Number and Operations Fractions

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2 Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. Lesson CC..NF. Common Denominators and Equivalent Fractions Lesson CC..NF. Add and Subtract Fractions Lesson CC..NF. Add and Subtract Mixed Numbers Lesson CC..NF. Subtraction with Renaming Lesson CC..NF. Algebra Patterns with Fractions Lesson 7 CC..NF. Algebra Use Properties of Addition Lesson CC..NF. Addition with Unlike Denominators Lesson CC..NF. Subtraction with Unlike Denominators Lesson 0 CC..NF. Estimate Fraction Sums and Differences Lesson CC..NF. Problem Solving Practice Addition and Subtraction Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Lesson CC..NF. Interpret the Remainder Lesson CC..NF. Connect Fractions to Division Lesson CC..NF.a Find Part of a Group Lesson CC..NF.a Multiply Fractions and Whole Numbers Lesson CC..NF.a Fraction and Whole Number Multiplication..... Lesson 7 CC..NF.a Fraction Multiplication Lesson CC..NF.b Multiply Fractions Lesson CC..NF.b Area and Mixed Numbers Lesson 70 CC..NF.a Compare Fraction Factors and Products Lesson 7 CC..NF.a Compare Mixed Number Factors and Products.... Lesson 7 CC..NF.b Problem Solving Find Unknown Lengths..... Lesson 7 CC..NF. Multiply Mixed Numbers Lesson 7 CC..NF.7a Divide Fractions and Whole Numbers CC..NF.7b Lesson 7 CC..NF.7b Problem Solving Use Multiplication Lesson 7 CC..NF.7c Fraction and Whole-Number Division Lesson 77 CC..NF.7c Interpret Division with Fractions v

3 LESSON Common Denominators and Equivalent Fractions OBJECTIVE Find a common denominator or a least common denominator to write equivalent fractions. CC..NF. You can find a common denominator of two fractions. A common denominator of two fractions is a common multiple of their denominators. Find a common denominator of _ and 7 0. Rewrite the pair of fractions using a common denominator. Step Identify the denominators. The denominators are and 0. Step List the multiples of the greater denominator, 0. Multiples of 0: 0, 0, 0, 0, 0, 0,... Step Check if any of the multiples of the greater denominator are evenly divisible by the other denominator. Both 0 and 0 are evenly divisible by. Common denominators of _ and 7 0 are 0 and 0. Step Rewrite the fractions with a denominator of 0. Multiply the numerator and the denominator of each fraction by the same number so that the denominator results in 0. = = = 7 0 = 0 Use a common denominator to write an equivalent fraction for each fraction. Possible answers are given.., common denominator:,., common denominator:,., common denominator:, 0., 0 common denominator: 0 0, 0 0 Number and Operations Fractions 0

4 Common Denominators and Equivalent Fractions Use a common denominator to write an equivalent fraction for each fraction. Possible answers are given. CC..NF.., common denominator:., common 0 denominator:., common denominator: Think: 0 is a multiple of and. Find equivalent fractions with a denominator of 0. 0, 0,,., common denominator:., common denominator:., common denominator:,,, Use the least common denominator to write an equivalent fraction for each fraction. 7.,.,.,, Problem Solving 0. Ella spends _ hour practicing the piano each day. She also spends _ hour jogging. What is the least common denominator of the fractions?,,. In a science experiment, a plant grew _ inch one week and _ inch the next week. Use a common denominator to write an equivalent fraction for each fraction. Possible answer: and 0 Lesson

5 LESSON Add and Subtract Fractions OBJECTIVE Use equivalent fractions to add and subtract fractions. CC..NF. To add or subtract fractions with unlike denominators, you need to rename them as fractions with like denominators. You can do this by making a list of equivalent fractions. Add. + Step Write equivalent fractions for. Step Write equivalent fractions for. Step Rewrite the problem using the equivalent fractions. + Then add. becomes 0 + =. Subtract. 0 - Step Write equivalent fractions for 0., 0,, 0,, 0, 0, 7 0, 0 Step Write equivalent fractions for.,,,, 0 Step Rewrite the problem using the equivalent fractions. Then subtract. 0 - becomes 0-0 =. Written in simplest form, 0 0 =. Stop when you find two fractions with the same denominator. Find the sum or difference. Write your answer in simplest form Number and Operations Fractions 0

6 Add and Subtract Fractions CC..NF. Find the sum or difference. Write your answer in simplest form Problem Solving. Kaylin mixed two liquids for a science experiment. One container held 7_ cup and the other held 0 cup. What is the total amount of the mixture?. Henry bought _ pound of screws and _ pound of nails to build a skateboard ramp. What is the total weight of the screws and nails? 0 cups 0 pound 0 Lesson

7 LESSON Add and Subtract Mixed Numbers OBJECTIVE Add and subtract mixed numbers with unlike denominators. CC..NF. When you add or subtract mixed numbers, you may need to rename the fractions as fractions with a common denominator. Find the sum. Write the answer in simplest form. + Step Model and. Step A common denominator for and is, so rename as and as. Step Add the fractions. + = Step Add the whole numbers. So, + + = 7 Add the sums. Write the answer in simplest form. + 7 = 7, or =. Find the sum or difference. Write your answer in simplest form Number and Operations Fractions 07

