™ Content Coaching for Rigor, Relevance, Richness @normabgordon CMC South 2015 Session #356 11/6/2015.

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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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TICKET TO LEAVE

Send yourself an email! Subject: One Thing I’ll Try, cc: > 1

person you met today

Tell me, how I did: http://bit.ly/CC43Rs_CMCSouth15 ; random

draw for a class subscription!

POLLEVERYWHERE send text to this number: 37607

SCALE3 strongly agree2 agree1 disagree0 strongly disagree

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MAKE MATH SOCIAL

Norma Gordon

[email protected]

@normabgordon,

@CueThink