Assessment Management. Math Boxes 8 2 Math Journal 2, p. 253 Students practice and maintain skills through Math Box problems.

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1 Adding Mixed Numbers Objectives To develop addition concepts related to mixed numbers. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Find equivalent fractions in simplest form. [Number and Numeration Goal ] Convert between and simplify fractions and mixed numbers. [Number and Numeration Goal ] Add fractions and mixed numbers. [Operations and Computation Goal ] Use benchmarks to estimate sums. [Operations and Computation Goal ] Key Activities Students review fraction addition. They add mixed numbers in which the fractional parts have like or unlike denominators and rename the sums in simplest form. Students use benchmarks to estimate sums. Informing Instruction See page. Recognizing Student Achievement Use an Exit Slip (Math Masters, page ). [Number and Numeration Goal ; Operations and Computation Goal ] Materials Math Journal, pp. and Study Link Math Masters, p. slate Class Data Pad (optional) Advance Preparation Math Boxes Math Journal, p. Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. Students practice and maintain skills through Study Link activities. READINESS Adding Mixed Numbers Math Journal, p. Students explore an alternate method for adding mixed numbers. EXTRA PRACTICE Playing Fraction Capture Math Journal, p. 9 Math Masters, p. 0 per partnership: six-sided dice Students practice comparing fractions and finding equivalent fractions. EXTRA PRACTICE Solving Mixed-Number Addition Problems Math Masters, p. A Students practice adding mixed numbers with like and unlike denominators. Teacher s Reference Manual, Grades pp., Unit Fractions and Ratios

2 Getting Started Mental Math and Reflexes Have students rename each fraction as a whole number or mixed number and each mixed number as an improper fraction. _ 7 7_ 7 _ Math Message Solve Problems 9 at the top of journal page. Use benchmarks to estimate the sums and to check the reasonableness of your solutions. Study Link Follow-Up Have partners compare answers and resolve differences. Ask volunteers to share their explanations for Problems 7,, and. Teaching the Lesson Math Message Follow-Up (Math Journal, p. ) ELL WHOLE-CLASS Ask students to share their strategies for estimating the sums for Problems. Make sure students make reference to the benchmarks when estimating their sums. Ask volunteers to share their strategies for renaming the sums in Problems to a whole or mixed number. Encourage students to use their understanding of multiplication facts to recognize when the simplest form will be a whole number. If the sum is an improper fraction and the numerator is not a multiple of the denominator, the simplest form will be a mixed number. If the numerator is a multiple of the denominator, the simplest form will be a whole number. Ask volunteers to explain how to recognize an improper fraction. If the numerator is greater than or equal to the denominator, the fraction is an improper fraction. To support English language learners, write and label examples of improper fractions on the board or Class Data Pad. Ask students to share their estimating strategies for Problem 7 using benchmarks. Sample answer: _ is less than _, and _ is greater than _. I estimated my answer to be about. Survey students for what methods they used to find the common denominators for Problems 7 9. Expect a mixture of the methods discussed in Lesson -. Summarize the methods on the board or Class Data Pad for student reference throughout the lesson. Date Math Message Time Add. Write the sums in simplest form Adding Mixed Numbers Add. Write each sum as a whole number or mixed number Adding Fractions Fill in the missing numbers Student Page Add. Write each sum as a mixed number in simplest form Math Journal, p. Lesson

