Transcript January 5, 2011 Cypher IV K-3 Session 2

Cypher IV Math Leadership
Project
K-3 - Session 2 Developing Early
Number Concepts and
Number Sense
(Re) Introductions
Paula
Bernadette
Cathy
Kathryn
Kim
Shari
Tammy
Tina
Kathleen
Jenna
Nita
Dana
Homework Review (Small Group)
 Discuss
group
 What
in a small
have you tried in
your classroom as a
result of the last
session?
 What role did you play
in the teaching and
learning of math?
 What role did the
students play in their
learning?
 What
discoveries did
you and your students
make?
 What misconceptions, if
any, surfaced about the
topic? How did you
redirect the students?
 What suggestions do
you have for others
when they try this?
Objectives
Focus
on the Big Ideas of early number
concepts
Examine counting on and counting back
Discover the four key number relationships
for numbers from 1 to 10
Discuss relationships for numbers up to
100
Number Sense (Partner)
Discuss
What
with a partner
does it mean for a student to have a good
sense of intuition of numbers?
What implications does teaching to encourage
number sense have on how we work with
students and what we emphasize in our
classrooms?
Rejoin
the large group in 10 minutes. If
time permits, you may be asked to share.
Big Ideas (Small Group)
Read
the Big Ideas for this chapter (p.
37).
Share an example from your teaching that
illustrates the Big Ideas with your small
group.
I will ask each small group to share one of
their examples with the whole group.
Rejoin the large group in 5 minutes.
Counting On & Counting Back
(Large Group)
A
number card from my pile of 20 is chosen.
Beginning with the next player in the list,
players count backwards down the list until one
of the players says zero.
The player who says zero takes a counter and
puts it near their name on the whiteboard.
I will choose another number card.
Play continues until someone has three
counters. (The score board is on the next slide.)
As a large group, we will discuss our findings.
Points
Paula
Bernadette
Cathy
Kathryn
Kim
Shari
Tammy
Tina
Kathleen
Jenna
Nita
Dana
Counting On & Counting Back
A
different way to play the game is to count on.
Instead of counting back from the number,
players count up too the highest number in the
number cards. (In this case, it is 20. For
younger students, teachers may choose to have
the cards go up to 10.) The player who reaches
that number takes a counter and play continues
until someone has three counters.
Any further comments?
Spatial Relationships
Teaching
Student-Centered Mathematics
states, “Children can learn to recognize
sets of objects in patterned arrangements
and tell how many without counting” (p. 42).
I
am going to quickly flash a ten-frame on the
screen for about half a second.
Say the number that you saw out loud.
Spatial Relationships (cont’d)
Say
QuickTime™ and a
decompressor
are needed to see this picture.
the number
you saw out loud.
Spatial Relationships (cont’d)
QuickTime™ and a
decompressor
are needed to see this picture.
Say
the number
you saw out loud.
Spatial Relationships (cont’d)
10-frames
are useful for meeting the
needs of visual learners who need to
“see” the mathematics.
One & Two More, One & Two Less
These
relationships involve more than just the
ability to count on 2 or back 2. Children should
know that 7, for example, is 1 more than 6 and
also 2 less than 9. Such relationships are
essential for working with the early numbers,
and later, for relating to numbers from 10 to
20. To explore this relationship, we will try an
activity similar to Activity 2.11, Make a TwoMore-Than Set (p. 45).
Make a Two-More-Than Set
Construct
a set of
counters that is
two more than:




Make a Two-Less-Than Set
Construct
a set of
counters that is
two less than the
card shown:




Anchoring Numbers to 5 & 10
The
numbers 5 & 10 can be used as
anchors. They are especially useful
when thinking about combinations of
numbers. A key model to use with
students to illustrate these
relationships is the 10-frame.
Anchoring #s to 5 & 10 (cont’d)
Here
is a ten frame. To build the 7-frame:
Always
fill the top row first, starting on the
left - the same way that you read.
When the top row is full, counters can be
placed in the bottom row, also starting on the
left.
Anchoring #s to 5 & 10 (cont’d)
 Build
8
 Share
what you know about the number 8 from
looking at the ten-frame.
 How could you use ten-frames to help students
develop 5 & 10 benchmark relationships?
Part-Part-Whole Relationships
(Small Groups)
Think
about the number 8 divided into two
different amounts. By using manipulatives
or drawing a picture, show how eight things
can be shown as two parts. Invent a story
to go with your picture or display.
With your group, share how you arranged
your materials into different parts.
Rejoin the large group in 10 minutes.
Dot Cards
 There
are many activities that will help students
develop their number sense. Activities can involve
more than 1 of the relationships discussed in this
chapter. Dot cards can be used for activities. Dot
cards display:
instantly recognizable patterns,
 patterns that require counting,
combinations of 2 & 3 simple patterns,
10-frames with standard placements of dots, &
10-frames with unusual placements of dots.
Dot Cards (4 Small Groups)
 Divide
yourselves into four small groups. Group 1:
Activity 2.22, Double War (p. 53), Group 2:
Activity 2.23, Dot-Card Trains (p. 53), Group 3:
Activity 2.24, Difference War (p. 53), Group 4:
Activity 2.25, Number Sandwiches (p. 53)
What number relationships are being
addressed? What extensions could be made in
the classroom? Other ideas for using the dot
cards? Prepared to share, rejoin the large
group in 10 min.
Numbers to 100
Look
for patterns in the hundreds
chart.
Let’s share the patterns with the
large group to emphasize the wide
variety of patterns that can be found.
After
What
does it mean for a student to have a
good sense or intuition of numbers?
What implications does teaching to
encourage number sense have on how we
work with students and what we emphasize
in our classrooms?
Did anyone experience any Ah-ha moments?
Are there any points that need to be shared?
Homework
Try
a variety of activities from the
chapter with your students and be
ready to share your experiences with
the group at the next session.
Read Chapter 3, Developing Meaning
for the Operations and Solving Story
Problems (pp. 65-93).