Grade 6 Module 2 Lessons 1 8

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1 Eureka Math Grade Module Lessons 1 8 Eureka Math, Published by the non-profit Great Minds. Copyright 01 Great Minds. No part of this work may be reproduced, distributed, modified, sold, or commercialized, in whole or in part, without consent of the copyright holder. Please see our User Agreement for more information. Great Minds and Eureka Math are registered trademarks of Great Minds.

2 01-1 G-M-Lesson 1: Interpreting Division of a Fraction by a Whole Number (Visual Models) Find the value of each in its simplest form To divide by four, I can create four rows. From the model, I can see that I am finding 1 of 1. 4 I see that 1 4 is the same as The diagram begins with one whole unit. I can divide it into two equal parts (columns) and shade one part to represent 1. The shared area (dark blue) is one out of eight total pieces, or = 44 = 88. Three loads of sand weigh tons. Find the weight of 1 load of sand The shared area (dark blue) is three out of twelve total pieces, or = 44 = = 44? The diagram begins with three fourths. I need to find out how many one of those three fourths is. If three units represents three fourths, then one unit is fourths = 1 fourth. Lesson 1: Interpreting Division of a Fraction by a Whole Number (Visual Models) 1 G-M-HWH

3 01-1. Sammy cooked 1 the amount of chicken he bought. He plans on cooking the rest equally over the next four days. a. What fraction of the chicken will Sammy cook each day? = I begin with the whole amount of chicken,, and then take away the 1 he cooked. I divide the remaining by 4 to find the fraction for each day. 44 = 44 = b. If Sammy has 48 pieces of chicken, how many pieces will he cook on Wednesday and Thursday? (4444) = ; he will cook pieces each day, so + =. He will cook pieces of chicken on Wednesday and Thursday. 4. Sandra cooked 1 of her sausages and put 1 of the remaining sausages in the refrigerator to cook later. 4 The rest of the sausages she divided equally into portions and placed in the freezer. a. What fraction of sausage was in each container that went in the freezer? = 1 is cooked, so there are remaining. cooked remaining To find a fourth of the remaining, I need to divide the remaining into 4 equal pieces. 44 = 44 = = The darkest shaded value is 1 4 the amount of the tape diagram. = = = = 44 To find half of the remaining, I need 1 to divide by two. Lesson 1: Interpreting Division of a Fraction by a Whole Number (Visual Models) G-M-HWH

4 01-1 b. If Sandra placed 0 sausages in the freezer, how many sausages did she start with? or is of what size??? unit = units = = 4444 Sandra started with 4444 sausages. Lesson 1: Interpreting Division of a Fraction by a Whole Number (Visual Models) G-M-HWH

5 01-1 G-M-Lesson : Interpreting Division of a Whole Number by a Fraction (Visual Models) 1. Ken used of his wrapping paper to wrap gifts. If he used 1 feet of wrapping paper, how much did he start with?? I can think of this as, 1 is of what number? out of the units represents the amount of paper Ken used, which is 1 feet. units = unit = = units = = Ken started with feet of wrapping paper. I can divide 1 by to determine the value of one unit. I need to find the value of one unit to determine the value of all six units.. Robbie has 4 meters of ribbon. He cuts the ribbon into pieces 1 meters long. How many pieces will he make? thirds third = = Robbie will make 1 pieces of ribbon. I can think of this as, How many groups of 1 are in 4? Lesson : Interpreting Division of a Whole Number by a Fraction (Visual Models) 4 G-M-HWH

6 01-1. Savannah spent 4 of her money on clothes before spending 1 of the remaining money on accessories. If the accessories cost $1, how much money did she have to begin with? Amount Spent Amount Remaining I can divide each unit into three equal units to find a third of the remaining money. Each of these units represents $1. unit = units = = Savannah had $ at first. 4. Isa s class was surveyed about their favorite foods. 1 of the students preferred pizza, 1 of the students preferred hamburgers, and 1 of the remaining students preferred tacos. If 9 students preferred tacos, how many students were surveyed? One third of the total amount of pizza students preferred pizza. I can represent this with a tape diagram. pizza ham I can divide each of the three units into two equal units to find one sixth. pizza ham tacos I can divide each of the six units into two equal units to find half of the remainder. remaining Lesson : Interpreting Division of a Whole Number by a Fraction (Visual Models) G-M-HWH