3 Adding Mixed Numbers with Fractions Having Like Denominators WHOLE-CLASS Explain that one way to find the sum of mixed numbers is to treat the fraction and whole number parts separately. Write the problem below on the board or a transparency: _ + or _ Add the whole-number parts. Then add the fraction parts. Ask students to solve 7_ the following problem: + _ Informing Instruction Watch for students who have difficulty renaming mixed-number sums such as _. Discuss the meanings of numerator and denominator, and have students rename the fractional parts in the mixed numbers. Suggestions: _ 7 7_ = _ + _ = + _ = _ + _ = + 7 7_ = _ + _ = + _ Discuss students solution strategies. Make sure the following strategy is presented:. Add the whole-number parts. 7_. Add the fraction parts. +. Rename _ in simplest form. _ = _ + _ = + _ = _ Since _ = _, then _ = + + _ = _, or _. Model renaming _ with a picture. _ = _ Pose a few more addition problems in which the addends are mixed numbers with like denominators. Suggestions: _ 7 + _ 7 _ +, or _ _ + _ 9 7_ Madeleine purchased _ yards of red ribbon and 7_ yards of purple ribbon. How much ribbon did Madeleine purchase? _, or _ yards Mr. Marcus s class ate _ pizzas and Mr. Samuel s class ate _ pizzas. How many pizzas did the two classes eat? _ pizzas Unit Fractions and Ratios

4 Adding Mixed Numbers with Fractions Having Unlike Denominators WHOLE-CLASS Write the following problem on the board, and ask students to find the sum: _ + 7_ After a few minutes, ask students to share solution strategies. Make sure the following method is discussed:. Find a common denominator for _ and 7_,,,,.... Rename the fraction parts of the mixed numbers so they have the same denominator. In this case, the least common denominator,, is the easiest to use. _ _. Add. _. Rename the sum. _ = + _ + _ = + + _ = _ Pose a few more problems that involve finding common denominators to add mixed numbers. Suggestions: _ + _ 7_ _ + _ 7_, or 7_ _ + 0 Juanita needs 7_ yards of fabric for a dress and _ yards for a jacket. How many total yards does she need? 7 _ yards The costumes for the lead roles in the school musical require _ yards of one type of fabric and _ yards of another type of fabric. How much fabric needs to be purchased? _ yards Adding Mixed Numbers (Math Journal, pp. and ) _ + _ 0_ 0 7_ + _ 0 _ Have students complete journal pages and. Circulate and assist. Recognizing Student Achievement PARTNER Exit Slip Use an Exit Slip (Math Masters, page ) to assess students facility with adding mixed numbers. Have students explain how they found the answer to Problem on journal page. Students are making adequate progress if their responses demonstrate an understanding of renaming fractions to have common denominators and to be in simplest form. [Number and Numeration Goal ; Operations and Computation Goal ] Date Time To add mixed numbers in which the fractions do not have the same denominator, you must first rename one or both fractions so that both fractions have a common denominator. Example: _ + _ =? Find a common denominator. The QCD of _ and _ is =. Write the problem in vertical form, and rename the fractions. Add. Adding Mixed Numbers _ + _ 9_ + _ 0 9_ Rename the sum. 9_ = + _ + _ = + + _ = 7 _ Add. Write each sum as a mixed number in simplest form. Show your work.. _ + _ =. _ + _ =. _ + _ 9 =. _ + _ =. Sam purchased _ yards of fleece fabric for a jacket and _ yards of fleece fabric to make a blanket. How much fabric did he purchase? 0 _ 7 yards Student Page 7_ 7 9_ Math Journal, p. Lesson 7