8 Add and Subtract Mixed Numbers CC..NF. Find the sum or difference. Write your answer in simplest form Problem Solving. Jacobi bought 7 _ pounds of meatballs. He decided to cook _ pounds and freeze the rest. How many pounds did he freeze?. Jill walked _ miles to a park and then 7 _ miles home. How many miles did she walk in all? pounds 0 miles 0 Lesson

9 LESSON Subtraction with Renaming OBJECTIVE Rename to find the difference of two mixed numbers. CC..NF. You can use a common denominator to find the difference of two mixed numbers. Estimate. - Step Estimate by using 0, and as benchmarks. - - = So, the difference should be close to. Step Identify a common denominator. - A common denominator of and is. Step Write equivalent fractions using the common denominator. = + = = + = Step Rename if needed. Then subtract. Since <, rename Subtract. - as. = So, - =. Since the difference of is close to, the answer is reasonable. Estimate. Then find the difference and write it in simplest form.. Estimate: - = Possible estimates are given Estimate: = -. Estimate: = 7 -. Estimate: - - = 0 Number and Operations Fractions 0

10 Subtraction with Renaming Possible estimates are given. CC..NF. Estimate. Then find the difference and write it in simplest form.. Estimate: - =. Estimate: - =. Estimate: - = Estimate: - =. Estimate: - =. Estimate: - = Estimate: - =. Estimate: - =. Estimate: 0 - = Problem Solving - 0. Carlene bought yards of ribbon to decorate a shirt. She only used _ yards. How much ribbon does she have left over? During his first vet visit, Pedro s puppy weighed _ pounds. On his second visit, he weighed pounds. How much weight did he gain between visits? yards pounds 0 Lesson

11 LESSON Algebra Patterns with Fractions OBJECTIVE Identify, describe, and create numeric patterns with fractions. CC..NF. You can find an unknown term in a sequence by finding a rule for the sequence. Find the unknown term in the sequence., 7 0,,, Step Find equivalent fractions with a common denominator for all of the terms. The denominators are and 0. A common denominator is 0. = 0 and = 0 Step Write the terms in the sequence using the common denominator. 0, 7 0,,, 0 Step Write a rule that describes the pattern. The sequence increases. To find the difference between terms, subtract at least two pairs of consecutive terms = = 0 So, a rule is to add 0. Step Use the rule to find the unknown term. Add to the third term to find the unknown term = 0 Write a rule for the sequence. Then, find the unknown term..,,,,., 7,,, Rule: add Rule: subtract Number and Operations Fractions

12 Algebra Patterns with Fractions CC..NF. Write a rule for the sequence. Then, find the unknown term..,,,, Think: The pattern is increasing. Add to find the next term. Rule: add. 0, 7 0,, 0, 0.,,,, 7 Rule: add.,,,, Rule: subtract Rule: subtract Write the first four terms of the sequence.. Rule: start at, add. Rule: start at, and subtract,,, 7. Rule: start at, add,,, 7. Rule: start at, and subtract Problem Solving, 7 0, 7 0, 0. Jarett s puppy weighed ounces at birth. At one week old, the puppy weighed ounces. At two weeks old, the puppy weighed ounces. If the weight gain continues in this pattern, how much will the puppy weigh at three weeks old?,,, 0. A baker started out with cups of flour. She had cups of flour left after the first batch of batter she made. She had cups of flour left after the second batch of batter she made. If she makes two more batches of batter, how many cups of flour will be left? 7 7 ounces cup of flour Lesson

13 LESSON 7 Algebra Use Properties of Addition OBJECTIVE Add fractions and mixed numbers with unlike denominators using the properties. CC..NF. You can use the properties of addition to help you add fractions with unlike denominators. Use the Commutative Property and the Associative Property. Add. ( + ) 7 + ( + ) 7 + = ( ) = 7 + ( + ) = 7 + = 7 + = = 7 Use the Commutative Property to order fractions with like denominators. Use the Associative Property to group fractions with like denominators. Use mental math to add the fractions with like denominators. Write equivalent fractions with like denominators. Then add. Rename and simplify. Use the properties and mental math to solve. Write your answer in simplest form.. ( 7 + ) ( + ) ( + ) ( ) ( ) 7 0 Number and Operations Fractions

14 Algebra Use Properties of Addition Use the properties and mental math to solve. Write your answer in simplest form. CC..NF.. ( + ) + = ( + + ) = + ( + = + = 7 ). + ( +. 0) ( ) ( 7 + 0). ( + + ). + ( + ) (7 + 7 ) ( + ). + ( 7 + ) 7 Problem Solving Elizabeth rode her bike _ miles from her house to the library and then another _ miles to her friend Milo s house. If Carson s house is _ miles beyond Milo s house, how far would she travel from her house to Carson s house? miles 7. Hassan made a vegetable salad with _ pounds of tomatoes, _ pounds of asparagus, and 7_ pounds of potatoes. How many pounds of vegetables did he use altogether? pounds Lesson 7

