Day 1

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Professional Learning for Mathematics Leaders and
CoachesNot just a 3-part series
Day 1
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Whats important about the Math we Teach?A Focus
on Big Ideas
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Minds-On
A linear growing pattern starts at -10 and
grows very slowly. What might the pattern be?
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Minds-On
How could you convince someone the pattern
grows slowly?
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Characteristics of Minds-On
How does this minds-on engage students? How
is it open?
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What is the important math?
What do you think the important underlying math
idea is?
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The minds-on might lead to students being able to
respond to
What makes a pattern linear is
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Or
It makes sense that there are a lot of linear
patterns that start with the same term
because Context matters in deciding how fast a
pattern grows because
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What are Big Ideas?
Randy Charles A Big Idea is a statement of an
idea that is central to the learning of
mathematics,
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Marian Small .one that connects numerous
mathematical understandings into a coherent
whole.
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Big Idea
NOT a topic name nor an overall expectation.
BUT a statement that describes a fundamental
mathematical connection.
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It provides a lens in which to embed new
learning.
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Big Ideas for pattern algebra
A set of big ideas for patterns and algebra are
listed in the program booklet youve received.
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Big Ideas for pattern algebra
Have a look at those ideas. Notice that our
minds-on activity relates to both BI 1 and BI
5.
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Getting a feel for the big ideas
Two sets of questions will be circulated that
are designed to bring out the big ideas.
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Getting a feel for the big ideas
Choose one of those sets of questions. Match
each question to the big idea it is most likely
to elicit.
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Some questions about your task
Which big idea did you find easiest to match
first? Which did you find hardest to match
first?
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Some questions about your task
Which of the questions did you like best?
Why? What do you notice about the question
styles?
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Some questions about your task
Why do you think its important that students
know that pattern rules need to be defined? (Big
Idea 1)
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Some questions about your task
Can you think of other instances where number,
geometry, measurement or data topics are taught
using pattern concepts? (BI 2)
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Some questions about your task
How do the questions that matched Big Idea 3
show the notion of generalization? Analyzing
relationships or change?
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Some questions about your task
How could the questions that matched Big Idea 4
broaden a students understanding of the value of
multiple representations?
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Some questions about your task
How could the questions that matched Big Idea 5
help broaden students ideas of what kinds of
relationships there are?
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Some questions about your task
Why do you think Big Idea 6 is a valuable one
for student focus?
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You just experienced
a parallel task. We will talk more about these,
but these two very related tasks were adjusted to
meet your needs but treated together in our
consolidation.
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Why use big ideas?
By thinking about the big ideas, it becomes
easier to develop appropriate lesson goals and
appropriate consolidating questions to bring them
out.
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For example..

• If you are thinking about the Big Idea
  Comparing patterns reveals classes of patterns.

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For example..

• You are likely to ask Which two of these
  patterns do you think are most alike and why
• 5, 8, 11, 14, 17, 20,
• 5, 10, 20, 40, 80,..
• 5, 10, 15, 20, 25,..
• 5, 20, 35, 50, ?

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For example..

• rather than simply asking for a definition of a
  linear growing pattern.

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Sharing big ideas with students..
makes it easier for them to make connections to
prior knowledge and to move forward in new
directions.
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Building lesson goals
You can use a big idea to hone in on an
appropriate lesson goal.
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Relationship among Expectations, Big Ideas, Goals
Topic
Big Ideas
Expectations
Goals
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Relationship among Expectations, Big Ideas, Goals
Sometimes you can reframe the big ideas for your
topic. For example, a trig big idea might be
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Relationship among Expectations, Big Ideas, Goals
Limited information about a periodic relationship
can sometimes, but not always, reveal other
information about that relationship.
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Or..
When a relationship appears to be periodic in
nature, then it is appropriate to consider a
trigonometric function to model the relationship.
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Relationship among Expectations, Big Ideas, Goals
We will use the Posing Powerful Questions
Template (PPQT) as a tool.
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For example

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What big idea?
Most likely BI 4
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List the big idea

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Create an appropriate goal

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What does this mean for consolidating the lesson?
You need to ask a question or two that gets
RIGHT to your goal.
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So a consolidation question might be
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Or.
Consider the expectation Solve first degree
equations with non-fractional coefficients using
a variety of tools (e.g. 2x 7 6x 1)..
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For example
Which big idea do you think it most closely
relates to?
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For example
You might have picked BI 4 thinking that
solving an equation means representing it in a
different, easier to recognize. form.
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For example
You might have picked BI 6 thinking that you
had some information that could give you other
information.
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For example
You might have picked BI 3 thinking that an
equation is a way to describe a change and
solving it is just about undoing the change.
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What could be the lesson goal
Your lesson goal should be informed by which of
those ideas you want to focus on.
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Option 1
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To clarify..
These equations are equivalent X 4 2x 7
1 3x 7 x 15
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What I mean
But its sure easier to see the unknown value in
one of them.
These equations are equivalent X 4 2x 7
1 3x 7 x 15
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Option 1
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Option 2
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Option 2
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Option 3
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Option 3
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Its so important
Getting a goal clear in your own mind can make
a big difference in increasing the likelihood
that students will learn what you hope they will
learn.
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That includes knowing why you have that goal.
--- Whats the point of it?
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Why you want to do this
If you decide on the goal, you are more likely
to know what questions to ask, what activity to
use,.
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Make it yours
Even if you get a lesson from a valued
resource, you have to make your OWN decision
about what to pull out of that lesson.
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For example
Lets look at this lesson from Grade 7 TIPS.
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For example
Stated goals
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If this were the goal..
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Maybe
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Here are several goals
The following stated goals were taken from a
series of lessons on linear relations in a grade
9 text.
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Represent a relation using a table of values, a
graph or an equation Identify direct and
partial variations Identify properties of
linear relations
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Represent a linear relation in a different
form Recognize whether a relation is linear or
nonlinear
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Im hoping that you will
With a partner, choose 1 or 2 of these
goals. Focus them to relate more explicitly to
one or more of the big ideas.
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Consolidating questions
We talked earlier about how consolidating
questions should tie to lesson goals. They
should tell you if your goal was achieved.
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If
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If
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Or
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Or
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Now..
Choose a lesson in the resource you brought.
Work with a partner to restate the goal to focus
more on a big idea.
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Now..
Write consolidating questions to match your goal.
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Now..
Use the PPQT to record all of your thinking.
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Lets consolidate
Walk over to someone youve not talked to
before.
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Lets consolidate
Share one idea that came up that reinforces
what you already do when creating lesson goals.
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Lets consolidate
Offer one idea that came up that might change
how you create lesson goals.
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