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DIVISION WITH FRACTIONS Grade 5 01/04/2022 - 01/20/2022 Revised: 11/22/2021 UNIT PLAN DAY TARGET STANDARD Day 1 I can interpret a fraction as division of the numerator by the denominator. MAFS.5.NF.2.3 Day 2 I can solve word problems involving division of whole numbers with fractions or mixed numbers as the quotient. MAFS.5.NF.2.3 Day 3 I can determine situations that could be represented by fractions or whole numbers. MAFS.5.NF.2.3 Day 4 I can interpret division of a unit fraction by a non-zero whole number and compute such quotients. MAFS.5.NF.2.7 MAFS.5.NF.2.7a Day 5 I can solve real world problems involving division of unit fractions by non-zero whole numbers. MAFS.5.NF.2.7a MAFS.5.NF.2.7c UNIT PLAN DAY TARGET STANDARD Day 6 I can interpret division of a whole number by a unit fraction and compute such quotients. MAFS.5.NF.2.7 MAFS.5.NF.2.7b Day 7 I can solve real world problems involving division of whole numbers by a unit fraction. MAFS.5.NF.2.7b MAFS.5.NF.2.7c Day 8 Review Day N/A Day 9 Assessment Day N/A Day 10 Re-teach/Flex Day N/A Day 11 Re-teach/Flex Day N/A Day 12 Re-Teach/Flex Day UNIT SCALE - GOAL LEVEL Students will be able to: π 3 GOAL β’ Interpret a fraction as division of the numerator by the denominator ( = π a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (5.NF.2.3) β’ Interpret division of a unit fraction by a non-zero whole number and compute such quotients (5.NF.2.7a) β’ Interpret division of a whole number by a unit fraction and compute such quotients (5.NF.2.7b) β’ Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions (5.NF.2.7c) UNIT SCALE β ON YOUR WAY TO THE GOAL LEVEL Students will be able to: π 2 β’ Interpret a fraction as division of the numerator by the denominator ( = π a ÷ b) (5.NF.2.3) β’ Represent division problems by creating pictorial representations (5.NF.2.7a, 5.NF.2.7b, 5.NF.2.7c) 1 β’ Identify the fraction bar (horizontal line or slanted line between the numerator and denominator) as a division sign (5.NF.2.3) β’ Represent division problems by creating concrete representations (5.NF.2.7a, 5.NF.2.7b, 5.NF.2.7c) UNIT SCALE β ABOVE THE GOAL LEVEL 4 Students will be able to: β’ Explain the pattern observed when dividing the numerator by the denominator of a fraction greater than 1 versus a fraction less than 1 (5.NF.2.3) β’ Explain the difference between dividing a unit fraction by a whole number and dividing a whole number by a unit fraction (5.NF.2.7a, 5.NF.2.7b) β’ Identify a situation in their life which involved dividing unit fractions by non-zero whole numbers or whole numbers by unit fractions and explain why being able to do the math is beneficial (5.NF.2.7c) UNIT RESOURCE SLIDE Student Slides Student Slide Deck *If the hyperlink on the slide does not work, copy and paste the link from the notes into Google Chrome. Student Handouts Day 3 Determine Situations Represented By Fractions Or Whole Numbers Compilation of Daily Formatives (Handouts may also be included in the student slide deck.) Anchor Charts Dividing Fractions ADDITIONAL RESOURCES Standards Optional Suggestions for Additional Practice from iReady Teacher Toolbox Optional Suggestions for Additional Practice from Think Central Unit Number Lesson Number Student Resource MAFS.5.NF.2.3 2 12 Standards Practice MAFS.5.NF.2.7.a 2 17 - 18 Standards Practice MAFS.5.NF.2.7.b 2 17 - 18 Standards Practice MAFS.5.NF.2.7.c 2 17 - 18 Standards Practice Think Central Teacher Guide How would you mentally solve this problem? 36 ÷ 12 Day 1 β Interpret a Fraction as Division How would you mentally solve this problem? 48 ÷ 24 Day 1 β Interpret a Fraction as Division DAILY LEARNING TARGET β Interpret a Fraction as Division I can interpret a fraction as division of the numerator by the denominator. STANDARD/S MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by π the denominator ( = a ÷ b). Solve word problems involving π 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. Day 1 β Interpret a Fraction as Division Three piano players share 9 hours of practice time. How many hours will each player get to practice? 9÷3=? Day 1 β Interpret a Fraction as Division Molly and four friends want to share four oranges. How much of the four oranges will each person receive? 4÷5=a How many oranges are there to share? How many people are sharing the four oranges? What equation can represent the question? Use a to represent the unknown. What are the next steps? Day 1 β Interpret a Fraction as Division Molly and four friends want to share four oranges. How much of the four oranges will each person receive? 4 = 5 4÷5 Dividend β Numerator Divisor β Denominator Day 1 β Interpret a Fraction as Division What is the relationship between division and multiplication? 