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- tgunn@doe.k12.ga.us
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 5th 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
o
Students must understand the magnitude of numbers given
the place (location) of a digit and the value (worth) of the digit.
Example: In the number 1,557, the five in the tens place is
worth 50 and the 5 in the hundreds place is worth 500. 500 is
10 times as much as 50. 50 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 4th 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
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., 347.392 = 3 × 100 + 4 × 10
+ 7 × 1 + 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., 347.392 = 3 × 100 + 4 × 10
+ 7 × 1 + 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
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., 347.392 = 3 × 100 + 4 × 10
+ 7 × 1 + 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
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
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 5th 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
Addition Number Talk Strings
Make Wholes
Make a Landmark #
0.5 + 0.5
0.5 + 0.6 + 0.5
0.5 + 0.9 + 0.5
1.9 + 0.2
1.9 + 0.5
1.9 + 0.8
1.9 + 1.2
Adapted from Number Talks by Sherry Parrish
Number Talk Strings
Addition
Adding Up in Chunks
Subtraction
Adding Up
1.6 + 1
1.6 + 2
1.6 + 4
1.6 + 4.2
2 – 1.5
2 – 1.4
2 – 0.9
2 – 0.8
Students might also a break each number
into its place value strategy.
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-PairShare 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:
http://www.k-5mathteachingresources.com/5thgrade-number-activities.html
 PDF Documents: 1 Task & 2 Base Ten Tools
Activate your Brain
An ant has massof approx imately 4  103 gramsand
an elephant has a massof approx imately 8  106 grams.
How many ants does it take to have the same mass as
an elephant?
Hey, this looks
like my 8th
grade webinar!
Adapted from Illustrative Mathematics – 8.EE.3 Ant and Elephant
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
Get those 5
solving this problem? graders ready!
Share your ideas!
th
Activate your Brain
How many ants does it take to have the same mass as
an elephant?
8  106
grams
4  103
grams
Activate your Brain
100 101
102
103
Activate your Brain
102
100 101
103
102
101
103
100
Activate your Brain
…
102
100 101
…
103
103
…
102
101
100
Activate your Brain
How many ants does it take to have the same mass as
an elephant?
4
3
10
x( )
8 x (106 )
3
(4 10 ) a

8 10 
6
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.“
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
http://ccgpsmathematicsk-5.wikispaces.com/
Turtle Toms- tgunn@doe.k12.ga.us
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 http://ccgpsmathematicsk-5.wikispaces.com/ to share your feedback, ask
questions, and share your ideas and resources!
Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx
to join the K-5 Mathematics email listserve.
Follow on Twitter!
Follow @GaDOEMath
Turtle Toms
Program Specialist (K-5)
tgunn@doe.k12.ga.us
These materials are for nonprofit educational purposes only.
Any other use may constitute copyright infringement.