Objective
Solve division problems when the quotient is a fraction or mixed number, including cases with larger values.
Common Core Standards
Core Standards
The core standards covered in this lesson
5.NF.B.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.For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Number and Operations—Fractions
5.NF.B.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.For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Foundational Standards
The foundational standards covered in this lesson
4.NF.B.3
Number and Operations—Fractions
4.NF.B.3— Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.4
Number and Operations—Fractions
4.NF.B.4— Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
3.OA.A.1
Operations and Algebraic Thinking
3.OA.A.1— Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.A.2
Operations and Algebraic Thinking
3.OA.A.2— Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.B.6
Operations and Algebraic Thinking
3.OA.B.6— Understand division as an unknown-factor problem.For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (MP.4).
- Check the solution to a division problem with a fractional quotient using multiplication and/or repeated addition.
- Explain how the fractional part of a mixed-number quotient is related to the remainder in the problem (MP.3).
- Determine which two whole numbers a mixed-number quotient is in between.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
- In Grade 5, students connect fractions with division, understanding numerical instances of $$\frac{a}{b}=a\div b$$for whole numbers $$a$$and $$b$$, with$$b$$ not equal to zero (MP.8)” (NF Progression, p. 6).
- As mentioned in Lesson 1, Students can use the group size unknown interpretation of division (also called partitive or sharing division) to explain that $$\frac{a}{b}=a\div b$$. Students will continue to see many group size unknown division problems to continue to develop this understanding, but they will also start to see some other division problem types to generalize this understanding.
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Problem 1
32 students shared 6 pizzas equally. How much pizza will each student get?
a.Find the exact answer.
b.Check your work.
Guiding Questions
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Student Response
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References
EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic B > Lesson 5—Concept Development
Grade 5 Mathematics > Module 4 > Topic B > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 2
32 gallons of water is used to completely fill 6 fish tanks. If each tank holds the same amount of water, how many gallons will each tank hold?
a.Find the exact answer. Write it as a fraction and as a mixed number.
b.Determine which two whole numbers the answer is in between.
c.Explain how the fractional part of the mixed number is related to the remainder in the problem.
d.Check your work.
Guiding Questions
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Student Response
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References
EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic B > Lesson 4—Concept Development
Grade 5 Mathematics > Module 4 > Topic B > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 3
Solve the following problems. Think about the main differences between each one.
a.A teacher has 21 batteries. Each calculator uses 4 batteries. How many calculators can the teacher fill with batteries?
b.Four children can ride in a car. How many cars are needed to take 21 children to the museum?
c.Ms. Cole bakes 21 cookies and wants to share them out fairly to 4 friends. How many cookies will each friend get?
Guiding Questions
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Student Response
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Problem Set
15-20 minutes
Problem Set
Problem Set Answer Key
Discussion of Problem Set
- How did you determine how many inches each piece of paper would be in #1?
- Look at #2. What was different about this problem compared to the previous one? How should the remainder have been interpreted in this problem versus the other ones? How can we make that distinction in general?
- How did you determine which number was the dividend versus the divisor in each part of #3?
- In #4a, why dothe quotient and remainder have different units? In other words, the 7 represents the number of glasses Jorge will fill and 1 represents the number of cups Jorge will have left. Why?
- What unit should Linda’s answer have in #4b?
- Whose answer is correct in #4? Justify your reasoning.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Problem 1
Oxana builds a tower of 15 Jenga blocks stacked on top of each other. The tower is 9 inches tall. What is the height, in inches, of one Jenga block?
Student Response
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Problem 2
Mr. Keil is trying to split 22 cups of punch equally between 8 glasses. How many cups of punch should he put in each glass? Between what two whole numbers does your answer lie?
Student Response
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Additional Practice
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
Extra Practice Problems
Extra Practice Problems Answer Key
Word Problems and Fluency Activities
Word Problems and Fluency Activities
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Lesson 2
Lesson 4
