Objective
Multiply mixed numbers by whole numbers.
Common Core Standards
Core Standards
The core standards covered in this lesson
5.NF.B.4— Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Number and Operations—Fractions
5.NF.B.4— Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.5— Interpret multiplication as scaling (resizing), by:
Number and Operations—Fractions
5.NF.B.5— Interpret multiplication as scaling (resizing), by:
5.NF.B.6— Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Number and Operations—Fractions
5.NF.B.6— Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Foundational Standards
The foundational standards covered in this lesson
3.MD.C.7
Measurement and Data
3.MD.C.7— Relate area to the operations of multiplication and addition.
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.
5.NF.A.1
Number and Operations—Fractions
5.NF.A.1— Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Multiply a mixed number by a whole number.
- Relate the area model to the distributive property.
- Solve word problems that involve the multiplication of a mixed number by a whole number (MP.4).
- Estimate the size of a product of a mixed number and a whole number in comparison to the size of its factors.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
- Students learned how to multiply a mixed number by a whole number in Grade 4 (4.NF.4). However, this lesson is included to serve as a review before moving on to more advanced types of multiplication involving mixed numbers. You may decide to cut this lesson if students do not seem to need it.
Lesson Materials
- Quarter inch graph paper (1 per student)
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Problem 1
a.A construction worker is tiling a bathroom floor. The bathroom floor is $$3$$ tiles long and$${2{1\over4}}$$ tiles wide. How many tiles are needed in total for the whole bathroom floor? Give an exact answer that includes the fractions of a tile she will need.
b.A rectangular playroom has a length of $${5{7\over8}}$$meters and a width of $$2$$meters. What is the area of the playroom?
Guiding Questions
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References
EngageNY Mathematics Grade 5 Mathematics > Module 5 > Topic C > Lesson 10—Concept Development
Grade 5 Mathematics > Module 5 > Topic C > Lesson 10 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.
Achievement First Grade 5, Unit 6, Lesson 10 (2016-2017)—Test the Conjecture, #2
Grade 5, Unit 6, Lesson 10 (2016-2017) is made available byAchievement Firstas a part of theirOpen Source web portalunder a CC BY 4.0 license. Copyright©1999-2017 Achievement First. Accessed April 27, 2018, 12:47 p.m..
Problem 2
a.Maya buys a bag of onions that weighs $${1{2\over3}}$$ kilograms. She also buys a bag of potatoes that weighs twice as much as the bag of onions. How much does the bag of potatoes weigh, in kilograms?
b.Anne wants to make four friendship bracelets. She needs $${8{3\over4}}$$inches of string for each bracelet. How much string, in inches, does Anne need?
Guiding Questions
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Problem 3
Solve. Show or explain your work.
a.$${4\times2{1\over5}}$$
b.$${2{2\over9}\times3}$$
c.$${3{3\over4}\times 5}$$
d.$${3\times4{2\over3}}$$
Guiding Questions
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Problem Set
Problem Set
Answer Keys
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Discussion of Problem Set
- Look at #3. What was Valerie’s error? How would you show or explain to Valerie what mistake she made?
- Look at #5. The recommended daily sugar intake is 2 tablespoons of sugar. If you have a can of Coca-Cola, are you over or under the daily recommended amount of sugar? By how much?
- Look at #6. Why is Jackson’s statement incorrect? Under what circ*mstances is it correct? How can you rewrite it so that it is correct?
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Problem 1
Solve. Show or explain your work.
a.$${4 \times 2{1\over6}}$$
b.$${3{2\over3} \times 6}$$
Student Response
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Problem 2
Stan eats$$1\tfrac{3}{4}$$ cups of fruit each day. How many total cups of fruit does Stan eat in 7 days?
Student Response
An example response to the Target Task at the level of detail expected of the students.
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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
Answer Keys
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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 12
Lesson 14
