Number and Operations in Base Ten. Number and Operations Fractions

Transcription

1

2 Number and Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. Lesson CC..NBT. Round to the Nearest Ten or Hundred Lesson CC..NBT. Estimate Sums Lesson CC..NBT. Estimate Differences Lesson 5 CC..NBT. Mental Math Strategies for Addition Lesson CC..NBT. Algebra Use Properties to Add Lesson 7 CC..NBT. Use the Break Apart Strategy to Add Lesson CC..NBT. Use Place Value to Add Lesson 9 CC..NBT. Mental Math Strategies for Subtraction Lesson 50 CC..NBT. Use Place Value to Subtract Lesson 5 CC..NBT. Combine Place Values to Subtract Lesson 5 CC..NBT. Problem Solving Use the Distributive Property Lesson 5 CC..NBT. Multiplication Strategies with Multiples of Lesson 5 CC..NBT. Multiply Multiples of 0 by -Digit Numbers Number and Operations Fractions Develop understanding of fractions as numbers. Lesson 55 CC..NF. Equal Parts of a Whole Lesson 5 CC..NF. Equal Shares Lesson 57 CC..NF. Unit Fractions of a Whole Lesson 5 CC..NF. Fractions of a Whole Lesson 59 CC..NF. Fractions of a Group Lesson 0 CC..NF. Find Part of a Group Using Unit Fractions Lesson CC..NF. Problem Solving Find the Whole Group Using Unit Fractions Lesson CC..NF.a Fractions on a Number Line CC..NF.b Lesson CC..NF.a Model Equivalent Fractions Lesson CC..NF.b Equivalent Fractions Lesson 5 CC..NF.c Relate Fractions and Whole Numbers Lesson CC..NF.d Problem Solving Compare Fractions Lesson 7 CC..NF.d Compare Fractions with the Same Denominator... Lesson CC..NF.d Compare Fractions with the Same Numerator....5 Lesson 9 CC..NF.d Compare Fractions Lesson 70 CC..NF.d Compare and Order Fractions v

3 LESSON 55 Equal Parts of a Whole OBJECTIVE Explore and identify equal parts of a whole. CC..NF. When you divide a shape into equal parts, each part must be exactly the same size. This rectangle is divided into equal parts, or halves. This rectangle is divided into equal parts, or thirds. This rectangle is divided into equal parts, or fourths. Write the number of equal parts. Then write the name for the parts.... equal parts equal parts equal parts fourths halves thirds Write whether each shape is divided into equal parts or unequal parts equal parts unequal parts Draw lines to divide the squares into equal parts. equal parts Possible lines are shown. 7. thirds. sixths 9. eighths Number and Operations Fractions 09

4 Equal Parts of a Whole CC..NF. Write the number of equal parts. Then write the name for the parts... equal parts equal parts fourths thirds.. equal parts halves equal parts sixths Write whether the shape is divided into equal parts or unequal parts. 5.. unequal Problem Solving parts 7. Diego cuts a round pizza into eight equal slices. What is the name for the parts? equal parts. Madison is making a place mat. She divides it into equal parts to color. What is the name for the parts? eighths sixths 0 Lesson 55

5 LESSON 5 Equal Shares OBJECTIVE Divide models to make equal shares. CC..NF. Six brothers share 5 sandwiches equally. How much does each brother get? Draw to model the problem. Step Draw 5 squares for the sandwiches. Step There are brothers. Draw lines to divide each sandwich into equal parts. Step Each brother will get equal part from each sandwich. So, each brother gets 5 sixths of a sandwich. Draw lines to show how much each person gets. Write the answer. Check students lines. Possible answers are given.. sisters share pies equally.. friends share fruit bars equally. fourths, or half and fourth, sixths, or half, of a fruit bar of a pie Number and Operations Fractions

6 Equal Shares For, draw lines to show how much each person gets. Write the answer. For, check students lines. CC..NF.. friends share sandwiches equally. Possible answer: half or sixths of a sandwich. classmates share pizzas equally. Possible answer: eighths, or half, of a pizza. teammates share 5 granola bars equally. Draw to show how much each person gets. Shade the amount that one person gets. Write the answer. Problem Solving. Three brothers share sandwiches equally. How much of a sandwich does each brother get? Possible answers are given. Possible answer: whole and fourth, or 5 fourths, of a granola bar 5. Six neighbors share pies equally. How much of a pie does each neighbor get? thirds, or half and sixth, of a sandwich sixths, or half and sixth, of a pie Lesson 5

