Lesson 24 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

Solve real-world problems involving measurement conversions.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Measurement and Data

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Foundational Standards

The foundational standards covered in this lesson

4.MD.A.1

Measurement and Data

4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
4.MD.A.2

Measurement and Data

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Make sense of a three-act task and persevere in solving it (MP.1).
Solve multi-step word problems involving measurement conversions (MP.4).
Assess the reasonableness of a solution by rounding to estimate or by checking a solution using multiplication (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lesson Materials

Grade 5 MCAS Reference Sheet (1 per student) — Teachers in different states will need to find and use their own state's reference sheet

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Act 1: Watch the video The Fish Tank (Act 1).

a. What do you notice? What do you wonder?

b. How long will it take to fill the fish tank? Make an estimate.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Questioning My Metacognition The Fish Tank — Act 1 video: the Fish Tank (Act-1)

The Fish Tank by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Sept. 23, 2019, 1 a.m..

Problem 2

Act 2: Use the following information to solve:

It takes 10 seconds to fill 1 cup.
The dimensions of the fish tank are:

A quart is 58 cubic inches.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Questioning My Metacognition The Fish Tank — Act 2 image

The Fish Tank by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Sept. 23, 2019, 1 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Watch the video The Fish Tank (Act 3) to see how long it took to fill the fish tank. Was your answer reasonable? Why or why not?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Questioning My Metacognition The Fish Tank — Act 3 video: the Fish Tank (Act 3)

The Fish Tank by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Sept. 23, 2019, 1 a.m..

Problem 4

Act 4: If you doubled all of the dimensions of the fish tank, how long would it take to fill it?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How did you solve #5?
How did you solve #7? How did you convert from cups to gallons? What is a cup expressed as a fraction of a gallon? How did you figure that out?
How did you solve #11? How is this problem similar to problems in previous units related to volume? How is it different?
How did you solve #13? How is this problem similar to problems in previous units related to line plots? How is it different?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Owen lives 1.2 kilometers from school. Lucia lives 0.86 kilometers from school. Ignacio lives 90 meters from school. If Owen, Lucia, and Ignacio all walk to and from school, how far, in kilometers, did they all walk in total?

Problem 2

Manouel is driving to visit his brother. He listens to a podcast on the way that is 57 minutes long. The drive to his brother’s house is $$1\tfrac{3}{4}$$ hours long. How much longer, in minutes, is the drive than the podcast?

Student Response

An example response to the Target Task at the level of detail expected of the students.

Create a free account or sign in to view Student Response

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

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 23

Lesson Map

Topic A: Multiplying Decimals

Multiply a single-digit whole number by a decimal in cases that involve basic facts. Estimate the product of a single-digit whole number with a decimal by rounding numbers to their largest place.

5.NBT.B.7

Multiply a single-digit whole number by a decimal.

5.NBT.B.7

Construct viable arguments and critique the reasoning of others regarding the placement of the decimal point in computations that involve multiplying a single-digit whole number by a decimal.

5.NBT.B.7

Multiply a multi-digit whole number by a decimal.

5.NBT.B.7

Multiply a decimal by a decimal in cases that involve basic facts. Estimate the product of two decimals by rounding numbers to their largest place.

5.NBT.B.7

Multiply a decimal by a decimal.

5.NBT.B.7

Multiply with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic B: Dividing Decimals

Divide a decimal by a single-digit whole number in cases that involve basic facts. Estimate quotients with single-digit divisors by rounding numbers to compatible numbers.

5.NBT.B.7

Divide a decimal by a single-digit whole number.

5.NBT.B.7

Divide a decimal by a single-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a decimal by a two-digit whole number.

5.NBT.B.7

Divide a decimal by a two-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a whole number or a decimal by 1 tenth or 1 hundredth.

5.NBT.B.7

Divide a whole number or a decimal by a decimal in cases that involve basic facts. Estimate quotients with decimal divisors by rounding numbers to compatible numbers.

5.NBT.B.7

Divide a whole number or a decimal by a decimal.

5.NBT.B.7

Divide with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic C: Decimal Expressions and Real-World Problems

Solve real-world problems that require interpretation of the remainder involving all possible cases, including further decomposition into a decimal.

5.NBT.B.7

Solve real-world problems involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.2

Write and evaluate numerical expressions involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.1 5.OA.A.2

Topic D: Measurement Conversion and Real-World Problems

Express measurements in a whole number of larger units or mixed units in terms of a smaller unit.

5.MD.A.1

Express measurements in a fractional or decimal number of larger units in terms of a smaller unit.

5.MD.A.1

Express measurements in a whole number of smaller units in terms of a larger unit.

5.MD.A.1

Express measurements in a fractional or decimal number of smaller units in terms of a larger unit.

5.MD.A.1

Solve real-world problems involving measurement conversions.

5.MD.A.1

Multiplication and Division of Decimals

Objective

Common Core Standards

Core Standards

Measurement and Data

Foundational Standards

Measurement and Data

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem 4

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy