™ content coaching for rigor, relevance, richness @normabgordon cmc south 2015 session #356...
TRANSCRIPT
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Content Coaching for Rigor, Relevance, Richness
@normabgordon
CMC South 2015Session #356
11/6/2015
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BIG QUESTION
What raises the rigor, relevance and richness of application problems in math classrooms?
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AGENDA
LaunchSetting the stage(1:30 – 1:35)
WorkshopRead and discuss(1:35 – 1:45)OER and resources (1:45 – 1:50) Makeover examples (1:55 – 2:00) Workshop* (2:00 – 2:40)
Wrap UpShare out (2:40 – 2:55) Session feedback (2:55 – 3:00)
*with CueThink option
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MATHEMATICS TEACHING PRACTICES
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JARGON
Rigorous, relevant and rich content (or math problems)(http://www.sciencegeek.net/lingo.html) ➔
“We will aggregate hands-on problem-solving across cognitive and affective domains.”
“We will deploy intuitive systems in authentic, real-world scenarios.”
“We will deliver innovative enduring understandings via self-reflection.”
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NOT JARGON
Multiple entry points
Multiple pathways
Opportunity for conflict, argument, critiquing
“constructive controversy” (@ddmeyer, #ATMNE15)
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Provides opportunity for deep discussion and learning; in many instances the actual “question” could be open-ended allowing for multiple solutions.
Provides opportunity for extension or modifications for accessibility without compromising the mathematical learning objective.
Is relevant and interesting to students.
Is aligned to the Common Core State Standards.
CUETHINK CRITERIA
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Cleo wants to make
guacamole dip for a party
she is going to. Mike will be
at the party too. Avocados
(needed to make
guacamole) are on sale for
$0.85 and Cleo has $11.25.
How many avocados will
she be able to buy?
MAKEOVER EXAMPLE
Here are two story problems. Explain
how you can use your answer to
EITHER one to solve the OTHER one?
Cleo needs avocados to make
guacamole for a party. Avocados are on
sale for $0.85 and Cleo has $11.25 to
spend. How many avocados can she
buy?
Mike’s class raised $112.50 for an
afternoon at the movies. Tickets are
$8.50. How many tickets can the class
buy?
BEFORE AFTER
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READ AND RESPOND JIGSAW-like
Read one or both
NCTM Editorial: bit.ly/Gojack_Rigor
Achieve The Core: bit.ly/Achieve_Rigor
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NCTM ARTICLE
NCTM Editorial: bit.ly/Gojack_Rigor
Learning experiences that involve rigor …
Experiences thatdo not involve rigor …
challenge students are more “difficult,” with no purpose (for example, adding 7ths and 15ths without a real context)
require effort and tenacity by students require minimal effort
focus on quality (rich tasks) focus on quantity (more pages to do)
include entry points and extensions for all students
are offered only to gifted students
are not always tidy, and can have multiple paths to possible solutions
are scripted, with a neat path to a solution
provide connections among mathematical ideas
do not connect to other mathematical ideas
contain rich mathematics that is relevant to students
contain routine procedures with little relevance
develop strategic and flexible thinking follow a rote procedure
encourage reasoning and sense making require memorization of rules and procedures without understanding
expect students to be actively involved in their own learning
often involve teachers doing the work while students watch
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FOCUS TAKE AWAY
NCTM Editorial: bit.ly/Gojack_Rigor
Learning experiences that involve rigor …
Experiences thatdo not involve rigor …
challenge students are more “difficult,” with no purpose (for example, adding 7ths and 15ths without a real context)
require effort and tenacity by students require minimal effort
focus on quality (rich tasks) focus on quantity (more pages to do)
include entry points and extensions for all students are offered only to gifted students
are not always tidy, and can have multiple paths to possible solutions
are scripted, with a neat path to a solution
provide connections among mathematical ideas do not connect to other mathematical ideas
contain rich mathematics that is relevant to students contain routine procedures with little relevance
develop strategic and flexible thinking follow a rote procedure
encourage reasoning and sense making require memorization of rules and procedures without understanding
expect students to be actively involved in their own learning often involve teachers doing the work while students watch
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ACHIEVE THE CORE
RigorIn major topics pursue: conceptual understanding, procedural skill and fluency, and application with equal intensity.
Conceptual understandingStudents must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.
Procedural skill and fluencyStudents are given opportunities to practice core functions so that they have access to more complex concepts and procedures.
ApplicationStudents use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.Achieve The Core: bit.ly/Achieve_Rigor
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FOCUS TAKE AWAY
RigorIn major topics pursue: conceptual understanding, procedural skill and fluency, and application with equal intensity.
Conceptual understandingStudents must be able to access concepts from a number of perspectives so that
they are able to see math as more than a set of mnemonics or discrete procedures.
Application
Students use math flexibly for applications in problem-solving contexts.
Achieve The Core: bit.ly/Achieve_Rigor
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RESPOND
How might you use these prompts when considering, coaching, editing application problems?
Respond here: http://bit.ly/CC_3Rs_jigsaw
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SHARE OUT
How might you use these prompts when considering, coaching, editing application problems?
http://bit.ly/CC_3Rs_jigsaw
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REFLECTING FOR RIGOR CHECKLIST
adapted from http://achievethecore.org/page/962/instructional-practice-guide-lesson-planning-detail-pg
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OTHER WAYS OF THINKING
Open
Thick
Assessing
Wide
Puzzle
Closed
Think
Advancing
Narrow
Procedure
VERSUS
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Increasing Rigor
What is the relationship between the digits in this number? (e.g. 777, etc.)
