What’s My
[number?]
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Common Core State
Standards for Math
K.OA.3 Decompose numbers less
than or equal to 10 into pairs in
more than one way, e.g., by using
objects or drawings, and record
each decomposition by a
drawing or equation
(e.g., 5 = 2 + 3 and 5 = 4 + 1
Number Bonds
Number bonds
emphasize…
O the
part/part/whole
relationship
O the relationship
between addition
and subtraction
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Composing and
Decomposing Numbers
“Young children in Singapore also spend a great
deal of time exploring, understanding,
manipulating, and talking about numbers to 10.
They learn the ‘number bonds’ to 10. A number
bond helps children visualize the
whole-part-part relationship of a number.”
(Jones Kuhns, 2009, p 7)
“Kindergarteners and first graders are
usually ready to begin these activities
working with either the number 4
or 5. Students should focus on just
one number at a time.”
(Jones Kuhns, 2009, p 8)
The Evolution of a
Number Bond
Build Understanding
through Concrete and
Pictorial Experiences
2
Differentiating—What’s
My Number?
O Building a number (composing) and breaking a
number apart (decomposing)
O Use the “hiding assessment” to determine each
child’s number
O Students should master the combinations for one
number before moving on to the next
O Independent practice, partner work, and small-
group instruction are all based on each student’s
number
O Ongoing…as in ALL YEAR LONG
Differentiating—What’s
My Number?
What is Subitizing?
Talk about it!
3
Subitizing
O “…that ability to ‘just see it’ without
counting is called subitizing.”
(Van de Walle, 2013, p 129)
O “Subitizing is a fundamental skill in the
development of students’ understanding
of number.” (Baroody, 1987, p 115)
O “Subitizing is an important component of
computation at the lower grades.”
(Parrish, 2010, p 39)
Use Manipulatives
for Concrete
Learning
Number Bracelets
http://bit.ly/MCCNumberBracelets
4
Number Bracelet
Routines
Students manipulate the beads and make
all the combinations for a given target
number.
Number Bracelet
Routines
Students can record their number
combinations in a math journal to connect
the concrete with the abstract (symbolic).
Number Bracelet
Routines
Partner activity—one
partner hides some
beads and the other
partner has to figure
out how many are
hidden.
O Number bracelets
are great for the
“hiding assessment”.
O
5
Rekenreks
http://bit.ly/MCCRekenreks
Rekenrek translates
loosely to calculation
rack or arithmetic
rack, and it was
designed by a Dutch
Mathematician. The
rekenrek is a great
visual model for
developing a strong
sense of 5 and 10,
and it supports a
strategy-based
approach for learning
calculations.
Rekenrek Routines
O
O
Introduce the rekenrek and allow students
to make observations.
“What do you notice?”
Teach the conventions of starting with the
beads on one side and moving beads in
groups, rather than one by one.
Rekenrek Routines
O
O
Call a number and have students show
the number in one move.
Show a number and have students tell
what number it is and how they know.
“Use the top
row to show
me 3 with
one move.”
6
Rekenrek Routines
Practice making five, using first only the top
row and then both rows.
“Move 3 red beads.
How many do we
need to make 5?
Right! 3 and 2
make 5.”
“Move 3 red beads.
How many do we
need on the bottom
row to make 5?
Right! 3 and 2
make 5.”
Rekenrek Routines
Practice making ten, using one or both
rows.
“Move 6 beads on top. Now make 10.”
Students can move 4
white beads on the
top row.
Or they can move 4
red beads on the
bottom row.
Rekenrek Routines
Build a Number—partners share a
rekenrek and build a number using the
top and bottom rows.
Make 7
Partner 1 shows
4 on the top
row, so Partner
2 moves 3 on
the bottom row.
4 and 3 make 7.
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Rekenrek Interactive
Resources
Professor Garfield,
What Do I See and
Push to Make
DreamBox, Numbers to
10 on the Math Rack
Shake and Spill
Works with any
simple graphic.
O A target number
of counters is
spilled onto the
mat. Count the
number on the
graphic and off.
O Record
combinations.
O Differentiate
based on student
needs.
O
Bingo Stamper Fun
Use two different
colors of bingo
stampers to
show all the
combinations of
a number.
