Intellectual Prep Protocol
Wednesday, June 25th, 2014
School Leaders Will Be Able To:
 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
ALT - IPP
Supporting Intellectual Lift in Planning & Execution - Math
Suggested Process for Rollout
The coach should bring people through this process in three phases:
Phase #
0
Picking the
Math
Description
This phase gets people to a
proficient level of understanding
the math by making key
preparation moves (content and
practice standards identification,
problem selection and validation).
Through supporting these strong
skills of problem selection and
alignment, the facilitator also sets
the standard for what a strong
problem looks like.
Participant Pre-Work
Participants select content and
practice standards, articulate the math
that should come to light for those
standards and choose a rich exercise,
problem or task that is conducive to
highlighting the desired math learning.
*Note: In the beginning, the facilitator
may opt to provide the participant
with the standards and
exercise/problem/task until the
participant is able to do so on his/her
own.
1
Depth &
Proficiency in
Content
(Identifying the
why, what and
how key
points)
This phase focuses on crafting the
representations and strategies for
the exercise or task, ordering
them by level of sophistication,
and articulating the links between
each representation from both an
adult and student lens. The phase
moves from crafting multiple
representations and strategies to
synthesizing key points based on
the underlying math concepts
applied.
This phase focuses on questioning
and misconceptions. What are
the big meaty questions that will
guide the discussions? What are
the likely misconceptions (both
gap and content) and how, with
questioning and other means, will
those misconceptions be
handled? The phase closes with a
revision of the questions and a
series of funneled questions for
responding to misconceptions
This phase focuses on practicing
the execution of the lesson. It
focuses on least invasive
facilitator moves that support
scholars in struggling to precision
and ensuring that all minds are
on.
Once participants have reached
proficiency with pre-work for phase 0,
participants complete phase 1 in its
entirety as pre-work, ready to present
their initial attempt at creating
representations, strategies and key
points to their coach. This allows for
more time to be allocated during the
protocol for phases 2 and 3.
Facilitator Pre-Work
Facilitator reviews the participant’s
pre-work prior to the protocol to
check for and provide feedback on
alignment between
content/practices and the
exercise/problem/task as well as
alignment of the
exercise/problem/task to the criteria
outlined in the FOI. Facilitator
checks for alignment of the math
content and practices within the
learning progression of the unit and
year.
Facilitator should do the
participant’s pre-work, paying
particular attention to the
connections between the
representations, strategies, and key
points. Facilitator should be
prepared to bring resources to share
with participant to facilitate learning
‘the math,’ as needed.
Once participants have reached
proficiency with pre-work for phases 0
and 1, participants complete phase 2
in its entirety as pre-work, ready to
present their initial planning. This
allows for more time to be allocated
during the protocol for phase 3.
Facilitator should do the
participant’s pre-work, paying
particular attention to crafting
conceptual misconceptions that a
large number of students will
experience in order to focus the
conversation during the protocol.
TBD
TBD
2
Questioning
and
Misconceptions
3
Practice
Math Intellectual Preparation Protocol: Overview
Phase #
Description
Phase 0 will begin with the coach and quickly become pre-work for the teacher
0 – Picking the Define the purpose of the unit
Name the focus for the lesson
Math
Select the problem
What students are thinking about
How students are thinking
Phase #
Description
Phases 1 and 2 should happen either in the meeting or as pre-work depending on the phase of facilitation/level of teacher proficiency.
Craft 2-3 possible solution pathways using multiple representations and strategies
1 – Depth &
Proficiency in
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
Draft focal questions to bring out key points
Identify misconceptions
Revise focal questions to draw out and address misconceptions
2 – Questioning
and
Misconceptions
Practice delivery
3 – Practice
Math Intellectual Preparation Protocol: Prompts & Resources
Phase #
Description
Prompts/Questions
Resources
Phase 0 will begin with the coach and quickly become pre-work for the teacher
Define the purpose of the unit
0
Picking the Math
Name the focus for the lesson
Select the problem
What students are thinking about
How students are thinking
Phase #
Description
What are the big ideas or concepts of the unit?
How will student comprehension of the enduring understandings be developed
in this unit?
How does this unit build on what students learned earlier in the year? In previous
grades?
How does this unit set students up for what comes next this year? Next year?
Which aims support or apply this concept (within this unit)?
Which content standards support or apply this concept?
Which focal SMP from the unit supports this concept?
Which concept(s) am I prioritizing developing during this lesson?
Select a problem that aligns to the prioritized math from steps 1 and 2
Do the problem as an initial check for alignment
How does the selection align to the prioritized math at this time in the unit?
(Aim(s) and concept(s) named?)