4 5 =4÷5 4 5x ? =4 5 Day 1 β Interpret a Fraction as Division Additional Practice Problems 1. Draw a visual fraction model to solve for d. 4÷7=d 2. Alberto and his five friends want to share three apples. How much of the three apples will each person receive? Day 1 β Interpret a Fraction as Division CHECK YOUR UNDERSTANDING 6÷8=π 1. Draw a visual fraction model to solve for the value of c. 2. Rewrite the division equation as a multiplication equation. Day 1 β Interpret a Fraction as Division STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 1 β Interpret a Fraction as Division GROUP/Student Names Stations to Complete TODAY Optional Stations Day 1 β Interpret a Fraction as Division How would you mentally solve this problem? 50 ÷ 25 Day 2 β Fractions or Mixed Numbers as the Quotient How would you mentally solve this problem? 56 ÷ 14 Day 2 β Fractions or Mixed Numbers as the Quotient DAILY LEARNING TARGET β Fractions or Mixed Numbers as the Quotient I can solve word problems involving division of whole numbers with fractions or mixed numbers as the quotient. STANDARD/S MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by π the denominator ( = a ÷ b). Solve word problems involving π 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. Day 2 β Fractions or Mixed Numbers as the Quotient Kasandra picked 14 apples for her 4 friends. If each friend gets the same amount, what fraction does each friend receive? Use any strategy to solve. 14 ÷ 4 = a . 4 apples 14 4 = 4 apples 2 3 4 = 1 3 2 4 apples 2 apples left over 1 1 1 1 1 1 1 1 + + + + + + + 4 4 4 4 4 4 4 4 Day 2 β Fractions or Mixed Numbers as the Quotient John and Sidney bought 17 candy bars. They want to equally share the candy bars between themselves and 4 other friends. How many candy bars does each friend get? β’ With your groups, write an equation that represents the word problem and the unknown. β’ Solve for the unknown. β’ Prove your answer with a drawing or visual using fraction models. Day 2 β Fractions or Mixed Numbers as the Quotient β’ Sidney solved the problem; Her work is below. β’ John solved the problem. His work is below. 6 17 - 6 (6 x 1) 11 - 6 (6 x 1) Is the work correct? Explain why or why not. 5 Day 2 β Fractions or Mixed Numbers as the Quotient Additional Practice Problems 1. Use a fraction model to solve for c. 18 ÷ 5 = c 2. Kasandra picked 16 pounds of oranges for her 5 friends. If each friend gets the same amount, what fraction does each friend receive? Use any strategy to solve. Day 2 β Fractions or Mixed Numbers as the Quotient Additional Practice Problems 3. Which of the following situations can be represented by 12 5 ? A. Harvey opens 5 bags of gummy bears, which she will split equally into 12 bowls for a party. B. Juan takes 5 apples from a bag containing 12 apples. C. Carlos has 12 packs of baseball cards with 5 cards in each pack. D. John pours 5 equal servings of apple juice from a jug containing 12 ounces. Day 2 β Fractions or Mixed Numbers as the Quotient CHECK YOUR UNDERSTANDING Mikala bought 19 subs for 9 friends. If each friend gets the same amount, what fraction of the sub does each friend receive? Use any strategy to solve. Day 2 β Fractions or Mixed Numbers as the Quotient STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 2 β Fractions or Mixed Numbers as the Quotient GROUP/Student Names Stations to Complete TODAY Optional Stations Day 2 β Fractions or Mixed Numbers as the Quotient How would you mentally solve this problem? 60 ÷ 15 Day 3 β Determine Situations Represented by Fractions or Whole Numbers How would you mentally solve this problem? 64 ÷ 16 Day 3 β Determine Situations Represented by Fractions or Whole Numbers DAILY LEARNING TARGET β Determine How Situations Can Be Represented by Fractions or Whole Numbers I can determine situations that could be represented by fractions or whole numbers. STANDARD/S MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by π the denominator ( = a ÷ b). Solve word problems involving π 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. Day 3 β Determine Situations Represented by Fractions or Whole Numbers What expression can be used for the following situation. Situation 1 Joy uses 24 apples to make 5 apple pies. How many apples are in each pie? 24 ÷ 5 24 5 4 5 4 Situation 2 Twenty-four students split 5 apple pies after the bake sale. How many apple pies does each student get? 5 ÷ 24 5 24 Day 3 β Determine Situations Represented by Fractions or Whole Numbers Each expression can represent one of the follow situations. Which ones belong to each? Situation 1 Situation 2 Joy uses 26 bananas to make 8 loaves of banana bread. How many bananas are in each loaf? Twenty-six