Big Ideas in Mathematics for Grades K-3
With Dr. Marian Small
Session 1 of 3
(*Focus on number)
Overview of Learning Opportunity: In this recorded webinar you will explore
the following questions:
 What are the big ideas you should bring to students’ attention when
teaching Math (number) in Division 1?
 How do they link to curriculum?
 How do teachers ask those critical questions that help students see
those ideas?
You will examine the big ideas in all four math strands and samples of how
thinking about big ideas can help shape lessons will be shared.
This conversation guide is intended for Professional Learning Communities,
instructional leaders or as a self-paced study to help guide instruction,
conversations and reflections on the big ideas in Math in Division 1 (number).
*Please visit the following link to access the handouts for this session
http://erlc.wikispaces.com/Big+Ideas+in+Math+K-3
Time
0:00
0:26
2:45
6:18
9:00
9:26
16:48
20:23
26:01
31:16
35:58
Webinar Outline/Table of Contents
Clip Information & Key Ideas
Welcome and Introductions
Try This
What Are Big Ideas?
What are big ideas anyway?
Big ideas are meant to…
The three sessions
Big Ideas in Number
The Big Ideas in Number
Big Idea in Early Number 2
Big Idea in Early Number 3
Big Idea in Early Number 4
Big Idea in Early Number 5
Big Ideas For Greater Whole Numbers
Big Idea for Greater Whole Numbers 1
39:27
45:25
48:29
49:07
51:27 1:07:19
1:08:32
1:11:21
Big Idea for Greater Whole Numbers 2
Big Idea for Greater Whole Numbers 3
Big Idea for Greater Whole Numbers 4
Big Idea for Greater Whole Numbers 5
Which Big Idea?
Suppose…
Closing Remarks
End of the webinar
This “Conversation Guide” provides an overview of the webinar with ideas for
continuing the conversation as well as questions for extended learning. This
guide may also assist with self-paced study when viewing the archived webinar.
Time
Code
Clip
Clip Information, Key Points &
Suggested Activities to use this
Webinar for your own PD Sessions.
 Introduce yourself
 Ask participants to introduce
themselves
*Session handouts are available at
http://erlc.wikispaces.com/Big+Ideas+in
+Math+K-3
0:00
Introductions,
Welcome
0:26
Try This

2:45
What are big
ideas anyway?

6:18
Big ideas are
meant to…





You are going to write a number
the “regular” way, e.g. 34 or 2, etc.
When you read the number, some
of the words you say are: hundred,
three, fifty
What could the number be?
Record some possibilities
What Are Big Ideas?
Which of these do you think is a big
idea?
A: Writing a number less than 100
in words
B: Place Value
C: Recognizing that different
representations of a number give
you different understandings about
it
D: Recording the hundreds, tens,
and ones digit of a number
Help you as a teacher see what
you are really going for
Provide you with a teaching
framework – to see how outcomes
are connected
Give purpose to the activities you
do
Help build connections
Help students see what’s the most
– see the forest for the trees
Questions for Extended
Learning Opportunities
What do you think is the
importance of this activity?
Have participants share
their answers with the
larger group and share why
they picked the answer
they did.
How do/might the big ideas
guide you in planning your
units and lessons?
What are some ways you
could share big ideas with
students and parents so
that they are aware of what
is currently being focused
on?
9:00
The three
sessions
9:26
The Big Ideas
in Number
16:48
Big Idea in
Early Number 2
20:23
Big Idea in
Early Number 3
26:01
Big Idea in
Early Number 4