15 LESSON Addition with Unlike Denominators OBJECTIVE Use models to add fractions with unlike denominators. CC..NF. Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on 0 of the string. How much of the string does Karen cover with beads? You can use fraction strips to help you add fractions with unlike denominators. Trade fraction strips of fractions with unlike denominators for equivalent strips of fractions with like denominators. Use fraction strips to find the sum. Write your answer in simplest form. + 0 Step Use a _ strip and three 0 strips to model fractions with unlike denominators. Step Trade the _ strip for five 0 strips. + 0 = 0 + sum 0 Step Add the fractions with like denominators = 0 Step Write the answer in simplest form. 0 = So, Karen covers of the string with beads. Use fraction strips to find the sum. Write your answer in simplest form. Check students work Number and Operations Fractions

16 Addition with Unlike Denominators Check students work. CC..NF. Use fraction strips to find the sum. Write your answer in simplest form = + =, or , or , or , or, or , or Problem Solving. +. Brandus bought _ pound of ground turkey and _ pound of ground beef to make sausages. How many pounds of meat did he buy? , or. To make a ribbon and bow for a hat, Stacey needs _ yard of black ribbon and _ yard of red ribbon. How much total ribbon does she need? pounds yards Lesson

17 LESSON Subtraction with Unlike Denominators OBJECTIVE Use models to subtract fractions with unlike denominators. CC..NF. You can use fraction strips to help you subtract fractions with unlike denominators. Trade fraction strips of fractions with unlike denominators for equivalent strips of fractions with like denominators. Use fraction strips to find the difference. Write your answer in simplest form. - 0 Step Use a _ fraction strip to model the first fraction. Step Trade the _ strip for five 0 strips. - 0 = 0-0 Step Subtract by taking away = 0 So, - 0 =. Written in simplest form, 0 0 =. Use fraction strips to find the difference. Write your answer in simplest form. Check students work Number and Operations Fractions 7

18 Subtraction with Unlike Denominators Use fraction strips to find the difference. Write your answer in simplest form. Check students work. CC..NF = - = Problem Solving. Amber had _ of a cake left after her party. She wrapped a piece that was _ of the original cake for her best friend. What fractional part did she have left for herself?. Wesley bought _ pound of nails for a project. When he finished the project, he had _ pound of the nails left. How many pounds of nails did he use? pound Lesson

19 LESSON 0 Estimate Fraction Sums and Differences OBJECTIVE Make reasonable estimates of fraction sums and differences. CC..NF. You can round fractions to 0, to, or to to estimate sums and differences. Estimate the sum. + Step Find _ on the number line. Is it closest to 0, _, or? The fraction _ is closest to _. Step Find _ on the number line. Is it closest to 0, _, or? The fraction _ is closest to 0. Step To estimate the sum _ + _, add the two rounded numbers. So, + is about = Estimate the sum or difference. Possible estimates are given Number and Operations Fractions

20 Estimate Fraction Sums and Differences Estimate the sum or difference. Possible estimates are given. CC..NF.. - Think: _ is closer to _ than to Estimate: 0 Estimate: Estimate: Estimate: Estimate: Estimate: Estimate: Estimate: Estimate: Estimate: Problem Solving Estimate:. For a fruit salad recipe, Jenna combined _ cup of raisins, 7_ cup of oranges, and _ cup of apples. About how many cups of fruit are in the salad? Estimate:. Tyler had 7 yards of fabric. He used _ yard to make a vest. About how much fabric did he have left? Accept or cups about yards 0 Lesson 0

21 Problem Solving Practice Addition and Subtraction OBJECTIVE Solve problems using the strategy work backward. LESSON CC..NF. Makayla walks for exercise. She wants to walk a total of miles. On Monday, she walked _ miles. On Tuesday, she walked _ miles. How many more miles does Makayla need to walk to reach her goal? Read the Problem Solve the Problem What do I need to find? I need to find the distance that Makayla needs to walk. What information do I need to use? I need to use the distance she wants to walk she has already walked. and the distance How will I use the information? First I can write an equation = _ + _ + X Then I can work backward to solve the problem.. Ben has _ cups of sugar. He uses _ cup of sugar to make cookies. Then he uses _ cups of sugar to make fresh lemonade. How many cups of sugar does Ben have left? Start with the equation. = + + X Subtraction is the inverse operation of addition. Use subtraction to work backward and rewrite the equation. - - = X Subtract to find the value of x. = - = - = - = Estimate to show that your answer is reasonable. + + = cups No, there is only 7 - So, Makayla has to walk more miles to reach her goal.. Cheryl has ft of ribbon. She cuts a _ -ft strip to make a hair bow. Then she cuts a _ -ft strip for a border on a scrapbook page. Is there enough ribbon for Cheryl to cut two _ -ft pieces to put on a picture frame? Explain. ft of ribbon left. Two _ -ft pieces is _ ft, and _ is more than. Number and Operations Fractions

