1. 5.NF.3 Dividing Whole Numbers Using Picture Models that Lead to Mixed Number Quotients 7 ÷ 4 = 1¾ 8 ÷ 3 = 2 ⅔ 9 ÷ 4 = 2¼ 11 ÷ 3 = 3 ⅔

2. Thank you for purchasing. This PowerPoint lesson uses pictures to demonstrate dividing whole numbers that lead to answers in the form of mixed numbers. Included in the PPT lesson is a step-by-step Guided Practice with fly-ins for immediate reinforcement. Students also have a chance to demonstrate their comprehension through completing a Practice problem that also has fly-ins for immediate feedback. Student involvement occurs throughout the lesson. Copyright © 2014. All rights reserved. For personal classroom use only. May not be duplicated. May not be resold. Credits: Boarder by RareArt Creations Crab by wpclipart.com Cookies and candy by OSCAL Visit my store often for new Common Core math product uploads. http://www.teacherspayteachers.com/Store/Joi9000

3. This skill is part of the Georgia Common Core Standard 5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b =a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. This PowerPoint lesson will demonstrate how to solve word problems involving division of whole numbers that lead to answers in the form of mixed numbers.

4. Let’s review the meaning of division. o Division is a math term used to refer to distributing an equal amount among a group. Division word problem: If you had 8 pieces of candy and you shared them equally with 3 of your friends, how many pieces would each of you get? o A division problem has three parts: the dividend – the number being divided into groups the divisor – the number of groups the dividend will be separated into the quotient – the answer, or the number that each receives

5. Let’s review continued. 8 ÷ 4 = Determine the dividend and the divisor of this word problem. dividend – the number being divided into groups 8 pieces of candy divisor – the number of groups the dividend will be separated into you and 3 of your friends = 4 To solve the problem, your will need to determine which number is the dividend and which is the divisor. Then you can find the quotient. If you had 8 pieces of candy and you shared them equally with 3 of your friends, how many pieces would each of you get? Your problem will look like this.

6.  We can use picture models to show the division. 8 ÷ 4 = 8 pieces of candy among you and 3 friends If you had 8 pieces of candy and you shared them equally with 3 of your friends, how many pieces would each of you get? Next, we will divide the candy to show the division.

7.  We will divide the 8 pieces of candy equally among 4 friends. 8 ÷ 4 = 2 8 pieces of candy among you and 3 friends There are 2 pieces of candy in each of the 4 circles. If you had 8 pieces of candy and you shared them equally among you and 3 of your friends, how many pieces would each of you get? Friend 1 Friend 4 Friend 3 Friend 2

8. A fraction is another way of representing the division of whole numbers. o The numerator of a fraction, the number on top, is the dividend. o The line is the divided by sign. o The denominator, the number on the bottom, the is the divisor. 4 __ 8 The division problem, 8 ÷ 4, can also be written as a fraction. 8 ÷ 48 ÷ 4 means the same as Fraction Division Division as Fractions

9. A mixed number is a whole number and a fraction added together. 2 2 __ 1 The 2 represents two wholes. The fraction represents a part of a whole. Sometimes when we divide whole numbers, the quotient, or answer, will be a mixed number. +=+ 2 2 __ 1 Example: 1 ½ 1

10. Let’s solve a division word problem using pictures models that will have a mixed number for the answer. Word problem:  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get.? To solve this problem we first need to figure out which number is the dividend, or numerator, and which number is the divisor, or denominator.  The dividend is the number of cupcakes that will be divided among the group.  The divisor is the number of team members that will get the cupcakes.

11. What do we want to divide among the group in this problem? How many groups will the dividend be separated into? Remember:  The dividend the number being divided into groups  The divisor is the number of groups the dividend will be separated into  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? 8 blueberry cupcakes3 groups for 3 team members

12. We can write this division problem two ways: 8 blueberry cupcakes divided among 3 team members  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? 8 ÷ 3 dividend divisor or 3 __ 8 dividend divisor Next, we will begin using picture models to divide the problem.

13. We know that we want to divide 8 cupcakes among 3 team members. 8 76 5 4 3 2  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? 1 We will use picture models to begin our division. We start with the 8 cupcakes, our dividend, or our numerator in a fraction.

14.  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? Now we’ll divide the cupcakes equally among the three. We will use ovals to represent the 3 team member then distribute the cupcakes among the three. We will stop when we don’t have an equal amount for each oval. There are 2 left. This is not enough for each team member.

15.  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? We will divide each of the 2 remaining cupcakes into 3 equal parts to distribute among the team players. Why 3 parts? We are sharing among 3 team members, so we need to divide the remaining cupcakes into 3 equal parts to share.

16.  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? We will distribute the remaining cupcakes equally among the 3. These cupcakes are now divided into 3 parts, or thirds.