7 LESSON 57 Unit Fractions of a Whole OBJECTIVE Use a fraction to name one part of a whole that is divided into equal parts. CC..NF. A fraction is a number. It names part of a whole or part of a group. 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 equal part of a whole. It always has as its top number. How much is part of a fruit bar that is cut into equal parts? Step Use fraction strips. Make a strip showing equal parts, or eighths. Step Shade of the parts and name it. This fraction is called. So, part of a fruit bar that can be divided into equal parts is. Write the number of equal parts in the whole. Then write the fraction that names the shaded part.... equal parts equal parts equal parts Number and Operations Fractions

8 Unit Fractions of a Whole Write the number of equal parts in the whole. Then write the fraction that names the shaded part. CC..NF... equal parts equal parts.. equal parts equal parts Draw a picture of the whole. Check students drawings. 5. is. is Problem Solving Possible drawings are shown. 7. Tyler made a pan of cornbread. He cut it into equal pieces and ate piece. What fraction of the cornbread did Tyler eat?. Anna cut an apple into equal pieces. She gave piece to her sister. What fraction of the apple did Anna give to her sister? Lesson 57

9 LESSON 5 Fractions of a Whole OBJECTIVE Read, write, and model fractions that represent more than one part of a whole that is divided into equal parts. CC..NF. Some shapes can be cut into equal parts. A fraction can name more than equal part of a whole. Write a fraction in words and in numbers to name the shaded part. How many equal parts make up the whole shape? equal parts How many parts are shaded? parts So, parts out of equal parts are shaded. Read: three sixths. Write: _. Shade three parts out of eight equal parts. Write a fraction in words and in numbers to name the shaded part. Read: Write: three eighths Possible shading is shown. Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.. Each part is.. Each part is.. Each part is. four sixths two fourths five 5 eighths Number and Operations Fractions 5

10 Fractions of a Whole Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part. CC..NF... Each part is. Each part is. three sixths five eighths 5.. Each part is. Each part is. two thirds three fourths Shade the fraction circle to model the fraction. Then write the fraction in numbers. 5. four out of six. eight out of eight Problem Solving 7. Emma makes a poster for the school s spring concert. She divides the poster into equal parts. She uses two of the parts for the title. What fraction of the poster does Emma use for the title?. Lucas makes a flag. It has equal parts. Five of the parts are red. What fraction of the flag is red? 5 Lesson 5

11 Fractions of a Group LESSON 59 CC..NF. OBJECTIVE Model, read, and write fractional parts of a group. Adam has a collection of cars. What fraction names the shaded part of the collection? Step Count how many cars are shaded. There are shaded cars. This number will be the numerator, or the top number of the fraction. Step Count the total number of cars. This number will be the denominator, or the bottom number of the fraction. Step Read the fraction: three eighths, or three out of eight. So, of Adam s cars are shaded. Write a fraction to name the shaded part of each group... Write a whole number and a fraction greater than to name the part filled.. Think: can =. Think: pan = Number and Operations Fractions 7

12 Fractions of a Group CC..NF. Write a fraction to name the shaded part of each group... or, or Write a whole number and a fraction greater than to name the part filled. Think: container =.. Draw a quick picture. Then, write a fraction to name the shaded part of the group. 5. Draw circles. Shade circles. Possible shading is shown.. Draw circles. Make groups. Shade group. Problem Solving 7. Brian has basketball cards and 5 baseball cards. What fraction of Brian s cards are baseball cards?, or. Sophia has pink tulips and white tulips. What fraction of Sophia s tulips are pink? 5, or Lesson 59

13 Find Part of a Group Using Unit Fractions LESSON 0 CC..NF. OBJECTIVE Find fractional parts of a group using unit fractions. Lauren bought stamps for postcards. She gave Brianna of them. How many stamps did Lauren give to Brianna? Step Find the total number of stamps. stamps Step Since you want to find of the group, there should be equal groups. Circle one of the groups to show. Step Find of the stamps. How many stamps are in group? stamps So, Lauren gave Brianna stamps. of = Circle equal groups to solve. Count the number of shapes in group. Check students circles.. of =. of 9 =. of =. of = Number and Operations Fractions 9

14 Find Part of a Group Using Unit Fractions CC..NF. Circle equal groups to solve. Count the number of items in group. Check students circles.. of =. of =. of =. of 9 = 5. of =. of = Problem Solving 7. Marco drew pictures. He drew of them in art class. How many pictures did Marco draw in art class?. Caroline has marbles. One eighth of them are blue. How many of Caroline s marbles are blue? pictures marbles 0 Lesson 0

