Welcome to
Number Sense K-2
Region 11Math and Science Center
Barb Abramson & Anne Bartel
Step In – Step Out
 Form a large circle around all the tables and face each
other.
 Step to the inside of the circle if the statement is true
for you.
Step In – Step Out
 I went to the MN Renaissance Fair this year.
 I drove more than 30 miles this morning to get
here.
 I got up before 5 AM this morning.
 I teach 1st grade / 2nd grade / 3rd grade
 I know what CGI in math education stands for.
 I like teaching math better than reading
Agenda & Parking Lot
Housekeeping Details
 Timeframe
 Lunch
 Restrooms
 Wi-fi access
 Sign-in
 Norms
 “Misery is optional”
Region 11 Math & Science
 Funded since 2007
 Focus on 3-5 and 6-8
 Focus this year on K-2: Number Sense
with 450-500 teachers
 Registration Concerns
 Folder Contents
This Year’s Goal
 Give teachers the time and opportunity to learn
how students think about math…
 …in an incremental, job-embedded, and
ongoing structure…
 …with support
 Good news and good news
Teacher Assessment
 Anonymous – we don’t want to know who
you are
 Code: Birthdate and first letter of your
last name
 E.g., 0 4 1 5 4 8 B
Take a Break
Beloved Child
 Work in groups of 3
 Think – Pair – Share
 What do you want for the child/children who
is/are most important to you?
 In 20 years, what do you want these children
to say about their memories of math?
Our Goals
 All children motivated to learn challenging
mathematics
 All children expecting math to make sense –
and expecting to understand it and use it
 All children able to explain and defend their
mathematical thinking
 All children pattern-seekers & connectionmakers
5 Practices
Choose the problem; then…
1. Anticipate
2. Monitor
3. Select
4. Sequence
5. Connect
Lunch – OK to bring it back
Cognitively Guided Instruction
 Most children come to school with a rich store of
informal mathematical knowledge.
 We (and they) are more successful if we
understand how they think about numbers and we
can build on that knowledge.
 Children do not always think about mathematics in
the same way as adults do.
From a ‘13-’14 teacher
 “I have always known that it was
important to listen to kids, but I never
knew what questions to ask or what to
listen for before now.”
JOIN Problem
 Riley has 5 cookies. Seth gives him 3 more cookies.
START + CHANGE = RESULT
5+3=?
5+?=8
?+3=8
SEPARATE Problem
 Wes has some bagels. Stella eats three of the bagels.
Now Wes has five bagels.
START – CHANGE = RESULT
?–3=5
8–3=?
8–?=5
PART-PART WHOLE
 There are five boys and three girls on the soccer team.
How many players are on the team?
PART + PART = WHOLE
5+3=?
?+3=8
or
5+?= 8
COMPARE Problem
 Gracie has 5 bones. Veronica has three more bones
than Gracie. How many bones does Veronica have?
Gracie:
Veronica:
COMPARE Problems
 Gracie has five bones. Veronica has three more bones than
Gracie. How many bones does Veronica have?
 (We don’t know the compare quantity.)
 Gracie has five bones. Veronica has eight bones. How many
more bones does Veronica have?
 (We don’t know the difference.)
•
Gracie has some bones. Veronica has three more than
Gracie. Veronica has eight bones. How many bones does
Gracie have?
 (We don’t know the referent quantity.)
COMPA PART
RE
PART
WHOLE
SEPAR- JOIN
ATE
Classification
JOIN
(result unknown)
JOIN
(change unknown)
JOIN
(start unknown)
SEPARATE
(result unknown)
SEPARATE
(change unknown)
SEPARATE
(start unknown)
PART-PART WHOLE PART-PART WHOLE PART-PART WHOLE
(whole unknown)
(part unknown)
(both parts unknown)
COMPARE
COMPARE
(difference unknown) (quantity unknown)
COMPARE
(referent quantity
unknown)
Problem Types Task
 Categorize each word problem –
 What type of problem is it?
 Where would it fit in the template?
 Use any resource available in your handout
or at your table.
 THIS IS NOT A TEST 
Handout, p. 5
 One way to write grade appropriate word
problems is to either…
 Choose appropriate numbers
 Have students choose appropriate numbers
Student Strategies
 Direct Modeling
 Counting
 Derived Fact* / Recall
8+5=?
Direct Modeling
 Counts out 8
 Counts out 5
 Counts total from the beginning: “1, 2, ….13”
Direct Modeling
 You can’t be a direct modeler unless you can
count
 These students use fingers or cubes or some
material to model exactly what they are hearing
in the problem; then they go back and count all
to get an answer.
8+5=?
