Day 2: Number Sense
Addition
R e g i o n 11 M a t h a n d S c i e n c e
T E A C H E R PA R T N E R S H I P
Agenda
 Reflections/Introductions
 Goals/Standards
 Visualizing Numbers using Quick Images
 Problem Types and Strategies Review
 Defining Number Sense
 What is the Rekenrek?
 Number Talks using Rekenreks
 Tens Frames
 Decomposing/Composing Numbers
 Number Talks Supporting Derived Facts
 Making 10
 Closure
 PLC Information
Reflect and Share
Be prepared to share out
1 insight and 1 question
from each group.
 What has happened with
your students since our
last session?
 New insights?
 What unanswered
questions are there?
Housekeeping Details
● Timeframe
● Lunch
● Restrooms
● Wi-fi access
● “Misery is optional”
Goals
Goals
Pg. 1
 I can use ten-frames and Rekenreks to
carry out number talks with my students
 I can help my students compose and
decompose numbers
 I can describe several strategies that
children use to derive addition facts
 I can describe the pre-requisite strategies
that children need to use a “make ten”
strategy when adding whole numbers.
Kindergarten Standards
Pg. 1
K.1.2
Use object and pictures to represent
situations involving combining and
separating.
K.1.2.1 Use objects and draw pictures to find the sums and
differences of numbers between 0 and 10.
K.1.2.2 Compose and decompose numbers up to 10 with
objects and pictures.
Grade 1 Standards
Pg. 1
1.1.2
1.2.2
Use a variety of models and
strategies to solve addition and
subtraction problems in realworld and mathematical
contexts.
Use number sentences involving
addition and subtraction basic facts to
represent and solve real-world and
mathematical problems; create realworld situations corresponding to
number sentences.
1.1.2.1 Use words, pictures, objects,
length-based models (connecting
cubes), numerals and number lines to
model and solve addition and
subtraction problems in part-parttotal, adding to, taking away from and
comparing situations.
1.2.2.1 Represent real-world situations
involving addition and subtraction basic
facts, using objects and number
sentences.
1.1.2.2 Compose and decompose
numbers up to 12 with an emphasis on
making ten.
1.2.2.2 Determine if equations
involving addition and subtraction are
true.
Grade 2 Standards
2.1.2
Pg. 1
2.2.2
Demonstrate mastery of addition
and subtraction basic facts; add
and subtract one- and two-digit
numbers in real-world and
mathematical problems
Use number sentences involving
addition, subtraction and unknowns to
represent and solve real-world and
mathematical problems; create realworld situations corresponding to
number sentences.
2.1.2.1 Use strategies to generate addition
and subtraction facts including making tens,
fact families, doubles plus or minus one,
counting on, counting back, and the
commutative and associative properties. Use
the relationship between addition and
subtraction to generate basic facts.
2.2.2.1 Understand how to interpret number
sentences involving addition, subtraction and
unknowns represented by letters. Use objects
and number lines and create real-world
situations to represent number sentences.
2.1.2.2 Demonstrate fluency with basic
addition facts and related subtraction facts.
2.2.2.2 Use number sentences involving
addition, subtraction, and unknowns to
represent given problem situations. Use
number sense and properties of addition and
subtraction to find values for the unknowns
that make the number sentences true.
Reflection on MN Standards
Pg. 1
 What do you see developing
across grade levels?
 What new ideas seem to
appear at a particular grade
level?
Quick Image #1
Quick Image #2
Prep for Quick Image #3
Quick Image #3
Quick Image #4
Quick Image #5
Classification of Problem Types
JOIN
JOIN
(result unknown)
SEPARATE SEPARATE
(result unknown)
JOIN
(change unknown)
JOIN
(start unknown)
SEPARATE
(change unknown)
SEPARATE
(start unknown)
PART-PART
WHOLE
(both parts
unknown)
PART
PART
WHOLE
PART-PART WHOLE
(whole unknown)
PART-PART
WHOLE
(part unknown)
COMPARE
COMPARE
(difference unknown)
COMPARE
COMPARE
(quantity unknown) (referent
unknown)
Problem Types and Strategies
Pg. 3
What is the Problem Type?
How many children are in the class? There are 7 boys and 8
girls in Ms. Weil’s class.
Write an example of how this could be solved
using each strategy below.
a) Direct Modeling
a)
Counting On
a)
Derived Facts (Number Sense)/Recall
Problem Types and Strategies
Pg. 4
What is the Problem Type?
Monica has 7 carrots. Abdi gives her some more carrots,
now Monica has 13 carrots.
How many carrots did Abdi give Monica?
Write an example of how this could be solved
using each strategy below.
a) Direct Modeling
a)
Counting On
a)
Derived Facts (Number Sense)/Recall
Problem Types & Strategies
Pg. 5
Write a separate (result unknown) for the
number sentence 14-8=?
Write an example of how this could be solved
using each strategy below.
a) Direct Modeling
a) Counting On
a) Derived Facts (Number Sense)/Recall
10 Minute Break
Jo Boaler
Math Professor, Stanford University
 Jo Boaler video (How to Learn
Math, session 5.1, YouTube)
So, what is
Number Sense
anyway?
Jo Boaler on Number Sense
5 Minute Reflection on Video
At your table, define number sense.