22 Problem Solving Practice Addition and Subtraction CC..NF. Read each problem and solve.. From a board feet in length, Emmet cut two _ -foot bookshelves. How much of the board remained? Write an equation: = + + x Rewrite the equation to work backward: - - = x Subtract twice to find the length remaining: feet. Lynne bought a bag of grapefruit, _ pounds of apples, and pounds of bananas. The total weight of her purchases was 7 _ pounds. How much did the bag of grapefruit weigh? pounds. Mattie s house consists of two stories and an attic. The first floor is _ feet tall, the second floor is _ feet tall, and the entire house is _ feet tall. How tall is the attic? 7 feet. It is 0 _ miles from Alston to Barton and _ miles from Barton to Chester. The distance from Alston to Durbin, via Barton and Chester, is miles. How far is it from Chester to Durbin?. Marcie bought a 0-foot roll of packing tape. She used two -foot lengths. How much tape is left on the roll?. Meg started her trip with _ gallons of gas in her car s gas tank. She bought an additional _ gallons on her trip and arrived back home with gallons left. How much gas did she 0 use on the trip? 0 mi feet gallons Lesson

23 Interpret the Remainder LESSON CC..NF. OBJECTIVE Solve division problems and decide when to write a remainder as a fraction. Erin has 7 ounces of trail mix. She puts an equal number of ounces in each of bags. How many ounces does she put in each bag? First, divide to find the quotient and remainder. Then, decide how to use the quotient and the remainder to answer the question. The dividend, 7, represents the total number of ounces of trail mix. The divisor,, represents the total number of bags. The quotient, 7, represents the whole-number part of the number of ounces in each bag. The remainder,, represents the number of ounces left over. Divide the ounces in the remainder by the divisor,, to write the remainder as a fraction: Write the fraction part in simplest form in your answer. 7 So, Erin puts _ ounces of trail mix in each bag. _ 7 r 7 - Interpret the remainder to solve.. Harry goes on a canoe trip with his scout troop. They will canoe a total of 7 miles and want to travel miles each day. How many days will they need to travel the entire distance?. There are 0 students eating lunch in the cafeteria. Each table seats students. All the tables are full, except for one table. How many students are sitting at the table that is not full?. Hannah and her family want to hike miles per day along a -mile-long trail. How many days will Hannah and her family hike exactly miles? 0 days days students. Emily buys 0 square feet of carpet. She can convert square feet to square yards by dividing the number of square feet by. How many square yards of carpet did Emily buy? (Hint: Write the remainder as a fraction.) sq yd Number and Operations Fractions

24 Interpret the Remainder CC..NF. Interpret the remainder to solve.. Warren spent 0 hours making wooden toy trucks for a craft fair. If he spent the same amount of time making each truck, how many hours did he spend making each truck?. Marcia has bouquets of flowers for centerpieces. She uses flowers for each centerpiece. How many centerpieces can she make? _ 0 - hours centerpieces. On the th grade class picnic, 0 students share 7 sandwiches equally. How many sandwiches does each student get?. One plant container holds tomato seedlings. If you have, seedlings, how many containers do you need to hold all the seedlings? sandwiches 0 containers Problem Solving. Fiona bought stickers to make a sticker book. If she places stickers on each page, how many pages will her sticker book have?. Jenny has 0 ounces of cleaning solution that she wants to divide equally among large containers. How much cleaning solution should she put in each container? pages ounces Lesson

25 Connect Fractions to Division LESSON CC..NF. OBJECTIVE Interpret a fraction as division and solve whole-number division problems that result in a fraction or mixed number. You can write a fraction as a division expression. = = There are students in a wood-working class and sheets of plywood for them to share equally. What fraction of a sheet of plywood will each student get? Divide. Use a drawing. Step Draw rectangles to represent sheets of plywood. Since there are students, draw lines to divide each piece of plywood into eighths. Each student s share of sheet of plywood is. Step Count the total number of eighths each student gets. Since there are sheets of plywood, each student will get of the eighths, or. Step Complete the number sentence. = Step Check your answer. Since =, the quotient is correct. So, each student will get Complete the number sentence to solve.. Ten friends share pizzas equally. What fraction of a pizza does each friend get? of a sheet of plywood.. Four students share 7 sandwiches equally. How much of a sandwich does each student get? 0 = 0, or 7 = 7, or Number and Operations Fractions

26 Connect Fractions to Division CC..NF. Complete the number sentence to solve.. Six students share apples equally. How many apples does each student get?. Ten boys share 7 cereal bars equally. What fraction of a cereal bar does each boy get? =, or 7 0 = 7 0. Eight friends share pies equally. How many pies does each friend get?. Three girls share yards of fabric equally. How many yards of fabric does each girl get? =, or =, or. Five bakers share loaves of bread equally. What fraction of a loaf of bread does each baker get?. Nine friends share cookies equally. What fraction of a cookie does each friend get? = =, or 7. Twelve students share pizzas equally. What fraction of a pizza does each student get?. Three sisters share sandwiches equally. How many sandwiches does each sister get? = Problem Solving, or. There are students in a jewelrymaking class and sets of charms. What fraction of a set of charms will each student get? Each student will get _ =, or 0. Five friends share cheesecakes equally. How many cheesecakes will each friend get? Each friend will get _ of a set. cheesecakes. Lesson

