Intellectual Preparation Protocol
All Leader Training: MS + HS Mathematics
Will Roble + Anne Pearson
June, 2014
Aims + Agenda = 
Aims:
GMISLWBAT
Understanding the thinking behind and process for planning Phase 0
Practice 2 critical facilitation moves (accountability for deep thinking & for
top quality responses) for phase 1 of the IPP protocol
Agenda:
Quick Review of the Protocol
Phase 0 at a Glance
Phase 1 Fishbowl
Debrief Facilitation Moves
Practice!
Implications for Implementation, and send Will/Anne feedback
2
Quick Review
Intellectual Preparation Protocol
Describe the purpose, outcome(s)
and steps of each phase
This is what intellectual preparation looks like according to
Google…if only it was this easy!
3
Phase 0
0 – Picking the Math
Define the purpose of the unit
Name the big ideas of the unit
Select the problem
What students are thinking about
How students are thinking
4
Phase 1
1 – Depth &
Craft 2-3 possible solution pathways using multiple representations and
Proficiency in strategies
Content
Final check for alignment and revise as needed
Select solution pathway that best illustrates the focal math concepts; and,
order alternate pathways to develop depth of understanding and connection
making in order to make sense of the most efficient pathway
Articulate the relationship between representations and strategies, and how
they validate and/or shed light on the underlying focal math concepts
Synthesize the key why, what and how points linking the focal math concepts
to the representations and strategies, and the relationships between them
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Phase 2
2 – Questioning and
Misconceptions
Draft focal questions to bring out
key points
Identify misconceptions
Revise focal questions to draw out
and address misconceptions
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Phase 3
Practice Delivery
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What do we intellectually Prep?
Exercises
• Usually one solution path and answer
• Not ambiguous
Tasks
• More ambiguous
• Less obvious entry point and solution
path
• Multiple solution paths and/or answers
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Lesson Types
Exercise Based
Opening
INM
PP
Debrief + CFU
IP
Closing + ET
Task Based
Understand
Exploration
Presentation +
Discussion
Extension
Evaluation
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Phase 0
Picking the Math
• Define the purpose of the unit
• Name the big ideas of the unit
• Select the problem
• Determine what students will be thinking about
• Determine how students will be thinking
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Preface
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Questions to consider during Phase 0
What skill, content knowledge or mindset is necessary to
be successful with phase 0?
What do you think your teachers will have the most
difficulty with?
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Big Ideas of the Unit
An expression in one variable defines a general calculation with the
variable representing the input and the expression calculating the
output. Choosing a variable to represent the output creates an equation
in two variables.
A linear equation in one variable can have one solution, no solution, or
infinitely many solutions. A linear equation in two variables has an
infinite number of solutions.
When two quantities, x and y, vary in such a way that one of them is a
constant multiple of the other, a model for that situation is y=kx where k
is the constant of proportionality or the constant ratio of y to x. An
equation is proportional if it includes the point (0,0) and is a straight line.
Rates of change communicate critical information
about a linear relationship. Rates of change are
synonymous with unit rate for proportional
relationships.
Lines have a constant rate of change because the ratio of the rise to
run between any two points on a line is the same.
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What Content Does this Exercise Build on?
In 7th grade, students learn to recognize proportional
relationships represented graphically, algebraically and
In tabular form. Additionally, they learn to describe the
unit rate as the Constant of Proportionality and
understand that proportional relationships are identified
by a unit rate.
Students build on a basic understanding of functions as
a means of representing a relationship between two
quantities. They have also just engaged with finding and
comparing rates of change given multiple
representations of these relationships (table, graph,
equation, and context) in the functions unit.
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What does this content set students up for?
A solid understanding of proportional relationships and
unit rate grounds students’ understanding of rates of
change.
Applications of Rates of Change when working with
graphs, tables, equations and data sets
HS – Facilitating meaningful engagement with non-linear
relationships and limits and derivatives
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Aims that support this learning
SWBAT graph proportional relationships, interpreting the
unit rate as the slope of the graph.
SWBAT determine if a relationship is proportional.
SWBAT compare two different proportional
relationships represented in different ways by
determining the unit rate (slope)
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Content Standards
8.EE.B – Understand the connections between
proportional relationships, lines and linear equations
8.EE.5 – Graph proportional relationships, interpreting
the unit rate as the as the slope of the graph. Compare
two different proportional relationships represented in
different ways
8.F.4 – Construct a function to model a linear
relationship between two quantities. Determine the rate
of change and initial value of the function from a
description of a relationship or from two (x,y) values,
including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear
function in terms of the situation it models, and in terms
of its graph or a table of values.
