Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 17
Math
Unit 5
5th Grade
Lesson 17 of 25
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Solve real-world problems involving multiplication with mixed numbers and create real-world contexts for expressions involving multiplication 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.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.
5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
The foundational standards covered in this lesson
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 — 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.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson follows a different structure than those in analogous lessons in previous topics, Lesson 7 and Lesson 12. This is for the sake of sustained work on a multi-step word problem that addresses the most challenging type of computation aligned to 5.NF.4. However, if students would benefit from more direct instruction aligned to Criteria for Success #2 and #3, create tasks similar to Lesson 6’s and Lesson 11’s Anchor Tasks #1 and #2 to include mixed number multiplication and include them before a consolidated three-act task as outlined in this lesson.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Act 1: Watch the following video – The Big Pad (Act: 1)
a. What do you notice? What do you wonder?
b. What is the area, in square centimeters, of the big pad? Make an estimate.
The Big Pad by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 1, 2019, 2:46 p.m..
Act 2: Use the following information to solve -
Act 3: Reveal the answer -
The area of the big pad is $$776\frac{124}{225}$$ square centimeters. Was your answer reasonable? Why or why not?
Act 4 (the sequel): Look at the following image of the dimensions mentioned on the big pad -
Do these dimensions result in the same area as what we computed in Anchor Task #3? Why or why not?
Problem Set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Susanna is studying for final exams in college. For a whole week, she studied for her history exam for $$2\frac14$$ hours every day and for her science exam for $$\frac23$$ as much time as her science exam. How many hours will she spend studying in total over the course of the whole week?
An example response to the Target Task at the level of detail expected of the students.
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.
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Lesson 16
Lesson 18
Topic A: Fractions as Division
Relate equal shares of objects to division expressions and visual representations of fractions.
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.
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Topic B: Multiplying a Fraction by a Whole Number
Multiply a fraction by a whole number where the product is a whole number.
5.NF.B.4.A 5.NF.B.6
Multiply a fraction by a whole number where the product is a whole number or a fraction.
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.A 5.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.4 5.NF.B.6 5.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.4 5.NF.B.5 5.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.
Develop a general method to multiply with mixed numbers.
Interpret multiplication as scaling.
5.NF.B.5 5.NF.B.5.A 5.NF.B.5.B
Topic E: Dividing with Fractions
Divide a unit fraction by a whole number.
5.NF.B.7.A 5.NF.B.7.C
Divide a whole number by a unit fraction.
5.NF.B.7.B 5.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.C 5.OA.A.2
Topic F: Fraction Expressions and Real-World Problems
Solve real-world problems involving multiplication and division with fractions.
5.NF.B.3 5.NF.B.6 5.NF.B.7
Write and evaluate numerical expressions involving operations with fractions.
5.NF.B.3 5.NF.B.4 5.NF.B.5 5.NF.B.6 5.NF.B.7 5.OA.A.1 5.OA.A.2
Topic G: Line Plots
Create line plots.
5.MD.B.2
Solve problems involving information presented in a line plot (dot plot).
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