏ П© 1бЋЏбЋЏ П 5. 4 ПЄ 2бЋЏбЋЏ П 6. 1бЋЏбЋЏ П© бЋЏбЋЏ П 4 4 4 1 4 3 3 2 3 Circle the numbers that are equivalent to 2бЋЏ4бЋЏ. 7 6 бЋЏбЋЏ 4 3 бЋЏбЋЏ 7 11 бЋЏбЋЏ 4 Practice Solve mentally. 8. 5 Вє 18 П 90 9. 6 Вє 41 П 246 145 146 Unit 4 Rational Number Uses and Operations C. 19 Tim is making papier-mГўchГ©. The recipe calls for 1бЋЏ4бЋЏ cups of paste. Using only 1 1 1 бЋЏбЋЏ -cup, бЋЏбЋЏ -cup, and бЋЏбЋЏ -cup measures, how can he measure the correct amount? 2 4 3 1 Sample answer: He can use three бЋЏ2бЋЏ-cup measures and 1 one бЋЏ4бЋЏ-cup measure. 134 276 24% 3 1бЋЏ4бЋЏ Math Journal 1, p. 134 7% B. 2 3. Luge Other Figure skating A. 1 A board is 6бЋЏ8бЋЏ inches long. Verna wants to cut enough 1 so that it will be 5бЋЏ8бЋЏ inches long. How much should she cut? 7. Ice hockey Explain why B is the best estimate. 2. 1743 П© m 136 137 7 Percent Who Chose This Answer E. I donвЂ™t know. m П© 1743 Suppose you multiplied each data value by 2. What would happen to the mean? Possible Answers Both fractions are close to 1, so their sum should be close to 2. 83 74 12 Estimate the answer to бЋЏ13бЋЏ П© бЋЏ8бЋЏ. You will not have enough time to solve the problem using paper and pencil. What mistake do you think the students who chose C made? They may have added only the numerators. b. 3. Find the median and mean for the a. median 1. 2. Add or subtract. Then simplify. Time Ш‰, ШЉ Fractions and Mixed Numbers 4 4 бњ 1. Write each fraction in simplest form. Sample answers: Date STUDY LINK Math Boxes бњ Math Masters, p. 118 10. 9 Вє 48 П 432 11. 7 Вє 45 П 315 Teaching Master Name 3 Differentiation Options Date LESSON Time Fraction Counts and Conversions 4 4 бњ Most calculators have a function that lets you repeat an operation, such 1 as adding бЋЏбЋЏ to a number. This is called the constant function. To use 4 1 the constant function of your calculator to count by бЋЏбЋЏs, follow one of the 4 key sequences below, depending on the calculator you are using. PARTNER ACTIVITY READINESS б¤ Using a Calculator for Calculator A Calculator B Op1 + Press: 1 n 4 d Op1 1 1бЋЏ4бЋЏ Display: 5 Fraction Counts Display: 1. 1 a. b. 2. 1 4 6 4 1 бЋЏбЋЏ 4 1 1бЋЏбЋЏ? 2 6 6 How many counts of бЋЏбЋЏ are needed to display бЋЏбЋЏ? How many counts of are needed to display Use a calculator to convert mixed numbers to improper fractions or whole numbers. 11 11 бЋЏбЋЏ бЋЏбЋЏ 3 7 4 4 a. 2 бЋЏбЋЏ П b. 1бЋЏбЋЏ П 4 3. 5 бЋЏбЋЏ 4 K Using a calculator, start at 0 and count by бЋЏ4бЋЏs to answer the following questions. c. б¤ Reading about Fractions 0 Display: 1бЋЏ4бЋЏ Display: бЋЏбЋЏ PARTNER ACTIVITY + + 1 5 4 (Math Masters, p. 119) ENRICHMENT 4 Press: Press: To provide experience with fractions and mixed numbers, have students use the constant function on a calculator to define and generate fraction counts. They also study and apply patterns involving unit fractions, improper fractions, and mixed numbers. 1 Press: Op1 Op1 Op1 Op1 Op1 5вЂ“15 Min 4 3 4 4 2 бЋЏбЋЏ П d. 6 12 4 3 бЋЏбЋЏ П 1 4 How many бЋЏбЋЏs are between the following numbers? 3 a. бЋЏбЋЏ 4 c. and 2 3 4 1бЋЏбЋЏ and 4 5 9 6 b. бЋЏбЋЏ 4 d. 3 4 and 2 бЋЏбЋЏ 1 2 3 and 4 бЋЏбЋЏ 5 6 5вЂ“15 Min in Poetry Math Masters, p. 119 Literature Link To further explore fractions, have students read the poem вЂњProper FractionsвЂќ in Math Talk: Mathematical Ideas in Poems for Two Voices. Suggest that students recite the poem in their spare time and present it to the class. PARTNER ACTIVITY EXTRA PRACTICE б¤ Modeling Mixed Numbers 5вЂ“15 Min with Bills and Coins To provide extra practice simplifying mixed numbers, have students use bills and coins to model renaming procedures. Suggestions: 4 13 2бЋЏ4бЋЏ $2 and 4 quarters; 3 9 3 бЋЏбЋЏ 2бЋЏ1бЋЏ 0 $2 and 13 dimes; 3 10 1 1бЋЏ4бЋЏ $1 and 9 quarters; 3бЋЏ4бЋЏ 31 11 бЋЏбЋЏ 3бЋЏ2бЋЏ 0 $3 and 31 nickels; 4 20 Lesson 4 4 бњ 277

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