17. All cupcakes have been distributed equally. We can now find the quotient, 0r our answer. Since all 3 groups have equal amounts, count the amount in one of the groups. Each group has an equal amount:  There are 8 blueberry cupcakes to share among 3 team members. How many cupcakes will each team member get? 1 1 ⅓ ⅓ ++ + 8 ÷ 3 = 2⅔ 1 + 1 + ⅓ + ⅓ = 2⅔.

18. Slides 19 – 25 involve the step-by-step Guided Practice. It is my suggestion that students use paper and pencil to follow along and complete each step. Guidance on how to complete each step is provided. Then students will follow the instructions to complete the steps on their paper. Fly-ins for immediate feedback is provided so students can check their own progress. The Guided Practice

19. Let’s do another problem dividing whole numbers that will lead to an answer that is a mixed number. For this example, get your paper and pencil and follow along with each step of the problem. Word problem:  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? To solve this problem, we first need to figure out which number is the dividend, or numerator, and which number is the divisor, or denominator.  Which number will be the dividend, or numerator? Hint: What’s divided among the brothers?  Which number will be the divisor, or denominator? Hint: How many brothers? Guided Practice 7 chocolate chip cookies – 7 is the dividend 4 brothers – 4 is the divisor

20. We have determined the dividend and the divisor. Dividend – 7 Divisor 4  Write the problem first as a division problem and then as a fraction. For the fraction, the dividend is the numerator and the divisor is the denominator.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? 7 ÷ 4, 4 __ 7 Guided Practice

21.  Draw picture models of 7 chocolate chip cookies to be divided among the brothers.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? You can draw some round circles. Guided Practice

22.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? Now distribute the cookies.  Draw 4 circles to represent the four brothers and put one cookie in each until they all have the same number of cookies. Some cookies will be left over. Hint: On your paper, mark an ‘X’ to show you have distributed a cookie. Guided Practice

23.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? Divide the remaining cookies.  There are 3 cookies left. Divide each of the 3 cookies into 4 equal pieces. Each of the cookies are now divided into fourths Guided Practice and can be distributed equally among the brothers.

24.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? Distribute the divided pieces of cookies.  Put one fourth of each cookie into each circle until all pieces are gone. Hint: Mark each fourth of a cookie with an ‘X’ as you distribute them. Guided Practice

25.  There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get? Each group has an equal amount of cookies. Determine your answer.  Count the cookies in one of the groups to find how many each will get. Each of the 4 groups has an equal amount: 1 ¼ ¼ ¼ + + + = 1¾ Guided Practice 1 + ¼ + ¼ + ¼ = 1¾. 7 ÷ 4 = 1¾

26. In the following Practice slides, #28 – 33, students are given the steps to complete but are not informed how to perform the steps. This is a great opportunity for the teacher to roam around the room and observe students’ comprehension of the skill and provided one-on-one assistance as needed. The Practice

27. Practice Get ready to show how easy it is to divide whole numbers leading to answers in the form of mixed numbers. You will be given a problem to solve one step at a time. Then you can check your work against the slide after each step.

28. Word problem Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive?  Decide which number is the dividend and which is the divisor.  Write the operation as a division problem. Then write it as a fraction. Dividend: 11 Divisor: 3 Division: 11 ÷ 3 Fraction: 3 _____ 11 Practice 11 pieces of candy 3 friends

29.  Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive?  Draw picture models for the dividend. Draw pictures for the items to be divided among the group. You can draw rectangles. Practice

30. Practice  Distribute the candy equally among each person. You will have some pieces left over.  Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive?

31.  Divide the remaining pieces of candy into equal parts. Determine how many equal parts you will need then divide the remaining pieces of candy. Practice Each of the remaining will need three equal parts to share among the three friends.  Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive?

32.  Distribute the parts of each remaining pieces of candy. Each person will get an equal number of parts. Practice  Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive?

33.  Determine the quotient. Each group has the same amount. Remember to count the parts as fractions. Practice ++ + + = 3⅔ 11 ÷ 3 = 3⅔  Three friends were given a pack of candy to share equally among each other. There were 11 pieces of candy in the pack. How many pieces of candy will each receive? 1 1 1 ⅓ ⅓

34. You have learned in this lesson how you can divide whole numbers leading to answers in the form of mixed numbers. You have also learned that a fraction is also a division problem and to interpret a fraction as division of the numerator by the denominator.

35. Draw picture models to solve these division word problems. Sean painted 8 wooden houses in 5 days on his job. What is the number of houses he painted on average per day? Sandy’s dad brought home 7 brownies for her and her 3 sisters. How many brownies will each of them get? What is the dividend?_______ What is the divisor? _______ What is the dividend? _______ Write the division problem as a fraction._______ Use picture models to solve the problem below. 5.NF.3 Dividing Whole Numbers Using Picture Models that Lead to Mixed Number Quotients