5 Date. Add. a. b. c. d. e.. The school band practiced hours on Saturday and hours on Sunday. Was the band s total practice time more or less than hours? More than hours. Solve. Solution a. 9 x b. y0 w c. 9 d. 7 z 9 e. 77 v Math Boxes, or x 0 y w z v 7 Explain. Sample answer: 9 7 Student Page Math Journal, p. Time. Use the patterns to fill in the missing numbers. a.,,,, b.,,,, c.,,, 9, d. 0,,,, 7 e. 00,, 0,, 0. Make each sentence true by inserting parentheses. a. ) 0 b. ( ) ( c. 7 ) d. ( 7 ) e. ( 7 ). Circle the congruent line segments. a. b. c. d. ( 0 Ongoing Learning & Practice Math Boxes (Math Journal, p. ) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews Unit 9 content. Writing/Reasoning Have students write a response to the following: Explain your strategy for finding the values of the variables in Problem. Sample answer: I looked for the common factor of the numerators or denominators that were complete. Then I used the multiplication rule or the division rule to multiply or divide to find the values for the variables. NOTE Alternately, students may use a table or chart to find an equivalent fraction with the given denominator or numerator. Study Link (Math Masters, p. ) INDEPENDENT Home Connection Students practice adding mixed numbers and renaming improper fractions as mixed numbers in simplest form. Name Date Time STUDY LINK Adding Mixed Numbers Rename each mixed number in simplest form Add. Write each sum as a whole number or mixed number in simplest form Add Practice Study Link Master 90 7.,0., ,00 / (90 ),7 70 Differentiation Options READINESS Adding Mixed Numbers (Math Journal, p. ) SMALL-GROUP 0 Min To explore mixed-number addition, have students use an oppositechange algorithm. Have students change one of the addends to a whole number. Pose the following problem: _ + 7_. Change _ to a whole number by adding _ : _ + _ =.. Subtract _ from 7_ : _ = _ ; 7_ - _ = 7_.. Add the new addends: + 7 _ = 9_, or 9_. This strategy is most efficient when the sum of the fraction parts is greater than. Discuss how to recognize that the fraction parts are greater than. Have students use this method to solve the following problems: Math Masters, p. Unit Fractions and Ratios

6 _ + 7 _ 0 _ _, or 9_ _ _ 0 + _ 9_ 0 Before students begin journal page, have them identify problems for which this algorithm might apply. Problems EXTRA PRACTICE PARTNER Playing Fraction Capture (Math Journal, p. 9; Math Masters, p. 0) 0 Min Game Master Name Date Time Fraction Capture Gameboard Students practice comparing fractions and finding equivalent fractions by playing Fraction Capture. Players roll dice, form fractions, and claim corresponding sections of squares. The rules are on Math Journal, page 9, and the gameboard is on Math Masters, page 0. Math Masters, p. 0 EXTRA PRACTICE PARTNER Solving Mixed-Number Addition Problems (Math Masters, p. A) 0 Min Students practice adding mixed numbers with like and unlike denominators and use reasoning skills to compare sums of mixed numbers with whole numbers. Teaching Master Name Date Time Solving Mixed-Number Addition Problems Add. Write each sum as a mixed number in simplest form. Show your work.. _ + _ =. _ + _ 0 = 7 0. _ + _ = _. _ + _ 7 =. Josiah was painting his garage. Before lunch, he painted _ walls. After lunch, he painted another _ walls. How many walls did he paint during the day? _ walls. Julie s mom made muffins for Julie and her friends to share. Julie ate _ muffins. Her friends ate _ muffins. How many muffins did Julie and her friends eat altogether? _ muffins Without adding the mixed numbers, insert <, >, or =. Explain how you got your answer. 7. _ + _ > Sample answer: The sum of _ 9 and _ is. But _ is greater than _ 9, so the sum is greater than.. < _ + 7_ Sample answer: You only need to add _ to 7_ to get another whole. But _ is greater than _, so _ + 7_ is greater than. Math Masters, p. A Lesson 9

7 Name Date Time Solving Mixed-Number Addition Problems Add. Write each sum as a mixed number in simplest form. Show your work.. _ + _ =. _ + _ 0 =. _ + _ =. _ + _ =. Josiah was painting his garage. Before lunch, he painted _ walls. After lunch, he painted another _ walls. How many walls did he paint during the day?. Julie s mom made muffins for Julie and her friends to share. Julie ate _ muffins. Her friends ate _ muffins. How many muffins did Julie and her friends eat altogether? Without adding the mixed numbers, insert <, >, or =. Explain how you got your answer. 7. _ + _. _ + 7 _ Copyright Wright Group/McGraw-Hill A