27 Find Part of a Group LESSON CC..NF.a OBJECTIVE Model to find the fractional part of a group. Lauren bought stamps for postcards. She gave Brianna _ of them. How many stamps did Lauren give to Brianna? Find of. Step What is the denominator in the fraction of the stamps Lauren gave to Brianna? So, divide the stamps into equal groups. Circle the groups. Step Each group represents of the stamps. How many stamps are in group? So, of is, or is. So, Lauren gave Brianna stamps. Use a model to solve. Check students models.. =. =. 0 =. = Number and Operations Fractions 7

28 Find Part of a Group CC..NF.a Use a model to solve. Check students models.. =. 7 =. 0 0 =. =. =. 0 = Problem Solving 7. Marco drew 0 pictures. He drew _ of them in art class. How many pictures did Marco draw in art class?. Caroline has 0 marbles. One half of them are blue. How many of Caroline s marbles are blue? pictures marbles Lesson

29 Multiply Fractions and Whole Numbers LESSON CC..NF.a OBJECTIVE Model the product of a fraction and a whole number. Find the product. Step Draw rectangles to represent the factor. Step The denominator of the factor _ is. So, divide the rectangles into equal parts. Step The numerator of the factor _ the parts. is. So, shade of Step The rectangles have shaded parts. Each rectangle is divided into equal parts. So, _ of the rectangles are shaded. So, _ is _, or _. Find the product.. =. =. 7, or =. 7 = 0. 0 =. 7, or 7, or = 7, or, or =. =., or, or = Number and Operations Fractions

30 Multiply Fractions and Whole Numbers CC..NF.a Use the model to find the product.. =., or =, or Find the product.. =. 7 =., or =, or. 7 = 7. =., or, or = Problem Solving. Jody has a -pound bag of potatoes. She uses _ of the bag to make potato salad. How many pounds of potatoes does Jody use for the potato salad? pounds 0. Lucas lives _ mile from school. Kenny lives twice as far as Lucas from school. How many miles does Kenny live from school? 0, or miles 0 Lesson

31 Fraction and Whole Number Multiplication LESSON CC..NF.a OBJECTIVE Multiply fractions and whole numbers. Find the product. = = Write the whole-number factor,, as. Multiply the numerators. Then multiply the denominators. = =, or Write the product as a mixed number in simplest form. So, is. Find the product. Write the product in simplest form.. =. = = =, or. =. =., or, or =. = 7. =. 7, or 0 =, or 7, or Number and Operations Fractions

32 Fraction and Whole Number Multiplication CC..NF.a Find the product. Write the product in simplest form.. =. =. 0 = = 0 0 =, or. = 7. =. 7, or 0, or = 7, or 7. =. =., or 0 = 7 0, or =. 7 =., or, or = Problem Solving. Leah makes aprons to sell at a craft fair. She needs _ yard of material to make each apron. How much material does Leah need to make aprons?. The gas tank of Mr. Tanaka s car holds gallons of gas. He used _ of a tank of gas last week. How many gallons of gas did Mr. Tanaka use? yards 0 gallons Lesson

33 Fraction Multiplication LESSON 7 CC..NF.a OBJECTIVE Multiply fractions. To multiply fractions, you can multiply the numerators, then multiply the denominators. Write the product in simplest form. Multiply. 0 Step Multiply the numerators. Multiply the denominators. 0 = 0 = 0 Step Write the product in simplest form. 0 = 0 = So, 0 is. Find the product. Write the product in simplest form , or. Number and Operations Fractions

34 Fraction Multiplication CC..NF.a Find the product. Write the product in simplest form.. 7 = 7 = 0 = , or Karen raked _ of the yard. Minni raked _ of the amount Karen raked. How much of the yard did Minni rake?. In the pet show, _ of the pets are dogs. Of the dogs, _ have long hair. What fraction of the pets are dogs with long hair? of the yard of the pets Algebra Evaluate for the given value of the variable.. 7 c for c =. t for t = 7 Problem Solving 7. Jason ran _ of the distance around 7 the school track. Sara ran _ of Jason s distance. What fraction of the total distance around the track did Sara run?. s for s = 0. y for y = 0. A group of students attend a math club. Half of the students are boys and _ of the boys have brown eyes. What fraction of the group are boys with brown eyes? 7 Lesson 7

35 LESSON Multiply Fractions OBJECTIVE Multiply fractions using models. CC..NF.b You can use a model to help you multiply two fractions. Multiply. Step Draw a rectangle. Divide it into equal columns. To represent the factor _, shade of the columns. Step Now divide the rectangle into equal rows. Shade _ of the _ you already shaded. The rectangle is divided into smaller rectangles. This is the denominator of the product. There are smaller rectangles that contain both types of shading. So, is the numerator of the product. So of the rectangles contain both types of shading. = Think: What is of? Find the product. Draw a model.. Check students models... =, or. = 0, or = 0, or 0 =, or Number and Operations Fractions