How are the selected content standards being addressed in this problem?
Does the selection address the content standards at the right level?
What are the opportunities for students to engage in the prioritized SMP?
To what extent does the problem provide opportunity for students to apply
additional standards of mathematical practice?
To what extent does the exercise or task meet the criteria defined in the FOI for
this lesson type?
Unit Plan
Prompts/Questions
Resources
Unit Plan
Resources named in FOI
Unit Plan
CC Standards
Document
FOI
CC Standards
Document
1
Depth & Proficiency in Content
Phases 1 and 2 should happen either in the meeting or as pre-work depending on the phase of facilitation/level of teacher proficiency.
Craft 2-3 possible solution pathways using
multiple representations and strategies
What are all the ways to approach the exercise/problem/task?
How would you approach this concretely? Pictorially? Abstractly?
Final check for alignment and revise as needed
Is the math selected the most natural way to approach the selected problem or a
natural build upon student understanding to culminate in new learning?
Which solution pathway most naturally addresses the underlying math concepts?
In what order should the alternate pathways be presented by students in order
to lead their classmates to understand the target pathway?
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
How does understanding each representation and strategy support the
understanding of the others and the math being applied?
Unit Plan and
Assessment, Engage NY
Materials, Progression
Documents, Source of
exercise or task,
colleagues/coach
See above
See above
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
Draft focal questions to bring out key points
2
Questions and Misconceptions
Identify misconceptions
3
Practice
Revise focal questions to draw out and address
misconceptions
In development
In kid friendly language, what are the key points (why, what and how)?
See above
What do students need to be considering in order to be ready to engage in the
logic of the concepts?
What sense making, reasoning and probing questions will support students in
thinking about and developing an understanding of the focal strategies,
representations, practices and concepts needed to tackle the problem?
What are the questions that get kids to consider the most important ideas while
preserving or pushing student thinking?
Grade level content misconceptions
What are the 1-2 misconceptions students will likely have that impede
comprehension?
How will you respond to each one?
Will you play out the misconception or fix it?
If played out, to what end?
If fixed, will it be for an individual, the whole group or a small group?
What do kids need to experience or see in order to change their logic/increase
their mathematical intuition?
Pre-requisite content knowledge gaps + misconceptions
What are the 1-2 pre-requisite knowledge and skill issues you are likely to see?
How will those prevent students from accessing the content?
Will you fix them beforehand or in the moment? Using:
Adjusting the entry point
Tools/manipulatives provided
Language
The exercise/problem/task
Student groupings
Do your initial focal questions provide an opportunity for misconceptions to
come to life and lead students through an experience that shift their thinking and
solidify their understanding?
What additional questions do you need incorporate to draw out and address
misconceptions in order to help students see the logic required to understand
the focal concepts?
AF Mathematics
Questioning Guide
NA
NA
“Transformative
Assessment in Action.”
James Popham.
Unit plan
Colleagues
Participant Note Taking Sheet
Phase 0: Picking the Math
Purpose of the Unit
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.
Builds on the following:
Sets students up for the following:
In 7th grade, students learn to recognize proportional
A solid understanding of proportional relationships and
relationships represented graphically, algebraically and unit rate grounds students’ understanding of rates of
In tabular form. Additionally, they learn to describe the change.
unit rate as the Constant of Proportionality and
understand that proportional relationships are
Throughout the rest of the unit on linear equations,
identified by a unit rate.
students will continue to apply rates of change to work
with graphs, tables and equations as well as systems of
Students build on a basic understanding of functions as equations. Additionally, when students learn about
a means of representing a relationship between two
bivariate data, they will apply their understanding of
quantities. They have also just engaged with finding
Rates of Change in order to understand trends and
and comparing rates of change given multiple
make predictions.
representations of these relationships (table, graph,
equation, and context) in the functions unit.
Eventually, in High School, students will build on their
understanding of rates of change as they apply them to
non-linear relationships using average rate of change,
which eventually facilitates meaningful engagement
with limits and derivatives
The Focus of the Lesson
Which aim(s) am I prioritizing?
Which content standard does this aim connect to?
SWBAT graph proportional relationships, interpreting the 8.EE.B – Understand the connections between
unit rate as the slope of the graph.
proportional relationships, lines and linear equations
SWBAT determine if a relationship is proportional.
8.EE.5 – Graph proportional relationships,
SWBAT compare two different proportional
interpreting the unit rate as the as the slope of the
relationships represented in different ways by
graph. Compare two different proportional
determining the unit/rate slope and graphing
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
Which focal SMP supports this concept?
Which concept(s) am I prioritizing during this lesson?
