Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 16
Math
Unit 5
5th Grade
Lesson 16 of 24
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Develop a general method to multiply with mixed numbers.
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.
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.
The foundational standards covered in this lesson
3.MD.C.7 — Relate area to the operations of multiplication and addition.
4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
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.)
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In Lessons 13-15, students “reason[ed] repeatedly from many examples (MP.8), using strips of paper, tape diagrams, and number line diagrams” (NF Progression, p. 18) to multiply with mixed numbers. While “Grade 5 students need not express the formula in [a] general algebraic form, but rather recognize numerical instances from” their repeated reasoning, this lesson serves to consolidate that repeated reasoning into a few strategies that they can use to solve any problem involving multiplication with mixed numbers.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Sophia and Zack are multiplying $${2{2\over3}}$$ and $${3{1\over4}}$$. Their work is shown below.
a. Do both of these strategies result in the same product?
b. Which method do you prefer? Why?
Upgrade to Fishtank Plus to view Sample Response.
Solve each of the following problems using two strategies. Then determine which strategy is more efficient for each problem.
a. $$1\frac{1}{3} \times 3\frac{3}{4}$$
b. $$16\frac{1}{2} \times 4\frac{1}{4}$$
Grade 5 Mathematics > Module 5 > Topic C > Lesson 13 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 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Estimate the following products. Then, solve using whichever strategy you think is most efficient.
a. $$\frac{2}{3} \times 6\frac{1}{2}$$
b. $$2\frac{2}{3} \times 3\frac{3}{4}$$
c. $$2\frac{4}{5} \times 4$$
d. $$5\frac{5}{8} \times 6\frac{1}{4}$$
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Solve each problem in two different ways.
a. $${3{1\over3} \times 1{1\over4}}$$
b. $${5{2\over5} \times 3{4\over9}}$$
Which strategy was more efficient for each problem above? Explain.
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
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Next
Solve real-world problems involving multiplication with mixed numbers and create real-world contexts for expressions involving multiplication with mixed numbers.
Topic A: Fractions as Division
Relate equal shares of objects to division expressions and visual representations of fractions.
Standards
5.NF.B.3
Write division expressions that represent fractions and vice versa.
Solve division problems when the quotient is a fraction or mixed number, including cases with larger values.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Multiplying a Fraction by a Whole Number
Multiply a unit fraction by a whole number.
5.NF.B.4.A5.NF.B.6
Multiply a non-unit fraction by a whole number.
Relate multiplication of a fraction by a whole number to multiplication of a whole number by a fraction and use this to develop a general method to multiply any fraction by any whole number (or vice versa).
5.NF.B.4.A5.NF.B.5
Solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers.
5.NF.B.45.NF.B.65.OA.A.2
Topic C: Multiplying a Fraction by a Fraction
Multiply a fraction by a fraction without subdivisions using tape diagrams and number lines.
5.NF.B.45.NF.B.55.NF.B.6
Multiply a fraction by a fraction with subdivisions using tape diagrams and number lines.
Multiply a fraction by a fraction with more complicated subdivisions using an area model.
Develop a general method to multiply a fraction by a fraction.
Solve real-world problems involving multiplication of fractions with fractions and create real-world contexts for expressions involving multiplication of fractions with fractions.
Topic D: Multiplying with Mixed Numbers
Multiply mixed numbers by whole numbers.
Multiply mixed numbers by fractions.
Multiply mixed numbers by mixed numbers.
Interpret multiplication as scaling.
5.NF.B.55.NF.B.5.A5.NF.B.5.B
Topic E: Dividing with Fractions
Divide a unit fraction by a whole number.
5.NF.B.7.A5.NF.B.7.C
Divide a whole number by a unit fraction.
5.NF.B.7.B5.NF.B.7.C
Solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions.
5.NF.B.7.C5.OA.A.2
Topic F: Fraction Real-World Problems and Line Plots
Solve real-world problems involving multiplication and division with fractions.
5.NF.B.35.NF.B.65.NF.B.7
Create line plots.
5.MD.B.2
Solve problems involving information presented in a line plot (dot plot).
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free