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Practice Standards
SMP1 – Make sense of problems and persevere in
solving them
SMP2 – Reason abstractly and quantitatively
SMP3 – Construct viable arguments
and critique the reasoning of others
SMP4 – Model with mathematics
SMP6 – Attend to precision
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Key Points
Why – The unit rate is a building block to understand rate of
change; Unit rates can be the most efficient means of
comparison.
What –
• When comparing rates, using the unit rate allows you to
find the amount of a unit per every one of the other unit
• Different representations of a problem are better for
different circumstances
• Unit rate only applies to proportional relationships because
there are equivalent ratios of corresponding values
How –
• Calculate the unit rate using an equation
• Compare the unit rates given the problem’s context
The Exercise
Problem: Anna and Jason have summer jobs stuffing
envelopes for two different companies. Anna
earns $1.53 for every 17 envelops she finishes. Jason
recorded his earnings in the table to the right. Who
makes more from stuffing the same number of
envelopes? How can you tell?
Earnings
Number of
envelopes
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$0.88
$1.76
$2.64
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The What of the Exercise
How does the problem align to the priority
standards, aims, and concepts of the unit?
The problem involves the comparison of two different
representations of relationships, both proportional, and a
justification of the conclusion of that comparison. This ties
directly to the prioritized aim “represented in different
ways by determining the unit rate/slope and graphing.”
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The How of the Exercise
How are students applying the focal SMP(s) in this
problem?
SMP3 – Construct viable arguments and critique
the reasoning of others
SMP4 – Model with mathematics
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Alignment to Exercise Criteria
Draws thinking towards mathematics to be used
and learned; is relatively narrowly focused on a
strategy, concept or skill
May be difficult or easy, complex or simple, but
never puzzling
The path(s) towards the solution is(are) often
apparent
Incorporates the Key Cognitive Strategies
(Conley)
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Quick Reflection on Phase 0
What skill, content knowledge or mindset is necessary to
be successful with phase 0?
What do you think your teachers will have the most
difficulty with?
24
Phase 0 – Thinking Strategically
0 – Picking the Math
Define the purpose of the unit
Name the big ideas of the unit
Select the problem
What students are thinking about
How students are thinking
25
Two Roles
We are going to do this better!!
Leader
Participant
• During the protocol, stay in character
• If leadership questions come up while you are a participant, write them down
for the debrief
• Struggle and be confident as though you are a teacher when a participant
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Phase 1
1 – Depth &
Craft 2-3 possible solution pathways using multiple representations and
Proficiency in strategies
Content
Final check for alignment and revise as needed
Select solution pathway that best illustrates the focal math concepts; and,
order alternate pathways to develop depth of understanding and connection
making in order to make sense of the most efficient pathway
Articulate the relationship between representations and strategies, and how
they validate and/or shed light on the underlying focal math concepts
Synthesize the key why, what and how points linking the focal math concepts
to the representations and strategies, and the relationships between them
27
Questions to consider during Phase 1
How is the facilitator engaging all participants in deep
thinking?
How is the facilitator pushing for top quality responses?
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Teacher Work 1
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Teacher Work 2
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Other Strategies?
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Ordering Solution Pathways
In what order should the alternate pathways be
presented by students in order to lead students to the
targeted learning? Why?
1) Table
2) Unit Rate
3) Graph
4) Proportion
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Connections
How does understanding each representation and
strategy support the understanding of the others and the
math being applied?
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Sum It All Up
How do the KPs live in the problem and student work?
Why – The unit rate is a building block to understand rate of change;
Unit rates can be the most efficient means of comparison.
What –
• When comparing rates, using the unit rate allows you to find the
amount of a unit per every one of the other unit
• Different representations of a problem are better for different
circumstances
• Unit rate only applies to proportional relationships because there
are equivalent ratios of corresponding values
How –
• Calculate the unit rate using an equation
• Compare the unit rates given the problem’s context
34
35
Questions to consider during Phase 1
How is the facilitator engaging all participants in deep
thinking?
How is the facilitator pushing for top quality responses?
36
Just a Reminder
Phase
Description
0
• Picking the Math
1
• Depth and Proficiency in Content
2
• Questions and Misconceptions
3
• Practice the execution of the lesson
• Focus on least invasive teacher moves that support
scholars in struggling to precision and ensuring that all
minds are on.
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Time to Practice
Use the same problem
Practice the facilitator moves modeled
Facilitate Phase 1
Groups of 4
2 rounds of practice (5 min) + feedback (2 min) = 20 min
Continue where the protocol left off
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Implications for Implementation
How will this experience shape how you will work with
and support your teachers?
How will you set yourself up for success?
How will you set your teachers up for success?
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