SMP1 – Make sense of problems and persevere in solving Rates of change communicate critical information
them
about a linear relationship.
SMP2 – Reason abstractly and quantitatively
SMP3 – Construct viable arguments and critique the
Rates of change are synonymous with unit rate for
reasoning of others
proportional relationships.
SMP4 – Model with mathematics
SMP6 – Attend to precision
Exercise or Task
Problem: Anna and Jason have summer jobs stuffing envelopes for two
Number of
Earnings
different companies. Anna earns $1.53 for every 17 envelops she finishes.
envelopes
Jason recorded his earnings in the table to the right. Who makes more from
11
$0.88
stuffing the same number of envelopes? How can you tell?
22
$1.76
33
$2.64
The What of the Problem
How does the problem align to the priority aims, standards, and concepts named above?
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,” and sets students up to understand the utility
of finding a unit rate for mathematical purposes and given the context. Also, students will have the opportunity
to make a connection between the slope and unit rate. The problem was tuned to incorporate multiple
representations so that it aligns fully to the 8th grade standard.
The How of the Problem
How are students applying the SMP(s) in this problem?
Students have to come up with a way of modeling the situation that allows for comparison. Whether that’s with
a graph, a table, equation, or with another method – they will be modeling and then constructing an argument
based on the conclusions they draw from their model. This process is how we are connecting to SMP 3 and 4.
While SMPs 1 and 2 are not a focus of the problem, the numbers were changed to increase the amount of
reasoning and sense making required of the students.
To what extent does the problem align to the FOI criteria?
The problem draws thinking towards the mathematics required, and we tweaked the problem in order to make
this math clearer. The problem is challenging, but relatively straight forward to interpret, and also requires
communication of a conclusion and the thinking behind that conclusion. The criteria that are more in the
background of this problem and not a clear focus are research, interpretation, precision and accuracy.
Criteria for Exercise
Criteria for Problem/Task
-
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 following Key Cognitive Strategies (Conley):
o Problem Formation: requires planning and use of reasoning
skills
o Research: lends itself to strategic selection and use of tools
o Interpretation: requires planning and use of reasoning skills;
requires understanding, identification and/or application of one
or more concepts and skills
o Communication: requires students to demonstrate evidence of
their thinking, fluency and conceptual understanding through
use of models, work shown and/or written explanations;
requires evidence to be provided and may require development
of logical argument for concepts or steps
o Precision & Accuracy: requires attention to appropriate rules of
precision when tending to work in written, oral, or symbolic
form
-
-
Draws thinking towards mathematics to be used and learned
Incorporates the following Key Cognitive Strategies (Conley):
o Problem Formation: requires planning and use of
reasoning skills
o Research: lends itself to strategic selection and use of tools
o Interpretation: requires planning and use of reasoning
skills; requires understanding, identification and/or
application of multiple concepts and skills
o Communication: requires students to demonstrate
evidence of their thinking, fluency and conceptual
understanding through use of models, work shown and/or
written explanations; requires evidence to be provided and
may require development of logical argument for concepts
o Precision & Accuracy: requires attention to appropriate
rules of precision when tending to work in written, oral, or
symbolic form
Non-routine and complex
Solution path is neither stated or obvious; may be multiple
solution paths; may be multiple solutions
Phase 1: Depth and Proficiency in Content
Craft 2-3 solution pathways using multiple representations and strategies
Scan and paste handwritten solution pathways.
** Check for natural alignment of exercise, problem or task to math focal points, and revise as needed
Prioritize and Order Pathways
Pathway 1
Pathway 2
Target Pathway
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
Why
What
How
Phase 2: Questioning and Misconceptions
What do students need to be considering in order to be ready to engage in the logic of the concepts?
What sense making, reasoning and probing questions will support students in thinking about and developing an understanding
of the focal strategies, representations, practices and concepts needed to tackle the exercise or task?
What are the questions that get kids to consider the most important ideas while preserving or pushing student thinking?
Questioning to Encourage Student Thinking
What questions will you ask to get students to:
Make sense of the problem?
Reason about the mathematical concepts being applied?
Reveal their depth of understanding?
Question
Type of Question
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Sense Making
Reasoning
Probing
Sense Making
Reasoning
Probing
Sense Making
Reasoning
Probing
Sense Making
Reasoning
Probing
Sense Making
Reasoning
Probing
Sense Making
Reasoning
Probing
Identifying Misconceptions
What are the key misconceptions that will obstruct student success?
Grade Level Content Misconceptions
What logic led to the misconception?
Teacher Response
Pre-requisite Misconceptions
What logic led to the misconception?
Teacher Response
** Revise focal questions to draw out and address misconceptions