15 LESSON Problem Solving Find the Whole Group Using Unit Fractions OBJECTIVE Solve fraction problems by using the strategy draw a diagram. There are apple juice boxes in the cooler. One fourth of the juice boxes in the cooler are apple juice. How many juice boxes are in the cooler? CC..NF. Read the Problem Solve the Problem What do I need to find? I need to find boxes are in the cooler. What information do I need to use? There are One fourth apple juice. how many juice apple juice boxes. of the juice boxes are How will I use the information? I will use the information in the problem to draw a diagram.. Max has beta fish in his fish tank. One half of his fish are beta fish. How many fish does Max have in his tank? Describe how to draw a diagram to solve. The denominator in _ tells you that there are parts in the whole group. Draw circles to show parts. Since juice boxes are _ of the group, draw counters in the first circle. Since there are counters in the first circle, draw counters in each of the remaining circles. Then count all of the counters. So, there are juice boxes in the cooler.. Two boys are standing in line. One sixth of the students in line are boys. How many students are standing in line? fish students Number and Operations Fractions

16 Problem Solving Find the Whole Group Using Unit Fractions CC..NF. Draw a quick picture to solve. Check students work.. Katrina has blue ribbons for her hair. One fourth of all her ribbons are blue. How many ribbons does Katrina have in all? ribbons. One eighth of Tony s books are mystery books. He has mystery books. How many books does Tony have in all? books. Brianna has pink bracelets. One third of all her bracelets are pink. How many bracelets does Brianna have? bracelets. Ramal filled pages in a stamp album. This is one sixth of the pages in the album. How many pages are there in Ramal s stamp album? 5. Jeff helped repair one half of the bicycles in a bike shop last week. If Jeff worked on 5 bicycles, how many bicycles did the shop repair in all last week?. Layla collects postcards. She has 7 postcards from Europe. Her postcards from Europe are one third of her total collection. How many postcards in all does Layla have? pages 0 bikes postcards Lesson

17 LESSON Fractions on a Number Line OBJECTIVE Represent and locate fractions on a number line. CC..NF.a, CC..NF.b Use the fraction strips to help name the points on the number line. Draw a point to show. Step The denominator is, so use fraction strips for thirds. Place the fraction strips above the number line. Use the fraction strips to divide the number line into three equal lengths. Step Label each mark on the number line. Think: The distance between each mark is _ of the total distance, so count the number of _ lengths. Step Draw a point on the number line to show of equal lengths of equal lengths of equal lengths of equal lengths. Complete the number line. Draw a point to show. 0 0 Write the fraction that names the point. 0 0 A B 5. point A. point B Number and Operations Fractions

18 Fractions on a Number Line Use fraction strips to help you complete the number line. Then locate and draw a point for the fraction.. 0 CC..NF.a, CC..NF.b Write the fraction that names the point. 0 0 A B C. point A. point B 5. point C 5 7 Problem Solving. Jade ran times around her neighborhood to complete a total of mile. How many times will she need to run to complete 5_ of a mile? 7. A missing fraction on a number line is located exactly halfway between _ and 5_. What is the missing fraction? 5 times Lesson

19 LESSON Model Equivalent Fractions OBJECTIVE Model equivalent fractions by using area models and number lines. CC..NF.a Equivalent fractions are two or more fractions that name the same amount. You can use fraction circles to model equivalent fractions. Find a fraction that is equivalent to. = Step Look at the first circle. It is divided into equal parts. Shade one part to show _. Step Draw a line to divide the circle into equal parts because is the denominator in the second fraction. Step Count the number of parts shaded now. There are parts out of parts shaded. = So, is equivalent to. Shade the model. Then divide the pieces to find the equivalent fraction. Possible shading is shown..... = = = = Number and Operations Fractions 5

20 Model Equivalent Fractions Shade the model. Then divide the pieces to find the equivalent fraction. Check students shadings. CC..NF.a.. = = Use the number line to find the equivalent fraction = = Problem Solving 5. Mike says that _ of his fraction model is shaded blue. Ryan says that _ of the same model is shaded blue. Are the two fractions equivalent? If so, what is another equivalent fraction?. Brett shaded _ of a sheet of notebook paper. Aisha says he shaded _ of the paper. Are the two fractions equivalent? If so, what is another equivalent fraction? Yes; possible answer: Yes; possible answer: Lesson