students split 8 loaves of banana bread after the bake sale. How many loaves of bread does each student get? 8 ÷ 26 26 8 2 3 8 26 ÷ 8 8 26 Day 3 β Determine Situations Represented by Fractions or Whole Numbers 10 ÷ 3 = π Situation 1 Situation 2 Zander and Alice are baking and made 10 jumbo cookies. They want to give them to 3 friends. Each friend will get the same amount. How many cookies will each friend get? Zander and Alice are baking and made 10 jumbo cookies. They want to give enough for themselves and 3 friends. Each person will get the same amount. How many cookies will each friend get? Day 3 β Determine Situations Represented by Fractions or Whole Numbers Additional Practice Problems Each expression can represent one of the follow situations. Which ones belong to each? Situation 1 Jose bought 22 submarine sandwiches to share with his 7 friends. If each friends gets an equal amount, how much of the submarine sandwiches does each friend get? 22 ÷ 7 7 22 Situation 2 Twenty-two students split 7 submarine sandwiches after recess. How many sandwiches will each student get? 1 3 7 22 7 7 ÷ 22 Day 3 β Determine Situations Represented by Fractions or Whole Numbers CHECK YOUR UNDERSTANDING Which of the following situations can be 16 represented by ? 6 ο± Hazel opens 6 bags of gummy bears, which she will split equally into 16 bowls for a party. ο± Jasper takes 6 apples from a bag containing 16 apples. ο± Levi has 16 packs of baseball cards with 6 cards in each pack. ο± Harper pours 6 equal servings of apple juice from a jug containing 16 ounces. Day 3 β Determine Situations Represented by Fractions or Whole Numbers STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 3 β Determine Situations Represented by Fractions or Whole Numbers GROUP/Student Names Stations to Complete TODAY Optional Stations Day 3 β Determine Situations Represented by Fractions or Whole Numbers How would you mentally solve this problem? 72 ÷ 12 Day 4 β Division of a Unit Fraction How would you mentally solve this problem? 84 ÷ 12 Day 4 β Division of a Unit Fraction DAILY LEARNING TARGET β Division of a Unit Fraction I can interpret division of a unit fraction by a non-zero whole number and compute such quotients. STANDARD/S MAFS.5.NF.2.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. MAFS.5.NF.2.7a Interpret division of a unit fraction by a non-zero whole number and compute such quotients. Day 4 β Division of a Unit Fraction 1 1 ÷4=x 8 2 Describe what the equation is asking for. Draw an illustration or make a model to show how you would try and solve. Letβs discuss the model. Day 4 β Division of a Unit Fraction 1 1 ÷4=x 8 2 Describe what the equation is asking for. Draw an illustration or make a model to show how you would try and solve. Letβs discuss the model. Day 4 β Division of a Unit Fraction 1 ÷6=x 4 Describe what the equation is asking for. Draw an illustration or make a model to show how you would try and solve. Letβs discuss your illustrations and models. Day 4 β Division of a Unit Fraction Jack solved by using the following visual. Is Jack correct? π π ÷ π = π; π = π ππ Day 4 β Division of a Unit Fraction Additional Practice Problems Describe what the equation is asking for. Draw an illustration or make a model to show how you would try to solve. 1 3 ÷4=x 1 2 ÷8=x Day 4 β Division of a Unit Fraction CHECK YOUR UNDERSTANDING 1 ÷5=x 6 Choose a strategy and solve for the quotient. Day 4 β Division of a Unit Fraction STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 4 β Division of a Unit Fraction GROUP/Student Names Stations to Complete TODAY Optional Stations Day 4 β Division of a Unit Fraction How would you mentally solve this problem? 84 ÷ 14 Day 5 β Word Problems and Unit Fractions How would you mentally solve this problem? 90 ÷ 15 Day 5 β Word Problems and Unit Fractions DAILY LEARNING TARGET β Word Problems & Unit Fractions I can solve real world problems involving division of unit fractions by non-zero whole numbers. STANDARD/S MAFS.5.NF.2.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. MAFS.5.NF.2.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Day 5 β Word Problems and Unit Fractions 1 5 Amiyah has of her book left to read for a book report. She has 3 days to finish the book. If she splits the reading evenly among 3 nights, how much will Amiyah read each night? = 3 6 9 12 π ππ 15 Day 5 β Word Problems and Unit Fractions 1 2 Rosa has cup of chocolate chips to share equally into 4 batches of cookies. How much chocolate chips are in each batch? Rosa used a model to determine the amount of chocolate chips in each batch. Do you agree with her? Why or why not? ½ Cup ¼ 1 2 ÷4= 11 1 ππ’π ÷ 4 = 4 2 8 cup Day 5 β Word Problems and Unit Fractions Additional Practice Problems 1 3 1. Kiran has of his science project left to complete. If he wants to spread out the work over the next three days, how much will Kiran complete each day? 1 4 2. Harris has bag of cat food. He wants to feed his cat an equal amount over the next 4 days. How much cat food will Harris feed his cat each day? Day 5 β Word Problems and Unit Fractions Additional Practice Problems 1 8 3. Dani is making muffins that call for 3 cups of flour. Her measuring cup only holds cup of flour. How many times will Dani need to fill the measuring cup to get the 3 cups of flour? 