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
Webinar Outline/Table of ContentsTime / Clip Information & Key Ideas
0:00 / Welcome and Introductions
0:26 / Try This
What Are Big Ideas?
2:45 / What are big ideas anyway?
6:18 / Big ideas are meant to…
9:00 / The three sessions
Big Ideas in Number
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
31:16 / Big Idea in Early Number 5
Big Ideas For Greater Whole Numbers
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
49:07 / Big Idea for Greater Whole Numbers 5
Which Big Idea?
51:27 -1:07:19 / Suppose…
1:08:32 / Closing Remarks
1:11:21 / 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. / Questions for Extended Learning Opportunities0:00 / Introductions, Welcome / · Introduce yourself
· Ask participants to introduce themselves
*Session handouts are available at
http://erlc.wikispaces.com/Big+Ideas+in+Math+K-3
0:26 / Try This / · 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 do you think is the importance of this activity?
What Are Big Ideas?
2:45 / What are big ideas anyway? / · 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 / Have participants share their answers with the larger group and share why they picked the answer they did.
6:18 / Big ideas are meant to… / · 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 / 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 / · 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
9:26 / The 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) / 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?
16:48 / Big Idea in Early Number 2 / 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.) / What forms of counting are addressed at your grade level? Be sure to check the Alberta Mathematics Program of Studies.
20:23 / Big Idea in Early Number 3 / 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) / What other activities might you create to help students understand this big idea?
26:01 / Big Idea in Early Number 4 / 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 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?
28:56 / Related / · Why is this a not-so-good bar
graph? / How might you adapt this example and share it with your students so that it addresses your grade level outcome(s)?
31:16 / Big Idea in Early Number 5 / 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? / If you changed the numbers in the example, what meaningful benchmark numbers do you think your students would use?
Big Ideas For Greater Whole Numbers
35:58 / Big Idea for Greater Whole Numbers 1 / 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 / What are some examples from everyday life where we create subgroups to count things?
39:27 / Big Idea for Greater Whole Numbers 2 / 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 / What outcome(s) at your grade level falls under this big idea?
45:25 / Big Idea for Greater Whole Numbers 3 / 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? / Think of another example similar to one presented that you could use with your students. What are some ways to represent the number?
48:29 / Big Idea for Greater Whole Numbers 4 / To compare and order numbers, we can compare them to more familiar benchmark numbers. (BIGWN 4)
· How does thinking of 138 and 173
in terms of 150 help you decide
which is greater? / What benchmark numbers would be familiar to your students? Create two examples using those benchmarks.
49:07 / Big Idea for Greater Whole Numbers 5 / 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?
51:27 / Suppose… / · I asked students how to solve 15¸3
Using multiplication, the addition,
then subtraction.
· What big idea might I be drawing
out? / Discuss this example and question with the larger group.
54:16 / Suppose… / · I asked students for three different
ways to solve 100-28.
What might they be?
· What big idea might I be drawing
out?
· No matter what computation you’re
doing, there is lots of ways to do it. / Discuss this example and questions with the larger group.
59:09 / Suppose… / · 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? / Discuss this example and questions with the larger group.
1:02:50 / Suppose… / · I asked students for three different
sums, that were close to, but not
exactly 90.
· What big idea might I be drawing
out? / Discuss this example and question with the larger group.
1:05:17 / Suppose… / · I asked students why this picture
actually shows three fractions.
What might they say?
· What big idea might I be drawing
out? / Discuss this example and questions with the larger group.
1:07:19 / Suppose… / · I asked how could 2/3 be less than
1/2?
What might they say?
· What big idea might I be drawing
out? / Discuss this example and questions with the larger group.
Closing Remarks
1:08:32 / Would you be willing to… / · Try out either one of the questions
we discussed or, even better, your
own question to bring out a big
idea in number.
1:09:47 / Website / www.onetwoinfinity.ca
1:11:21 / End of the webinar