21 LESSON Equivalent Fractions OBJECTIVE Generate equivalent fractions by using models. CC..NF.b Kaitlyn used of a sheet of wrapping paper. Find a fraction that is equivalent to. = Step The top fraction strip is divided into equal parts. Shade _ of the strip to show how much paper Kaitlyn used. Step The bottom strip is divided into equal parts. Shade parts of the strip until the same amount is shaded as in the top strip. parts of the bottom strip are shaded. = So, is equivalent to. Each shape is whole. Shade the model to find the equivalent fraction.... = = = Number and Operations Fractions 7

22 Equivalent Fractions CC..NF.b Each shape is whole. Shade the model to find the equivalent fraction... = = Circle equal groups to find the equivalent fraction... = = Problem Solving 5. May painted out of equal parts of a poster board blue. Jared painted out of equal parts of a same-size poster board red. Write fractions to show which part of the poster board each person painted. May: ; Jared. Are the fractions equivalent? Draw a model to explain. Check students drawings. yes Lesson

23 LESSON 5 Relate Fractions and Whole Numbers OBJECTIVE Relate fractions and whole numbers by expressing whole numbers as fractions and recognizing fractions that are equivalent to whole numbers. CC..NF.c A fraction greater than has a numerator greater than its denominator. Jason ran miles and Tyra ran _ Tyra run the same distance? miles. Did Jason and Step Use fraction strips to show the distances. Use whole strips to show Jason s distance. Use six _ -strips to show Tyra s distance. Jason Tyra = = Step Compare the fraction strips. Since the fraction strips for and _ are the same length, they are equal. So, Jason and Tyra ran the same distance. Use the number line to find whether the two numbers are equal. Write equal or not equal.. and. and. and equal not equal not equal Number and Operations Fractions 9

24 Relate Fractions and Whole Numbers Use the number line to find whether the two numbers are equal. Write equal or not equal. CC..NF.c and. and. and not equal equal not equal Each shape is whole. Write a fraction greater than for the parts that are shaded.. 5. = =. 7. Problem Solving =. Rachel jogged along a trail that was _ of a mile long. She jogged along the trail times. How many miles did Rachel jog in all? = 9. Jon ran around a track that was _ of a mile long. He ran around the track times. How many miles did Jon run in all?, or miles, or miles 0 Lesson 5

25 LESSON Problem Solving Compare Fractions OBJECTIVE Solve comparison problems by using the strategy act it out. CC..NF.d Nick walked _ mile to the gym. Then he walked _ Which distance is shorter? mile to the store. Read the Problem What do I need to find? I need to find which distance is shorter. What information do I need to use? Nick walked Then he walked store. mile to the gym. mile to the How will I use the information? I will use fraction strips and compare the lengths of the models to find which distance is shorter. Solve the Problem Compare the lengths. < The length of the _ model is less than the length of the _ model. So, the distance to the shorter. gym is. Mariana and Shawn each had pages to read. Mariana read _ of her pages. Shawn read _ of his pages. Who read more pages? Explain. Mariana; Possible explanation: >. Carlos ran _ of the race course. Lori ran _ of the same race course. Who ran farther? Explain. Lori; Possible explanation: > Number and Operations Fractions

26 Problem Solving Compare Fractions CC..NF.d Solve.. Luis skates _ mile from his home to school. Isabella skates _ mile to get to school. Who skates farther? Think: Use fraction strips to act it out. Luis. Sandra makes a pizza. She puts mushrooms on _ of the pizza. She adds green peppers to 5_ of the pizza. Which topping covers more of the pizza? green peppers. The jars of paint in the art room have different amounts of paint. The green paint jar is _ full. The purple paint jar is _ full. Which paint jar is less full? the green paint jar. Jan has a recipe for bread. She uses _ cup of flour and _ cup of chopped onion. Which ingredient does she use more of, flour or onion? 5. Edward walked _ mile from his home to the park. Then he walked _ mile from the park to the library. Which distance is shorter? flour mile Lesson

27 LESSON 7 Compare Fractions with the Same Denominator OBJECTIVE Compare fractions with the same denominator by using models and reasoning strategies. CC..NF.d Pete s Prize Pizzas makes a special pizza. Of the toppings, _ is peppers and _ is ham. Does the pizza have more peppers or ham? Compare and. Step The denominators of both fractions are the same,. Use fraction circles divided into fourths to model the fractions. Step Shade part of the first circle to show _. Shade parts of the second circle to show _. Step Compare. parts is more than part. > So, the pizza has more ham. Compare. Write <, >, or =.. >. = < > <. = Number and Operations Fractions