36 Multiply Fractions CC..NF.b Find the product... =, or =, or Find the product. Draw a model. Check students models.. = 0, or. =, or. =, or. = Problem Solving 7. Nora has a piece of ribbon that is _ yard long. She will use _ of it to make a bow. What length of the ribbon will she use for the bow?. Marlon bought 7_ pound of turkey at the deli. He used _ of it to make sandwiches for lunch. How much of the turkey did Marlon use for sandwiches? yard 7 pound Lesson

37 LESSON Area and Mixed Numbers OBJECTIVE Use a model to multiply two mixed numbers and find the area of a rectangle. CC..NF.b You can use an area model to help you multiply mixed numbers. Find the area. Step Rewrite each mixed-number factor as the sum of a whole number and a fraction. = + and = + Step Draw an area model to show the original multiplication problem. Step Draw dashed lines, and label each section to show how you broke apart the mixed numbers in Step. Step Find the area of each section. = = = = Step Add the areas of each of the sections to find the total area of the rectangle = So, is. Use an area model to solve. =, or.. 0. Number and Operations Fractions 7

38 Area and Mixed Numbers Use the grid to find the area.. Let each square represent _ unit by _ unit. =. Let each square represent unit. = CC..NF.b unit by squares cover the diagram. Each square is square unit. The area of the diagram is = = square units. The area is square units. Use an area model to solve.... Problem Solving. Ava s bedroom rug is _ feet long and _ feet wide. What is the area of the rug? 7. A painting is _ feet long and _ feet high. What is the area of the painting? 7_ square feet square feet Lesson

39 LESSON 70 Compare Fraction Factors and Products OBJECTIVE Relate the size of the product compared to the size of one factor when multiplying fractions. CC..NF.a You can use a model to determine how the size of the product compares to the size of one factor when multiplying fractions. The factor is : Draw a model to represent the factor. Divide it into equal sections. Shade of the sections to represent the factor. of the rectangle is shaded. So, is equal to. The factor is greater than : Draw two rectangles to represent the factor. Divide each rectangle into equal sections. Shade of sections in each to represent the factor. In all, sections are shaded, which is greater than the number of sections in one rectangle. So, is greater than. The factor is less than : Draw a rectangle. Divide it into equal columns. Shade of the columns to represent the factor. Now divide the rectangle into equal rows. Shade of the rows of the section already shaded to represent the factor. The rectangle is divided into sections. of the sections are shaded twice. sections is less than the sections that represent. So, is less than. Complete the statement with equal to, greater than, or less than.. 7 will be less than will be greater than 7.. will be equal to.. 7 will be less than. Number and Operations Fractions

40 Compare Fraction Factors and Products CC..NF.a Complete the statement with equal to, greater than, or less than.. 7 will be less than will be greater than 7. Think: _ is multiplied by a 7 number less than ; so, _ _ will be less than _ will be greater than.. will be equal to.. 7 will be less than will be equal to. Problem Solving 7. Starla is making hot cocoa. She plans to multiply the recipe by to make enough hot cocoa for the whole class. If the recipe calls for _ teaspoon vanilla extract, will she need more than _ teaspoon or less than _ teaspoon of vanilla extract to make all the hot cocoa?. Miles is planning to spend _ as many hours bicycling this week as he did last week. Is Miles going to spend more hours or fewer hours bicycling this week than last week? more than _ teaspoon vanilla extract fewer hours 0 Lesson 70

41 LESSON 7 Compare Mixed Number Factors and Products OBJECTIVE Relate the size of the product to the factors when multiplying fractions greater than one. CC..NF.a Complete each statement with equal to, greater than, or less than. _ is? _. The Identity Property of Multiplication states that the product of and any number is that number. So, _ is equal to _. _ _ is? _. Draw three rectangles. Divide each rectangle into equal columns. Shade completely the first two rectangles and one column of the last rectangle to represent _. Divide the rectangles into rows. Shade one row to represent the factor _. small rectangles are shaded. rectangles have both types of shading. rectangles is less than the rectangles that represent. So, is less than. When you multiply a mixed number by a fraction less than, the product will be less than the mixed number. _ _ is? _. Use what you know about the product of two whole numbers greater than to determine the size of the product of two mixed numbers. So, is greater than and greater than. When you multiply two mixed numbers, their product is greater than either factor. Complete the statement with equal to, greater than, or less than.. is less than is equal to.. is greater than.. is less than. Number and Operations Fractions

42 Compare Mixed Number Factors and Products CC..NF.a Complete the statement with equal to, greater than, or less than.. will be less than.. will be equal to. Think: _ is _. Since _ is less than, _ _ will be less than _.. 7 will be greater than 7.. will be greater than.. 7 will be greater than.. will be less than. Problem Solving 7. Fraser is making a scale drawing of a dog house. The dimensions of the drawing will be _ of the dimensions of the actual doghouse. The height of the actual doghouse is _ inches. Will the dimensions of Fraser s drawing be equal to, greater than, or less than the dimensions of the actual dog house? less than. Jorge has a recipe that calls for _ cups of flour. He plans to make _ times the recipe. Will the amount of flour Jorge needs be equal to, greater than, or less than the amount of flour his recipe calls for? greater than Lesson 7