7 01-1 units = 99 unit = 99 = units = = There were students surveyed.. Caroline received her pay for the week. She spent 1 of her pay on bills and deposited the remainder of 4 the money equally into bank accounts. a. What fraction of her pay did each bank account receive? 44 = = 44 = 88 I need to start with the total amount of her pay, which I can represent with 1 whole. b. If Caroline deposited $0 into each bank account, how much did she receive in her pay? units = unit = = 88 units = 88 = Caroline received $ in her pay. Lesson : Interpreting Division of a Whole Number by a Fraction (Visual Models) G-M-HWH

8 0-1 1 G-M-Lesson : Interpreting and Computing Division of a Fraction by a Fraction More Models Rewrite the expression in unit form. Find the quotient. Draw a model to support your answer 𝟔𝟔 eighths 𝟐𝟐 eighths = 𝟑𝟑 𝟏𝟏 group of 𝟐𝟐 𝟏𝟏 group of 𝟖𝟖 𝟐𝟐 𝟏𝟏 group of 𝟖𝟖 𝟐𝟐 𝟖𝟖 I can look at this as, How 8 8 many groups of can fit in? Rewrite the expression in unit form. Find the quotient 𝟕𝟕 𝟒𝟒 𝟕𝟕 sixths 𝟒𝟒 sixths = 𝟕𝟕 𝟒𝟒 = = The units are the same in the dividend and divisor. I can easily divide the numerators. 𝟑𝟑 𝟏𝟏 𝟒𝟒 Represent the division expression in unit form. Find the quotient A biker is miles from the finish line. If he can travel miles in one minute, how long until he reaches the finish line? 𝟔𝟔 𝟕𝟕 𝟕𝟕 𝟔𝟔 = 𝟔𝟔 sevenths sevenths = 𝟔𝟔 = = 𝟏𝟏 𝟏𝟏 𝟏𝟏 It will take him 𝟏𝟏 minutes, or 𝟏𝟏 minute and 𝟏𝟏𝟏𝟏 seconds, to reach the finish line. Lesson : G-M-HWH Interpreting and Computing Division of a Fraction by a Fraction More Models 7

9 A seamstress has. feet of ribbon. a. How many feet strips of ribbon can she cut? 10 Since this is a mixed number, she can only cut 8 whole strips.. = tenths; = tenths; tenths tenths = = or 88 She can cut eight feet of ribbon. b. How much ribbon is left over? tenths 4444 tenths = 44 tenths I can determine eight strips of feet 10 of ribbon by multiplying by tenths 8 = 48 tenths. She will have 44 feet of ribbon left over. Lesson : Interpreting and Computing Division of a Fraction by a Fraction More Models 8 G-M-HWH

10 0-1 1 G-M-Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction More Models Calculate the quotient. If needed, draw a model. 1. 𝟔𝟔 𝟔𝟔 fifteenths 𝟏𝟏𝟏𝟏 fifteenths = 𝟔𝟔 𝟏𝟏𝟏𝟏 = 𝟏𝟏𝟏𝟏, or. 𝟏𝟏𝟏𝟏 fifteenths 𝟗𝟗 fifteenths = 𝟏𝟏𝟏𝟏 𝟗𝟗 = 𝟏𝟏𝟏𝟏 𝟗𝟗 𝟑𝟑 = 𝟏𝟏 𝟏𝟏 𝟗𝟗 𝟏𝟏 𝟏𝟏 group of 𝟗𝟗 fifteenths. 𝟗𝟗 1 or 𝟏𝟏 or 𝟏𝟏 These fractions do not have the same denominator, or unit. I need to create like denominators to divide the numerators. or 𝟏𝟏 group of 𝟗𝟗 fifteenths I can shade out of columns to represent. To find how many 1 groups of are in that amount, I can divide each column into rows. There are 18 fifths. I can represent this as wholes and fifths, or. 𝟑𝟑 𝟏𝟏𝟏𝟏 𝟑𝟑 𝟏𝟏𝟏𝟏 thirtieths thirtieths = 𝟏𝟏𝟏𝟏 = = 𝟑𝟑 Lesson 4: G-M-HWH Interpreting and Computing Division of a Fraction by a Fraction More Models 9

11 group of group of group of I can shade out of columns to represent. To find how many groups of 1 are in that amount, I can divide each column into rows. There are 1 sixths. I can represent this as wholes and sixths, or 1. eighteenths eighteenths = = = Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction More Models 10 G-M-HWH

