CCGPS Mathematics 5th Grade Update Webinar Unit 2: Decimals September 10, 2013 Update presentations are the result of collaboration between members of 2012 and 2013 Unit Review and Revision Teams Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard Turtle Toms- Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Today’s presenters Emily Heck – Gwinnett County Trudy Ives – Gwinnett County Michelle Parker - Gordon County Jenise Sexton - Henry County

Webinar Guide Unit 2 Overview  Critical areas within this unit  Content standards  Practice standards  Decimal number talks Changes to Unit 2 tasks Resources

Critical Areas in 5 th Grade

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Content: o Students must understand the magnitude of numbers given the place (location) of a digit and the value (worth) of the digit. o Example: In the number 1,557, the five in the tens place is worth 50 and the 5 in the hundreds place is worth is 10 times as much as is one tenth of 500.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Strategies:  Activate prior knowledge from 4 th grade.  Work with base ten blocks, changing the value of the blocks.  Students construct concrete models of 0.4 and 0.04 using materials like meter sticks, money and base ten blocks to see the relationship between the two numbers.

Unit 2 Content, Strategies and Misconceptions

MCC.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Student Misconceptions: o Keep an eye out for students who see a multi-digit number as just a number. Students need to work with numbers in context so number sense ideas can be used when thinking about the number.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.3 Read, write, and compare decimals to thousandths.  a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = 3 × × × × (1/10) + 9 x (1/100) + 2 × (1/1000).  b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Content:  Students write numbers in a variety of forms using appropriate math language.  Students compare decimal numbers, drawing on knowledge of the magnitude of digits within the numbers to understand the size of each number.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.3 Read, write, and compare decimals to thousandths.  a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = 3 × × × × (1/10) + 9 x (1/100) + 2 × (1/1000).  b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Strategies:  Connect to students’ prior knowledge of magnitude of numbers to read and write decimal numbers in various forms.  Use base ten blocks and change the value of the blocks. Allow students to record names for the model, referring back to the place value of the blocks used.  Use open number lines to compare decimal numbers.

Unit 2 Content, Strategies and Misconceptions

MCC.5.NBT.3 Read, write, and compare decimals to thousandths.  a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = 3 × × × × (1/10) + 9 x (1/100) + 2 × (1/1000).  b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Student Misconceptions:  Students may not apply number sense when working with decimal numbers. Students should think about the value of the digits within numbers and the location of numbers within the number system.  Students may think that decimal numbers work in the same manner as whole numbers. (A number with more digits has a greater value.)

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.4 Use place value understanding to round decimals to any place. Content:  Students use number lines and place value knowledge to reason when rounding numbers.  Students have a deep understanding of place value knowledge that allows them to mover beyond procedures and rules for rounding.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.4 Use place value understanding to round decimals to any place. Strategies:  Students use open number lines to show how to round numbers. Students think about which two multiples the number falls in between, as well as what is halfway between the two multiples.  Provide real life context for decimal numbers and situations in which rounding is useful. (Example: I bought 2.14 pounds of apples at the store. )

Unit 2 Content, Strategies and Misconceptions

MCC.5.NBT.4 Use place value understanding to round decimals to any place. Student Misconceptions:  Students may have trouble knowing the multiples that a number falls between when dealing with decimal numbers.  Students may not be able to determine the halfway point between two multiples when dealing with decimal numbers.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.7 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. Content:  Students build an understanding of decimal addition and subtraction using concrete models and strategies involving representations so that they can better understand why the standard algorithm works.  Fluency with the standard algorithm is a sixth grade standard.

Unit 2 Content, Strategies and Misconceptions MCC.5.NBT.7 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. Strategies:  Provide plenty of opportunities for adding and subtracting decimal numbers using concrete models.  Use open number lines to develop strategies for adding and subtracting decimal numbers.  Compare and contrast adding and subtracting whole numbers to adding and subtracting decimal numbers.

Unit 2 Content, Strategies and Misconceptions

MCC.5.NBT.7 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. Student Misconceptions:  Students may line up digits without regard for the place value of the digits. Students need to use concrete models to understand why the decimal point is used to align the digits in decimal addition and subtraction.