43 LESSON 7 Problem Solving Find Unknown Lengths OBJECTIVE Solve problems using the strategy guess, check, and revise. CC..NF.b Zach built a rectangular deck in his backyard. The area of the deck is 00 square feet. The length of the deck is _ times as long as the width. What are the dimensions of the deck? Read the Problem What do I need to find? I need to find the dimensions of the deck. What information do I need to use? The deck has an area of 00 square feet, _ and the length is as long as the width. How will I use the information? I will guess the length and width of the deck. Then I will check my guess and revise it if it is not correct. Solve the Problem I can try different values for the length of the deck, each that is _ times as long as the width. Then I can multiply the length and width and compare to the correct area. Guess Check Revise Width (in feet) Length (in feet) ( _ times the width) Area of Deck (in square feet) _ = = too low Try a longer width. _ = = too high Try a shorter width. _ = 0 0 = 00 correct So, the dimensions of the deck are 0 feet by feet.. Abigail made a quilt that has an area of,00 square inches. The length of the quilt is _ times the width of the quilt. What are the dimensions of the quilt?. The width of the mirror in Shannon s bathroom is _ its length. The area of the mirror is 7 square inches. What are the dimensions of the mirror? 0 inches by 0 inches inches by inches Number and Operations Fractions

44 Problem Solving Find Unknown Lengths CC..NF.b. Kamal s bedroom has an area of 0 square feet. The width of the room is _ the length of the room. What are the dimensions of Kamal s bedroom? Guess: 0 = 0 Check: 0 = ; try a longer width. Guess: 0 = 0 Check: = 0. Correct! 0 feet by feet. Marisol is painting on a piece of canvas that has an area of 0 square inches. The length of the painting is _ times the width. What are the dimensions of the painting? inches by inches. A small plane is flying a banner in the shape of a rectangle. The area of the banner is square feet. The width of the banner is _ the length of the banner. What are the dimensions of the banner?. An artificial lake is in the shape of a rectangle and has an area of square mile. The width 0 of the lake is _ the length of the lake. What are the dimensions of the lake? feet by feet 0 mile by miles Lesson 7

45 LESSON 7 Multiply Mixed Numbers OBJECTIVE Multiply mixed numbers. CC..NF. You can use a multiplication square to multiply mixed numbers. Multiply. 7 Write the product in simplest form. Step Write the mixed numbers outside the square. Step Multiply the number in each column by the number in each row. Step Write each product inside the square Step Add the products inside the multiplication square. Find the least common denominator. Simplify. So, 7 is _ = = 7, or Find the product. Write the product in simplest form Use the Distributive Property to find the product , or Number and Operations Fractions

46 Multiply Mixed Numbers CC..NF. Find the product. Write the product in simplest form.. = = 0 = = , or , or 7, or, or Use the Distributive Property to find the product Problem Solving. Jake can carry _ pounds of wood in from the barn. His father can carry _ 7 times as much as Jake. How many pounds can Jake s father carry?. A glass can hold _ cups of water. A bowl can hold _ times the amount in the glass. How many cups can a bowl hold? 0 7 pounds cups Lesson 7

47 Divide Fractions and Whole Numbers LESSON 7 CC..NF.7a, OBJECTIVE Divide a whole number by a fraction and divide a fraction by a whole number. CC..NF.7b You can use a number line to help you divide a whole number by a fraction. Divide. Step Draw a number line from 0 to. Divide the number line into halves. Label each half on your number line, starting with _. Step Skip count by halves from 0 to to find _. Step Count the number of skips. It takes skips to go from 0 to. So the quotient is. = because =. You can use fraction strips to divide a fraction by a whole number Divide. Step Place a _ strip under a -whole strip. Step Find fraction strips, all with the same denominator, that fit exactly under the _ strip. Each part is of the whole. 0 Step Record and check the quotient. = 0 because 0 =. So, = 0. Divide. Draw a number line or use fraction strips.. =. =. =. =. = = 0 Number and Operations Fractions 7

48 Divide Fractions and Whole Numbers Divide and check the quotient. CC..NF.7a, CC..NF.7b. = because =... 0 = because =. = because =. Divide. Draw a number line or use fraction strips.. =. =. = 7. =. =. = 0 Problem Solving 0. Amy can run 0 mile per minute. How many minutes will it take Amy to run miles?. Jeremy has yards of ribbon to use for wrapping gifts. He cuts the ribbon into pieces that are _ yard long. How many pieces of ribbon does Jeremy have? 0 minutes pieces Lesson 7