Counting
 Says or thinks 8
 Counts on: “8…9, 10, 11, 12, 13”
Counting
 If students are counting on their fingers, they might be direct
modelers or counters. It depends on how they use their
fingers. In direct modeling, those fingers represent cookies
and kids are more successful when the numbers are less
than 10. In counting, those fingers represent numbers in the
counting sequence.
 Kids who are counters are able to hold onto the fact that 8
ones are also one group of 8 at the same time; this is what
allows them to hold onto the 8 in their minds.
 This is much more complicated because you have to hold
onto two counting sequences (e.g., I’m seeing one finger but
counting “9”)
8+5=?
Derived Fact / Recall
 Says “13” or uses relationships between the
numbers to find the solution
 Example:
•
8+5
8 + (2 + 3)
(8 + 2) + 3
10 + 3
13
How else might you solve this using a derived
fact?
Derived Facts / Recall
 Fact Recall is our ultimate goal, but we don’t want to
get their by sacrificing understanding.
 If students can derive the answers to facts fluently, they
have a good beginning number sense.
Elbow Partners
 Person A: Teacher
 Person B: Student
 Use handout pages 7-9
 The teacher selects one of the problems, creates a word
problem, and asks the student to solve it;
 The student solves it, using one of the strategies;
 The teacher identifies the strategy used;
 Discuss, especially if there is a difference of opinion.
Debrief Strategies
 These strategies are not always distinct.
 Some kids waver as they move from direct modeling to
counting.
 Some kids move back to less sophisticated strategies
when the numbers increase in size.
 Some kids might look less sophisticated because they
think you want to see their work, but when you ask
them to tell you what they really did, they use a more
sophisticated strategy.
Teaching Issues
 How do we encourage students to use more
sophisticated strategies?
 How do we help students who are stuck at
counting?
How Children Learn Number
Concepts
 Form groups of 3
 Read pages 43-47
 Find 3 statements that speak to your
experience or make you wonder about
something.
 Discuss: Take turns sharing your statements
and general reactions to the author’s
comments.
Why do Number Talks?
 Reinforces number sense
 Reinforces fluency
 Reinforces composing and decomposing
numbers
 Reinforces subitizing
 Discourages counting
 Communicates that math is about ‘making
sense’
What is a Number Talk?
 Short, daily routine
 Teacher presents intentionally selected
problems
 Students are not pressured to see things they
don’t see or use language they don’t
understand
 Students learn from others, but only if the
explanations of other students make sense to
them
Elements of a Number Talk
 A safe environment
 Problems of various levels of difficulty
 Concrete Models
 Interaction
 Self-correction
Problems can Include…
 Dot Cards
 Ten Frames
 Other Visual Images
 Towers of Unifix Cubes
 Written problems
Teacher’s Role
 Set a goal; select appropriate problems
 Facilitate the discussion
 Listen carefully to student thinking; record it if
appropriate
 Build connections among student strategies
 Limit time (5-10 minutes)
Adult Number Talk
Adult Number Talk
197 + 395
Resources
 Number Talks by Sherry Parrish
(See your PLC Facilitator)
 Math Perspectives
Websitehttp://www.mathperspectives.com/
 Search the Internet for Number Talks
PLC Calendar
 Day 1: Number Sense  3 PLC Meetings
 Day 2: Addition  3 PLC Meetings
 Day 3: Subtraction  3 PLC Meetings
 Day 4: Multiplication/Division  3 PLC
Meetings
 Day 5: Place Value
Professional Reading – articles & books
Developing Mental Math Number Talks
Developing Word Problems
How to fit with curriculum & District
Initiatives
3 PLCs
Classroom Conversation #1
 Use Region 11 word problem sets
 Use dot cards, strings of related
equations, own word problems
Interview
 Work with 2 students, individually or as
a pair
 Possibly follow same 2 students all
year
Classroom Conversation #2
 Use Region 11 word problem sets
 Use dot cards, strings of related
equations, own word problems
Artifacts
 Teacher notes, photos, or videos from a verbal
discussion, students acting out problems, or
using manipulatives
 Chart paper, photo or video showing a record
of student thinking & strategies
 Written student work
Adults learn best not merely by
listening, reading or doing but by
reflecting on what they hear, read or
do.
York-Barr, Sommers, Ghere, Montie. Reflective Practice to Improve
Schools: An Action Guide for Educators. Thousand Oaks, CA: Corwin
Press. 2001.
Thank You!
 For leaving your students
 For participating in today’s work
 For cooperating with your tablemates
 For asking questions
 For following the norms
 For all the work you do for students
CAPS Exit Slip
C: Something that CONFIRMS my
thinking . . .
A: A question that was ANSWERED . . .
P: I am still PONDERING . . .
S: Something that SURPRISED me . . .
And…any other feedback you would be
willing to share with us.