12 01-1 G-M-Lesson : Creating Division Stories 1. How many 1 teaspoons of honey are in a recipe calling for teaspoons of honey? = sixths sixths = = = There are one-third teaspoons of honey in teaspoons.. Write a measurement story problem for. I know that measurement interpretation means that I have to find out how many groups of are in. How many cups of milk are in a recipe calling for cups?. Fill in the blanks to complete the equation. Then, find the quotient, and draw a model to support your solution. 1 7 = 1 of 1 When I divide by 7, I know that is the same as taking a seventh, or 77 = 77 of multiplying by 1. The word of 7 tells me to multiply in this case. 4. Pam used 8 loads of soil to cover 4 of her garden. How many loads of soil will she need to cover the entire garden? 44 units = 88 unit = = units = = I can use the partitive interpretation of division here since I know both parts and need to determine the total amount. Pam needs loads of soil to cover the entire garden. Lesson : Creating Division Stories G-M-HWH

13 01-1. Becky plans to run miles on the track. Each lap is 1 miles. How many laps will Becky run? 4 44 = fourths fourth = = =. Becky will run laps.. Kaliah spent of her money on an outfit. She spent of the remaining money on a necklace. If she has 8 $1 left, how much did the outfit cost? = = = + = 88 = is of what number? units = unit = = units = = 4444 The outfit cost $4444. outfit is shaded in my diagram. What is left over is 1. Three eighths of that is spent on the necklace. The leftover is. If I split the remaining third into 8 eight equal parts, I need to split each of the other two thirds into eight equal parts. The entire amount is now in 4 parts. necklace remaining money $ units out of 4 represents the $1 left over. I can use unit form to determine what one unit represents. Lesson : Creating Division Stories 1 G-M-HWH

14 01-1 G-M-Lesson : Creating Division Stories 1. teaspoons is 1 group of what size? sixths sixths = = teaspoons is group of teaspoons.. Write a partitive division story problem for In partitive division, I know the parts and need to find the total amount. I can choose the unit of feet and create a story. Brendan had 77 foot of rope. This is the amount he needs. How much rope does he need in all?. Fill in the blanks to complete the equation. Then, find the quotient, and draw a model to support your solution. 4 = 4 of I can think of this as what is 1 4 of 44 = 44 of? is the total. I am looking for the part.? 44 units unit 44 = 44 = Lesson : Creating Division Stories 1 G-M-HWH

15 Karrie cleaned 1 of her house in 4 minutes. How long will it take her to clean the entire house? 4444 mmmmmm hhhh = 4444 mmmmmm hhhh = 44 hhhh. = twentieths 44 twentieths = = It will take Karrie hours to clean the entire house. 44 I can use conversions to determine the fraction of an hour that is represented by 4 minutes. I can look at this as partitive division. I know it takes hours to 4 clean 1 of the house. I m looking to find the total amount of hours needed to clean the whole house. Lesson : Creating Division Stories 14 G-M-HWH

16 01-1 G-M-Lesson 7: The Relationship Between Visual Fraction Models and Equations Invert and multiply to divide = = = I know that is of a number. Two units is represented by 7, so one unit is half of. 1 =. Three units is = 18. I multiplied by and by 1. I know this is the same as multiplying by. 7. Cody used 4 of his gas. If he used of a tank, how much gas did he start with? 7 I know that this problem is 77 asking me to determine 7 is 4 of what number.? is of what number? units = 77 unit = 77 = 77 = This shows why I can invert and multiply the second factor. 44 units = 44 = is of. Lesson 7: The Relationship Between Visual Fraction Models and Equations 1 G-M-HWH

17 01-1. Claire has 7 half-pound packages of trail mix. She wants to make packages that contain 1 1 pounds. How many packages can she make? = + = 77 is how many? I need to represent this mixed number with a fraction and then invert and multiply. 77 = 77 = = 77 = Claire can make two whole packages with enough left over for package. 4. Draw a model that shows 1. Find the quotient. I can think of this as, is 1 of what number?? = = = Lesson 7: The Relationship Between Visual Fraction Models and Equations 1 G-M-HWH

18 01-1 G-M-Lesson 8: Dividing Fractions and Mixed Numbers Calculate each quotient = = 77 = 77 = = 4444 Before I divide, I need to change 4 1 into a fraction. I know that 4 can be represented as 0. I can add that to 1 to determine the equivalent fraction = + + = 88 = 88 = = Before I divide, I need to change 1 into a fraction. I know that can be represented as 1. I can add that to 1 to determine the equivalent fraction. Lesson 8: Dividing Fractions and Mixed Numbers 17 G-M-HWH