8 Standards for Mathematical Practice From the classroom of Jessie Waters 5 th grade math/science classroom at Fairmount Elementary in Gordon County

8 Standards for Mathematical Practice I Can Practice Standards.

Standards for Mathematical Practice Describe how students will practice these in Unit 2

Number Talks

Make Wholes Make a Landmark # Addition Number Talk Strings Adapted from Number Talks by Sherry Parrish

Addition Adding Up in Chunks Addition Adding Up in Chunks Subtraction Adding Up Subtraction Adding Up Students might also a break each number into its place value strategy. 2 – – – – 0.8 Number Talk Strings Adapted from Number Talks by Sherry Parrish

Number Talks Number Talk Tips  Use hand signals to ensure 100% participation  OK to present multiple ways of solving  Don’t be afraid to use a Think-Pair- Share in your number talk  Create a class strategy chart  Use a ticket out the door and weekly assessments to give students pencil and paper opportunities to practice explaining their mental math strategies.

Task List Specific standards for each task are listed

Unit 2 Tasks SMP’s

Unit 2 Tasks Common Misconceptions

Unit 2 Tasks Included tasks to address all content standards Edited mistakes Amount of time to compete tasks will vary No expectation that every task in the unit will be completed

Unit 2 Tasks - Unchanged Decimal Designs Making “Cents” of Decimals Decimal Gardens Reasonable Rounding Batter Up Hit the Target Ten is the Winner It All Adds Up Rolling Around with Decimals

Unit 2 Tasks - Deleted Day Out

In the Paper MCC5.NBT.3

High Roller Revisited MCC5.NBT.1 & MCC5.NBT.3

High Roller Revisited

Decimal Line-Up MCC5.NBT.3

The Right Cut CTE Task: Designed to demonstrate how the Common Core and Career and Technical Education knowledge and skills can be integrated. The tasks provide teachers with realistic applications that combine mathematics and CTE content.

The Right Cut Rounding within a context Don’t be afraid

Check This Culminating Task MCC5.NBT.3, MCC5.NBT.4 & MCC5.NBT.7

Resources More great sources for tasks: grade-number-activities.html PDF Documents: 1 Task & 2 Base Ten Tools

Activate your Brain How many ants does it take to have the same mass as an elephant? Adapted from Illustrative Mathematics – 8.EE.3 Ant and Elephant Hey, this looks like my 8 th grade webinar!

Activate your Brain How many ants does it take to have the same mass as an elephant? Did you use a visual representation to help solve the problem? What types of visual representations might assist in solving this problem? Share your ideas! Get those 5 th graders ready!

Activate your Brain How many ants does it take to have the same mass as an elephant? grams

Activate your Brain

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How many ants does it take to have the same mass as an elephant? 4 x ( )8 x ( )

CCGPS Overview “educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.“educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.

Does this student have: procedural skill and fluency? conceptual understanding? the ability to apply mathematics?

Does this student have: procedural skill and fluency? conceptual understanding? the ability to apply mathematics?

Writing in Math Standards for Mathematical Practice require students to express their thinking and record their strategies in written form.

Standards for Mathematical Practice SMP 1 – Students are required to explain their thinking when making sense of a problem. SMP 2 – Students are required to construct viable arguments and critique the reasoning of others.

Why Write in Math Class? Marilyn Burns (2004): “Writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas—all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions and their feelings about the content.”

Math Journals Purposes: – Record strategies and solutions – Reflect upon learning – Explain and justify thinking – Provide a chronological record of student math thinking throughout the year – Means of assessment to guide future instruction

Can you see the connections? Visual images Recording thinking Explaining thinking Conceptual understanding Procedural fluency Application

Feedback Turtle Toms- Elementary Mathematics Specialist

Thank you! Emily Heck – Gwinnett County Trudy Ives – Gwinnett County Michelle Parker - Gordon County Jenise Sexton - Henry County Any advice for your colleagues as they begin work on Unit 2?

Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the K-5 Mathematics listserve. Follow on Twitter! Turtle Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.