Record the
combinations.
8
Ten-Frames and TwoColor Counters
“Show me 3. Add counters to make 5.
Three and two make five.”
Linking Cubes
Put two different
colors of linking
cubes in a bag.
Students draw
out the target
number of cubes
without looking
and record
combinations.
9
Multiple Representations
Students should see multiple
representations for the numbers.
Dot Cards
“Incorporating dot images into classroom number talks provides
opportunities to work on counting, seeing numbers in a variety of
ways, subitizing, and learning combinations.” (Parrish, 2012, p 41)
10
Dot Card Routines
O Develop and practice
procedures for dot card
routines. Avoid having
students shout out answers.
O Be sure to ask not only what
number they see, but also
how they see it.
O “Did anyone see it a different
way?”
Let’s try it!
Random Dot Patterns
Start with smaller numbers and
build to larger numbers that use
combinations of the smaller
numbers.
5- and 10-Frames
5- and 10-frames anchor to
the critical benchmarks of 5
and 10.
11
5- and 10-Frames
The process is the same as with
random dot cards, but
questioning can include the
relationship of the number
shown to 5 or 10.
Dot Card Interactive
Resources
NCTM Illuminations,
five- and ten-frame
tools
Fuel the Brain, # Flash
Dot Card Interactive
Resources
DreamBox, Numbers to 10 on
the Ten-Frame
12
Math Games
for
Meaningful
Practice
13
How Many to Make Ten?
 Materials: blank ten-frame, two-color counters,
10-sided die (0-9)
 Roll the die and put that number of counters on
the ten-frame using one color
 Use the other color to complete the ten-frame
 State the number sentence or combination
6 and 4 make 10
or
6 + 4 = 10
or
10 = 6 + 4
Roll and Cover
 Materials: game board, two-color counters, 10-
sided dice (0-9)
 Roll the dice and determine the number needed
to make 10; cover that number on the board
 Players take turns rolling and covering numbers
until all numbers are covered
Make 10 Go Fish
 Deal out five cards to each
player
 Spread the other cards face
down in the “fishing pond”
 Lay down any pairs of cards
that make 10
 Players take turns asking
for cards that would make a
ten
 Players lay down
combinations as they make
them
 If a player uses all his
cards, he takes 5 more from
the pile and play continues
14
Make 10 Memory
 Make 2 sets of the ten-




frame cards, so you’ll have
two 5s, but you might only
want to use 6 pairs to play
Lay cards face down in a 4
by 3 array
Players take turns turning
over cards; if the cards
make a ten, the player
keeps the cards; if not he
turns them back face down
Students should verbalize
their combinations
The player with the most
cards wins
Seven on Top
 Lay out seven cards face up
 Remove pairs of cards with a sum
of 10
 Replace cards, always leaving
seven
 If there are no pairs for ten in the
seven cards showing, lay down
another seven cards on top of the
others
 Variations:
 Show cards one at a time and have
students tell you the number that
makes ten
 Remove some cards and play
looking for combinations of other
numbers
Mathemagician Make Ten
 Remove the face cards and Jokers
from a standard deck of playing
cards; aces are ones
 One player chooses a card from the
deck and places it face down off to
the side
 Place all other cards face up in rows
and columns on the table
 Taking turns, players take pairs of
cards that combine to make 10 off the
table while stating the fact; 10s can
be taken off the table, and the player
would say 10 + 0
 At the end of the game, one card will
be left on the table; its pair is the one
hidden off to the side!
Note: if no cards are left on the table
at the end of the game, the hidden
card is a 10! 
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References
 Van de Walle, John A., LouAnn H. Lovin, Karen S. Karp, and Jennifer M.
Bay-Williams. (2014). Teaching Student-Centered Mathematics. New
York: Pearson Education.
 Richardson, Kathy. (2012). How Children Learn Number Concepts: A
Guide to the Critical Learning Phases. Bellingham, WA: Math
Perspectives
 Jones Kuhns, Catherine. (2009). Building Number Sense: Games and
Activities to Practice Combinations to 10. Peterborough, NH: Crystal
Springs Books.
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Donna Boucher, Math Coach’s Corner
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Freddy Frog Shake and Spill
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