 What did the video make you think more deeply
about?
What kinds of activities and experiences build
number sense?
A few Key Ideas with Rekenreks
 Show with “just one push” as students gain
experience with the Rekenrek.
 “Clear the space.”
 Store on right. Show on left.
Rekenreks
 Mathrack.com School Purchasing
 Math Learning Center Online Rekenrek
Pg. 6
5 Minute Number Talk
I saw 7.
How did
you see
them?
45 Minute Lunch
Video using a Rekenrek in a Number Talk
Number Talks K.2 Rekenreks
• Composing &
Decomposing Number
multiple ways
• Guess My Way game
Pg. 7
Video reflection
Pg. 7
1.
How does the Rekenrek warm-up with 4 and 6 provide
the teacher with information to guide her instructional
decisions?
1.
When does the teacher tell or show information to
students and when does she provide opportunities for
them to make sense of the mathematics?

2.
How is this similar to or different than your math instruction?
Are there number combinations that seem more
accessible to the students? How does the teacher build
on this foundation?
Your Turn
Practicing with Rekenreks
1. Letter and number off.
2. Go off with “like letters” and plan your 5
Minute Rekenrek number talk.
5 Minute Number Talk Rotations
Return to your Number Group space.
Timer
Key Components of a Number Talk
 Talk in your Groups. Write down a few key
components you don’t want to forget.
Pg. 8
Four Procedures and Expectations Essential
to Number Talks
(from Number Talks by Sherry Parrish)
Pg. 8
 Select a designated location that allows you to
maintain close proximity to your students for
informal observations and interactions.
 Provide appropriate wait time for the majority of
students to access the problem.
 Accept, respect, and consider all answers.
 Encourage student communication throughout the
number talk.
Some Large-Sized
Rekenreks
10
Rows of 10
Tens Frames
Pg. 9
 Math Learning Center Online Tens Frames
Kindergarten Number Talk: A
Kindergarten Number Talk: B
Kindergarten Number Talk: C
Grade 1 Number Talk: A
Grade 1 Number Talk: B
Grade 1 Number Talk: C
Rekenreks or Ten-Frames?
Compare and Contrast these tools in how they support
students learning to compose and decompose
numbers.
10 Minute Break
Grade 2 Number Talk:
Making 10s Using Number Sentences
8+2
8+5
Teacher Goal: Making Tens
Anticipate what students will
share.
Show sentences one at a time.
8+4
8+7
Plan how you will record their
thinking.
Grade 2 Number Talk: Looking for Landmark or
Friendly Numbers Using Number Sentences
40+4
39+4
39+15
39+39
Teacher Goal: Looking for
Landmark or Friendly
Numbers
Anticipate what students will
share.
Show sentences one at a time.
Plan how you will record their
thinking.
Composing and Decomposing Using a
Tens Frame
Pg. 12
Video: Number Talk
Pg. 14
Number Talks 2.1 Adding Numbers
 What do you notice about the teacher’s
recordings of student thinking?
 What else do you want to remember?
Planning a 5 Minute Number Talk
 Use the Critical Learning
Phases on pp.43-71 for ideas.
 What Math Talk would you
craft for your students, using a
single or double ten-frame,
Rekenrek, or number
sentences?
Pg. 15
Bring each time
Planning a 5 Minute Number Talk
Use the same groups as earlier.
Using pg. 13…
 Draw a picture of what you
would show to your students.
 Brainstorm a series of
questions you want to ask.
 Predict number sentences you
think will come up.
Pg. 13
5 Minute Number Talk Rotations
Return to your Number Group space.
Timer
“Make-a-10” for Addition Strategy
Pg. 16
3 Pre-requisites to use a make-a-ten
strategy effectively
They must…
1. Know what 2-digit number combinations equal
10 (e.g. 9+1, 8+2, etc.)
2. Be able to break numbers apart into any of its two
addends (e.g. 8=5+3 so that when they do 8+7
they can then do 5+3+7=5+10=15)
3. Know 10+single digits and beyond (e.g. 10+7=17)
(from Fuson Ch. 6 in Research Companion pg. 74)
Free Apps
http://www.mathlearningcenter.org/
•Rekenreks
•Ten Frames
•Number Lines
Math Learning Center
=>Bridges=>Resources=>Free Apps
2 Resources to Pick Up
1. CEU sheet
1. Classroom
Conversation A
Handout for PLC
Meeting 1
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
3 PLCs
#1. Classroom Conversation A
● Handout
● Use dot cards or own word problems
#2. Interview
● Will be posted online in Region 11 folder. Work with 2
students, individually or as a pair
● You might want to interview the same 2 students from last
time if wanting to follow them all year.
#3. Classroom Conversation B
● Will be posted online in Region 11 folder.
Bring Artifacts to PLCs
● 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
Goals
Goals
Pg. 1
 I can use ten-frames and Rekenreks to
carry out number talks with my students
 I can help my students compose and
decompose numbers
 I can describe several strategies that
children use to derive addition facts
 I can describe the pre-requisite strategies
that children need to use a “make ten”
strategy when adding whole numbers.
 See you in January.
 Have wonderful
teaching days in
November & December
and a GREAT winter
break!