Unit #: 3: Understanding Decimals Subject(s): _Math Grade(s): __5____ Designer(s): Rebecca Stoudt, Jamie Barringer, Sarah Scott, Danielle Lucas
Unit Title: _ Understanding Decimals_
Understandings: Students will understand that…

Understanding place value leads to number sense and efficient strategies for computing with numbers.
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Numbers can be written in different forms without their value changing.


The location of the digit in numbers determines the value.
Rounding should be sensible to the context of the problem
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Decimals can be represented with models
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Addition/Subtraction with decimals are based on the fundamental concept of adding and subtracting the digits in like position values
Students will know:
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STAGE 1 – DESIRED RESULTS
Key Vocabulary: decimal, decimal place, tenth, hundredth, thousandth, standard form, expanded form, word form, comparative symbols [<, >, =], addition, subtraction, sum, difference, compare, round
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Students will recognize the connection between their understandings of whole number place to decimal place value in a base 10 system.
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Students will understand the correlation between computing with whole numbers and decimals.
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Students will understand the concept of rounding and comparing for working with whole numbers and decimals
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Students will understand the relationship between whole numbers and decimals based on their location.
Essential Questions:
 How does a digit’s position affect its value?
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How does the digit to the right of a number affect how the number is rounded?
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How are addition and subtraction with decimals similar to computing with whole numbers?
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How can numbers be written in different forms?
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How can we use estimation to help us check the reasonableness of sums/differences?
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How is place value different from digit value?
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What are the various uses of decimals?
Students will be able to:
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Identify value of a number by its position up to the thousandths place.
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Round decimals to the thousandths.
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Read and write decimals to thousandths in standard form, expanded form, and word form.
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Compare two decimals up to thousandths by looking at the place value positions.
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Compute [add/subtract] with decimals up to thousandths.
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Model decimals in various ways
STAGE 1– STANDARDS
List the CCSS/NCES for this unit in the space below. Include all relevant content and process standards.
5.NBT.1
5.NBT.3
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to the its right and 1/10 of what it represents in the place to its left.
Read, write, and compare decimals to thousandths.
5.NBT.4
5.NBT.7
5.TT.1
Use place value understanding to round decimals to any place.
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Use technology tools and skills to reinforce classroom concepts and activities
Standards for Mathematical Practices
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005) 1

Unit #: 3: Understanding Decimals Subject(s): _Math Grade(s): __5____ Designer(s): Rebecca Stoudt, Jamie Barringer, Sarah Scott, Danielle Lucas
MP1
MP2
MP3
MP4
MP5
MP6
MP7
MP8
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
STAGE 2 – ASSESSMENT EVIDENCE
Performance Tasks:

Decimals Performance Task (Compare/order): http://insidemathematics.org/common-core-math-tasks/5th-grade/5-
2009%20Decimals.pdf
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Balancing Checkbook: http://nanunet.lhric.org/PerformanceTasks/Grade%205/perftempes3.htm
OR

Georgia “Check This” : https://www.georgiastandards.org/Common-
Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit2FrameworkSE
.pdf

Performance Tasks/Exit Slips: http://www.scoe.org/files/mars-grade5.pdf
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DPI Math Tasks
Key Criteria:
Other Evidence:

Investigations Unit 6: Investigation quizzes, unit assessment
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Links to formative assessment options organized by standard: https://grade5commoncoremath.wikispaces.hcpss.org/
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Discovery Education: 5 th Grade Math Unit 3 Assessment
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Balancing Checkbook Rubric/Exemplars : http://nanunet.lhric.org/PerformanceTasks/Grade%205/perftempes3.htm

Decimals Performance Task (Compare/order): http://insidemathematics.org/common-core-math-tasks/5th-grade/5-2009%20Decimals.pdf
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005) 2

Unit #: 3: Understanding Decimals Subject(s): _Math Grade(s): __5____ Designer(s): Rebecca Stoudt, Jamie Barringer, Sarah Scott, Danielle Lucas
STAGE 3 – LEARNING PLAN
District Resources:

Investigations Unit 6-
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Investigation 1-sessions 1.1-1.5
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Investigation 2-sessions 2.1-2.7 (games for 2.5-2.7)
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Lessons For Learning:
From http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathT asks-Grade5.pdf/375611936/CCSSMathTasks-Grade5.pdf

Building Powers of Ten

Decimal Clue Conundrum
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Window Time
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NCDPI: Lessons for Learning
(ncdpi math wiki): http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-
Grade5.pdf/375611936/CCSSMathTasks-Grade5.pdf
 “Decimal Clue Conundrum”
 “Multiplying Whole Numbers by Decimals”
Differentiated Resources (AIG, ESL, EC, Technology, etc.):

Investigations: See Differentiation and Intervention Guide
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Investigations- Intervention/Extension following each investigation
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EC Resources:

5.NBT.1
 http://qta.quantiles.com/qtaxon/goal/30573/

5.NBT.3
 http://qta.quantiles.com/qtaxon/goal/30575/
 http://qta.quantiles.com/qtaxon/goal/30576/

5.NBT.4
 http://qta.quantiles.com/qtaxon/goal/30577/

5.NBT.7
 http://qta.quantiles.com/qtaxon/goal/30580/

AIG Resource: Challenge Math Ch 5 Decimals
Supplemental Resources:

NYC math lounge: http://mathloungenyc.wikispaces.com/5th+Grade+Math+Unit+3

Georgia Department of Education Unit 2: https://www.georgiastandards.org/Common-
Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit2FrameworkSE.pdf

Every Breath You Take (fits with NBT1): http://illuminations.nctm.org/LessonDetail.aspx?ID=L243
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NBT3 Resources: https://grade5commoncoremath.wikispaces.hcpss.org/5.NBT.3
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NBT7 Resources: https://grade5commoncoremath.wikispaces.hcpss.org/5.NBT.7
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Heinemann Contexts For Learning: Mystery of the Meter- Decimals
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Technology:

Decimal Math Links: http://www.math-play.com/decimal-math-games.html
 http://mathcentral.uregina.ca/index.php
 http://www.mathplayground.com

Khan Academy: http://www.khanacademy.org/search?page_search_query=decimals

Math Live: http://www.learnalberta.ca/content/me5l/html/Math5.html

Elementary Mathematics: https://elementarymathematics.org/Grade_5_Unit_6.html
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005) 3

Unit #: 3: Understanding Decimals Subject(s): _Math Grade(s): __5____ Designer(s): Rebecca Stoudt, Jamie Barringer, Sarah Scott, Danielle Lucas
CATEGORY 4 3 2 1
Neatness and
Organization
The work is presented in a neat, clear, organized fashion that is easy to read.
The work is presented in a neat and organized fashion that is usually easy organized fashion but may be hard to unorganized. It is hard to know what to read.
The work is presented in an read at times.
The work appears sloppy and information goes together.
Diagrams and
Sketches
Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s).
Diagrams and/or sketches are clear and easy to understand.
Diagrams and/or sketches are somewhat difficult to understand.
Diagrams and/or sketches are difficult to understand or are not used.
Explanation Explanation is detailed and clear. Explanation is clear.
Explanation is a little difficult to understand, but includes critical components.
Explanation is difficult to understand and is missing several components
OR was not included.
Mathematical
Concepts
Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).
Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).
Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).
Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005) 4