How would adding a 0 to the end of a number affect the value of the
digits? (e.g. 75 becoming 750)
How do you think place value connects to other math operations? (e.g.
explore the relationship between place value and multiplication/division)
CCSS.MATH.CONTENT.4.NBT.A.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
HCPSS - example
https://grade4commoncoremath.wikispaces.hcpss.org/4.NBT.1 and http://www.corestandards.org/Math/Content/4/NBT/
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Increasing Rigor
What is the relationship between the digits in this number? (e.g. 777, etc.)
How would adding a 0 to the end of a number affect the value of the digits? (e.g. 75 becoming 750)
How do you think place value connects to other math
operations? (e.g. explore the relationship between place value and multiplication/division)
HCPSS - example
https://grade4commoncoremath.wikispaces.hcpss.org/4.NBT.1 and http://www.corestandards.org/Math/Content/4/NBT/
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Increasing Rigor
Why does the product of 5 x 80 have two zeros?
John says if you divide 5,624 by 100, you just move the decimal point to the
left two places to get the answer of 56.24. Is John right? Use your place
value understanding to explain why this works.
The approximate height (in feet) of the Statue of Liberty can be expressed
as 3 x 102. Using what you know about exponents and place value, what is
the height of the statue in whole numbers?
CCSS.MATH.CONTENT.5.NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the
placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote
powers of 10.
HCPSS - example
https://grade5commoncoremath.wikispaces.hcpss.org/5.NBT.2 and http://www.corestandards.org/Math/Content/5/NBT/
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Increasing Rigor
Why does the product of 5 x 80 have two zeros?
John says if you divide 5,624 by 100, you just move the decimal point to the left two places to
get the answer of 56.24. Is John right? Use your place value
understanding to explain why this works.
The approximate height (in feet) of the Statue of Liberty can be expressed as 3 x 102.
Using what you know about exponents and place value, what is the height of
the statue in whole numbers?
HCPSS- example
https://grade5commoncoremath.wikispaces.hcpss.org/5.NBT.2 and http://www.corestandards.org/Math/Content/5/NBT/
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What is the relationship between ___ and ___?
How would adding ___ affect the value of ___?
How do you think ___ connects to other math operations?
Why does the product/sum/f(x) of ___ have ___?
John says if you ___, you just ___ to get the answer of ___. Is
John right? Use your ___ understanding to explain why this
works.
The approximate ___ of ___can be expressed as ___ using
what you know about ___, what is the ___ of ___?
RIGOR RAISING SENTENCE FRAMES
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OER SITES THAT GET THIS RIGHT!
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When a baseball is thrown or hit into the air, its height in feet after t
seconds can be modeled by {equation} where {variable} is the initial
vertical velocity of the ball in feet per second and {other variable} is the
ballʼs initial height. A player throws the ball home from a height of {some
number} ft with an initial vertical velocity of {some number} ft/s.
The ball is caught at home plate at a height of {some number} ft. {some
number} seconds before the ball is thrown, a runner on third base starts
toward home plate at an average speed of {some number} ft/s.
Does the runner reach home plate before the ball does? Explain.
MAKEOVER EXAMPLE BEFORE
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When a baseball is thrown or hit into the air, its height in feet after t seconds can be modeled by {equation} where {variable} is
the initial vertical velocity of the ball in feet per second and {other variable} is the ballʼs initial height. A player throws the ball
home from a height of {some number} ft with an initial vertical velocity of {some number} ft/s.
The ball is caught at home plate. at a height of {some number} ft. {some number} seconds
Before the ball is thrown, a runner on third base starts toward
home plate. at an average speed of {some number} ft/s.
Does the runner reach home plate before the ball does? Explain.
Information:
Baseball motion model: {equation}, {variable}, {other variable}
A player throws the ball home from a height of {some number} ft with an initial vertical velocity of
{some number} ft/s.
The ball is caught at home plate at a height of {some number} ft.
{some number} seconds before the ball is thrown, a runner on third base starts toward home
plate at an average speed of {some number} ft/s.
MAKEOVER EXAMPLE AFTER
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Seb is making a round cake
for his sister Gabby. He has
used 6 sugar roses for
decoration. In between
each two roses, he has put
three candles. How old is
Gabby?
MAKEOVER EXAMPLES
Seb is making a round cake
for his sister Gabby. He has
used 6 sugar roses for
decoration. In between each
pair of roses, he has put three
candles. How old is Gabby?
Challenge: Can Seb use this
same pattern for her cake
next year? Be sure to show
or explain why or why not?
AFTERBEFORE
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Mack ate .25 of his pizza
and Justin ate 0.50 of his
pizza. Mack says that he
ate more pizza than Justin.
Explain. Show your thinking
by creating a model or
representation.
MAKEOVER EXAMPLES
Mack ate .25 of his pizza and
Justin ate 0.50 of his pizza.
Mack says that he ate more
pizza than Justin. Do you
agree with Mack? Explain
why or why not. Show your
thinking by creating a model
or representation.
BEFORE AFTER
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Find a problem
Read the related content standard (optional)
Review the prompts and sentence frames
Suggest a makeover!
MAKE OVER PROCESS – YOUR TURN
GOOGLE FORM TO
RECORD YOUR WORK *
http://bit.ly/3Rmakeovers
*option to use
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SHARE OUT
PARTICIPANT MAKEOVERS
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Send yourself an email! Subject: One Thing I’ll Try, cc: > 1
person you met today
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draw for a class subscription!
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SCALE3 strongly agree2 agree1 disagree0 strongly disagree