28 Compare Fractions with the Same Denominator CC..NF.d Compare. Write <, >, or =.. >. > 0. =. 5 < 5. 7 > 5. < > = > 0. <. > 0. = < > < Problem Solving. Ben mowed 5_ of his lawn in one hour. John mowed _ of his lawn in one hour. Who mowed less of his lawn in one hour? 7. Darcy baked muffins. She put blueberries in 5_ of the muffins. She put raspberries in _ of the muffins. Did more muffins have blueberries or raspberries? John blueberries Lesson 7

29 LESSON Compare Fractions with the Same Numerator OBJECTIVE Compare fractions with the same numerator by using models and reasoning strategies. CC..NF.d Ryan takes a survey of his class. _ of the class has dogs, and _ of the class has cats. Are there more dog owners or cat owners in Ryan s class? Compare the fractions. Step Divide the first circle into equal parts. Shade _ of the circle to show dog owners. Step Divide the second circle into equal parts. Shade _ of the circle to show cat owners. Step Compare the shaded parts of the circles. Which shaded part is larger? Dog Owners Cat Owners is larger than. So, there are more cat owners than dog owners in Ryan s class. < Compare. Write <, >, or = > >. 5. < > 5. > >.. 9. > < < 0... = > < Number and Operations Fractions 5

30 Compare Fractions with the Same Numerator CC..NF.d Compare. Write <, >, or =.. <. <. >. 5.. < < > > = < Problem Solving 0. Javier is buying food in the lunch line. The tray of salad plates is _ full. The tray of fruit plates is _ full. Which tray is more full?. Rachel bought some buttons. Of the buttons, _ are yellow and _ are red. Rachel bought more of which color buttons? the fruit plate tray yellow Lesson

31 LESSON 9 Compare Fractions OBJECTIVE Compare fractions by using models and strategies involving the size of the pieces in the whole. CC..NF.d Mrs. Brown s recipe uses _ cup of flour. Mrs. Young s recipe uses _ cup of flour. Which recipe uses more flour? Compare and. You can compare fractions using fraction strips. Step Model each fraction. Step Compare the lengths of the models. The length of the _ model is greater than the length of the _ model. > So, Mrs. Young s recipe uses more flour. Compare and. Which is greater? The denominators are the same, so compare the numerators. <, so <. So, is greater than. Compare. Write <, >, or =. Write the strategy you used... 7 < > same denominator > 5 Possible strategies are given. missing pieces.. > < 5 same numerator same denominator Number and Operations Fractions 7

32 Compare Fractions CC..NF.d Possible strategies are given. Compare. Write <, >, or =. Write the strategy you used.. < Think: The numerators are the same. Compare the denominators. The greater fraction will have the lesser denominator.. 7. < > same numerator missing same pieces denominator Name a fraction that is less than or greater than the given fraction. Draw to justify your answer. Answers and drawings will vary.. greater than 5. less than Problem Solving. At the third-grade party, two groups each had their own pizza. The blue group ate 7_ pizza. The green group ate _ pizza. Which group ate more of their pizza? 7. Ben and Antonio both take the same bus to school. Ben s ride is 7_ mile. Antonio s ride is _ mile. Who has a longer bus ride? the blue group Ben Lesson 9

33 LESSON 70 Compare and Order Fractions OBJECTIVE Compare and order fractions by using models and reasoning strategies. CC..NF.d You can use a number line to compare and order fractions. Order 5,, and 7 from least to greatest. Since you are comparing eighths, use a number line divided into eighths. Step Draw a point on the number line to show 5. Step Repeat for and Step Fractions increase in size as you move right on the number line. Write the fractions in order from left to right. So, the order from least to greatest is, 5, 7. 7 Write the fractions in order from least to greatest..,, 0 5 0,,.,,.,, Think: When the numerators are the same, look at the denominators to compare the size of the pieces.., 0,,,,, 0,, Number and Operations Fractions 9

34 Compare and Order Fractions Write the fractions in order from greatest to least. CC..NF.d.,,,, Think: The denominators are the same, so compare the numerators: > >.., 5, 5,,.,,,,.,,,, Write the fractions in order from least to greatest. 5.,,,,., 5,,, , 0, 0 7,,.,,,, Problem Solving 9. Mr. Jackson ran 7_ He ran _ mile on Monday. mile on Wednesday and 5_ mile on Friday. On which day did Mr. Jackson run the shortest distance? 0. Delia has three pieces of ribbon. Her red ribbon is _ foot long. Her green ribbon is _ foot long. Her yellow ribbon is _ foot long. She wants to use the longest piece for a project. Which color ribbon should Delia use? Wednesday green 0 Lesson 70