49 Problem Solving Use Multiplication LESSON 7 CC..NF.7b OBJECTIVE Solve problems using the strategy draw a diagram. Nathan makes batches of soup and divides each batch into halves. How many _ -batches of soup does he have? Read the Problem What do I need to find? I need to find the number of -batches of soup Nathan has. Solve the Problem Since Nathan makes batches of soup, my diagram needs to show circles to represent the batches. I can divide each of the circles in half. What information do I need to use? I need to use the size of each batch of soup and the total number of batches of soup Nathan makes. How will I use the information? I can make a diagram to organize the information from the problem. Then I can use the diagram to the number of -batches of find soup Nathan has after he divides the batches of soup Draw a diagram to help you solve the problem.. A nearby park has acres of land to use for gardens. The park divides each acre into fourths. How many _ -acre gardens does the park have?. To find the total number of halves in the batches, I can multiply by the number of halves in each circle. = = So, Nathan has of soup. one-half-batches. Clarissa has pints of ice tea that she divides into _ -pint servings. How many _ -pint servings does she have? -acre gardens one-half-pint servings Number and Operations Fractions

50 Problem Solving Use Multiplication CC..NF.7b. Sebastian bakes pies and cuts each pie into sixths. How many _ -pie slices does he have?. Ali has vegetable pizzas that she cuts into eighths. How many _ -size pieces does she have? To find the total number of sixths in the pies, multiply by the number of sixths in each pie. = = one-sixth-pie slices one-eighth-size pieces. A baker has loaves of bread. Each loaf weighs pound. He cuts each loaf into thirds. How many _ -pound loaves of bread does the chef now have? one-third-pound loaves. Suppose the baker has loaves of bread and cuts the loaves into halves. How many _ -pound loaves of bread would the baker have?. Madalyn has watermelons that she cuts into halves to give to her neighbors. How many neighbors will get a _ -size piece of watermelon?. A landscaper had tons of rock to build decorative walls. He used _ ton of rock for each wall. How many decorative walls did he build? one-half-pound loaves neighbors 0 decorative walls 0 Lesson 7

51 Fraction and Whole-Number Division LESSON 7 CC..NF.7c OBJECTIVE Divide a whole number by a fraction and divide a fraction by a whole number. You can divide fractions by solving a related multiplication sentence. Divide. Step Draw circles to represent the dividend,. Step Since the divisor is _, divide each circle into thirds. Step Count the total number of thirds. When you divide the circles into thirds, you are finding the number of thirds in circles, or finding groups of. There are thirds. Step Complete the number sentence. = = Use the model to complete the number sentence.. = = Write a related multiplication sentence to solve... = =... = 0 = = = 0 Number and Operations Fractions

52 Fraction and Whole-Number Division CC..NF.7c Write a related multiplication sentence to solve..... = = = = = 0 = = = = = 7 = = Problem Solving. Isaac has a piece of rope that is yards long. Into how many _ -yard pieces of rope can Isaac cut the rope? 0 one-half-yard pieces. Two friends share _ of a pineapple equally. What fraction of a whole pineapple does each friend get? of the pineapple Lesson 7

53 Interpret Division with Fractions LESSON 77 CC..NF.7c OBJECTIVE Represent division by drawing diagrams and writing story problems and equations. You can draw a diagram or write an equation to represent division with fractions. Beatriz has cups of applesauce. She divides the applesauce into _ -cup servings. How many servings of applesauce does she have? One Way Draw a diagram to solve the problem. Draw circles to represent the cups of applesauce. Since Beatriz divides the applesauce into _ -cup servings, draw lines to divide each cup into fourths. To find _, count the total number of fourths in the circles. So, Beatriz has one-fourth-cup servings of applesauce. Another Way Write an equation to solve. Write an equation. = n Write a related multiplication equation. = n Then solve. So, Beatriz has Possible diagram is shown.. Draw a diagram to represent the problem. Then solve. Drew has granola bars. He cuts the bars into halves. How many _ -bar pieces does he have? = n one-fourth-cup servings of applesauce.. Write an equation to represent the problem. Then solve. Three friends share _ pan of brownies. What fraction of the whole pan of brownies does each friend get? 0 one-half-bar pieces = n; = n; n = ; of a whole pan of brownies Number and Operations Fractions

54 Interpret Division with Fractions CC..NF.7c Write an equation to represent the problem. Then solve.. Daniel has a piece of wire that is _ yard long. He cuts the wire into equal pieces. What fraction of a yard is each piece? _ = n; _ _ = n; n = ; yard. Vita has a piece of ribbon that is meters long. She cuts the ribbon into pieces that are each _ meter long. How many pieces does she cut? = n; = n; n = ; pieces Check students diagrams. Draw a diagram to represent the problem. Then solve. Possible diagrams are shown.. Leah has muffins. She cuts each. Two friends share _ gallon of muffin into fourths. How many lemonade equally. What fraction of _ -muffin pieces does she have? the gallon of lemonade does each friend get? one-fourth-muffin pieces gallon. Write a story problem to represent _. Possible problem: Joe made sandwiches. He cuts each sandwich into halves. How many sandwich halves does he have?. Write a story problem to represent _. Possible problem: Penny has yard of ribbon. She cuts the ribbon into equal pieces. How long is each piece of ribbon? Problem Solving 7. Spencer has _ pound of nuts. He divides the nuts equally into bags. What fraction of a pound of nuts is in each bag? pound. Humma has apples. She slices each apple into eighths. How many _ -apple slices does she have? one-eighth-apple slices Lesson 77