1 A. 3 times 8 3 B. times 8 C. 24 times D. 11 times Day 5 β Word Problems and Unit Fractions CHECK YOUR UNDERSTANDING 1 6 Tonya has gallon of milk. She wants to drink equal amounts of the remaining milk in 3 days. How much milk will Tonya drink each day? Day 5 β Word Problems and Unit Fractions STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 5 β Word Problems and Unit Fractions GROUP/Student Names Stations to Complete TODAY Optional Stations Day 5 β Word Problems and Unit Fractions How would you mentally solve this problem? 80 ÷ 16 Day 6 β Division of a Whole Number How would you mentally solve this problem? 98 ÷ 14 Day 6 β Division of a Whole Number DAILY LEARNING TARGET β Division of a Whole Number I can interpret division of a whole number by a unit fraction and compute such quotients. STANDARD/S MAFS.5.NF.2.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. MAFS.5.NF.2.7b Interpret division of a whole number by a unit fraction and compute such quotients. Day 6 β Division of a Whole Number 1 7 ÷ because =x 21 3 1 3 21 x = 7 X = 21 Day 6 β Division of a Whole Number 1 1 6x = 36 ÷ because =x 2 2 1+ 1+1 + 1+ 1 + 1 = 6 X=6 0 π 1 ππ 2 ππ 3 π π 3 π Day 6 β Division of a Whole Number Additional Practice Problems 1 4 12 ÷ = x Use a model to solve the equation above. 9÷ 1 3 =x Use a number line to solve the equation above. Day 6 β Division of a Whole Number Day 6 β Formative CHECK YOUR UNDERSTANDING Lena was asked to solve the following equation: 1 5 ÷ = x. She solved using the strategy below. Is 4 her solution correct? Why or why not? 0 4 1 4 2 π π 4 3 4 5 ÷ = x and x = 4 4 5 ππ π Day 6 β Division of a Whole Number STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 6 β Division of a Whole Number GROUP/Student Names Stations to Complete TODAY Optional Stations Day 6 β Division of a Whole Number How would you mentally solve this problem? 96 ÷ 16 Day 7 β Real World Problems & Whole Numbers How would you mentally solve this problem? 24 ÷ 12 Day 7 β Real World Problems & Whole Numbers DAILY LEARNING TARGET β Real World Problems I can solve real world problems involving division of whole numbers by a unit fraction. STANDARD/S MAFS.5.NF.2.7b Interpret division of a whole number by a unit fraction and compute such quotients. MAFS.5.NF.2.7c Solve real world problems involving division of unit fraction by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Day 7 β Real World Problems & Whole Numbers Clint asked his teacher how many thirds would be in 8 macaroons. Clintβs teacher helped him 1 write the equation 8 ÷ = x, but Clint is still stuck. 3 How do you think he should finish solving? Day 7 β Real World Problems & Whole Numbers 1 2 Gina has 6 cupcakes. She wants to share them equally. If she divides each cupcake how many people can Gina share with? 1 by , 4 Day 7 β Real World Problems & Whole Numbers Additional Practice Problems 1. Hope has 6 donuts from Dunkin Donuts. If she 1 divides the donuts by , how 2 many people can Hope share with? Draw a model to represent your thinking. 2. David has 4 pizzas. If he divides the 1 pizza by , how many friends can David 2 share with? Draw a model to represent your thinking. Day 7 β Real World Problems & Whole Numbers Additional Practice Problems 3. Mariah has 9 pounds of cookie dough. She wants to put the dough into containers so 1 that each container has . 4 Part A Complete the following statement. Part B How many containers did Maria fill? Day 7 β Real World Problems & Whole Numbers CHECK YOUR UNDERSTANDING 1 2 Use the equation 9 ÷ = x to write a story problem, draw a visual representation, and solve. 1. Write a story problem. 2. Draw a visual representation of the problem. 3. Solve for the value of x. Day 7 β Real World Problems & Whole Numbers STATION NAME DESCRIPTION MUST DO or EXTRA TIME TIME i-Ready (Computer) Complete online lessons 3x per week 15 each time, 45 min/week Teacher Station Small group time with the teacher Must Do, Teacher will let Teacher will decide you know how often Day 7 β Real World Problems & Whole Numbers GROUP/Student Names Stations to Complete TODAY Optional Stations Day 7 β Real World Problems & Whole Numbers