Session 1 – A focus on number
Session 2 – A focus on pattern and
data
 Session 3 – A focus on geometry
and measurement
Big Ideas in Number
A number tells us how many in a group.
You usually count to determine the size
of a group. (BIEN 1)
 Early number and operation
 How do we make kids see this?
 Count the dots activity
BUT
 Does a number always tell how
many? Give an example when it
doesn’t.
 Help students understand when a
number is a count and when it is not
(Ex. group of dots vs. house number)
Counting is fundamental to number.
Forms of counting include rote
counting, counting all, counting on, skip
counting, and counting back. (BIEN 2)
 Your hopping on a number line and
just saying the numbers you land
on.
You can start wherever you want
What number might you say right
before you land on 12 if you land
on 12?
A: 11 or 10
B: 11 or 10 or 9
C: 11 or 10 or 9 or 8 D: anything 12
 Help students understand that you
can count in a variety of ways (Ex.
forward, backward, skip count, etc.)
You can represent a number in a
variety of ways. Each representation of
a number can focus on a different
aspect of the number. (BIEN 3)
 You need to represent the number
7 in a lot of different ways.
Which ways are alike?
 Help students understand that
different representations of number
show you different things. What
does the picture show you what
doesn’t it show you? (Ex. the
picture with the green dots clearly
shows you that 7 is an odd number)
To compare the numbers of items in
two sets, you can match the items, one
to one, in the two sets to see whether
one set has more. Or, you can
What other activities could
you use with students to
help them understand this
big idea?
What other real world
examples can you come up
with to help students
understand the difference
between when a number is
a count and when it is not?
What forms of counting are
addressed at your grade
level? Be sure to check the
Alberta Mathematics
Program of Studies.
What other activities might
you create to help students
understand this big idea?
28:56
Related
31:16
Big Idea in
Early Number 5
35:58
Big Idea for
Greater Whole
Numbers 1
39:27
Big Idea for
Greater Whole
Numbers 2
45:25
Big Idea for
Greater Whole
Numbers 3
48:29
Big Idea for
Greater Whole
Numbers 4
compare the position of the numbers
that describe the two quantities in the
number sequence (BIEN 4)
 How could you tell whether my
name has more letters in it than
yours if you could NOT count the
letters?
How could you tell if you could
count?
 Why is this a not-so-good bar
graph?
Students gain a sense of the size of
number by comparing them to
meaningful benchmark numbers. (BIEN
5)
 How do you know FOR SURE that
13 is more than 9?
What other number would be easy
to compare the same way?
Big Ideas For Greater Whole
Numbers
A number tells how many are in a
group. To count the number in a group,
we often create subgroups and count
the number of subgroups. (BIGWN 1)
 Which of these would you find
easier to count? Why?
A (first group) or B (second group)
Group A - dots are scattered
Group B - dots are organized
 If you create subgroups well, it will
be much easier to count
The place value system we use is built
on patterns to make our work with
numbers more efficient. (BIGWN 2)
 Have you seen a question that
brings out this big idea?
 You can show a number with 12
base ten blocks. What could it be?
93, 84, 75, 66, 57, 48, 39, 13, 21, 30
You can represent a number in a
variety of ways. Each representation of
a number can focus on a different
aspect of the number. (BIGWN 3)
 How could you represent175 to
show that:
It is 7 groups of 25?
It is 25 short of 200?
It is 17 tens and 5 more?
To compare and order numbers, we
can compare them to more familiar
benchmark numbers. (BIGWN 4)
 How does thinking of 138 and 173
How might you adapt this
example and share it with
your students so that it
addresses your grade level
outcome(s)?
If you changed the
numbers in the example,
what meaningful
benchmark numbers do
you think your students
would use?
What are some examples
from everyday life where
we create subgroups to
count things?
What outcome(s) at your
grade level falls under this
big idea?
Think of another example
similar to one presented
that you could use with
your students. What are
some ways to represent the
number?
What benchmark numbers
would be familiar to your
students? Create two
examples using those
49:07
Big Idea for
Greater Whole
Numbers 5
51:27
Suppose…
54:16
Suppose…
in terms of 150 help you decide
which is greater?
Students gain a sense of the size of
numbers by comparing them to
meaningful benchmark numbers.
(BIGWN 5)
 A number is about 300. What might
it be?
A: 295
B: 278
C: 328
D: all of the above
What do you think it couldn’t be?
Which Big Idea?
 I asked students how to solve 153
Using multiplication, the addition,
then subtraction.
 What big idea might I be drawing
out?
benchmarks.

Discuss this example and
questions with the larger
group.

59:09
Suppose…

No matter what computation you’re
doing, there is lots of ways to do it.

I asked students for three
situations to which 50-28 applied,
but they all had to sound really
different.
What might they be?
What big idea might I be drawing
out?
I asked students for three different
sums, that were close to, but not
exactly 90.
What big idea might I be drawing
out?
I asked students why this picture
actually shows three fractions.
What might they say?
What big idea might I be drawing
out?
I asked how could 2/3 be less than
1/2?
What might they say?
What big idea might I be drawing
out?
Closing Remarks
Try out either one of the questions
we discussed or, even better, your
own question to bring out a big
idea in number.

1:02:50
Suppose…


1:05:17
Suppose…


1:07:19
Suppose…
I asked students for three different
ways to solve 100-28.
What might they be?
What big idea might I be drawing
out?


1:08:32
Would you be
willing to…

1:09:47
Website
www.onetwoinfinity.ca
Discuss this example and
question with the larger
group.
Discuss this example and
questions with the larger
group.
Discuss this example and
question with the larger
group.
Discuss this example and
questions with the larger
group.
Discuss this example and
questions with the larger
group.
1:11:21
End of the webinar