Transcript Subitizing Presentation

NCTM Conference
April 2014
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Domain: Operations & Algebraic Thinking
 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).
 1.OA.6
 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10 by decomposing a
number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 =
9).
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3.OA.9
Identify arithmetic patterns (including
patterns in the addition table or
multiplication table), and explain them using
properties of operations. For example,
observe that 4 times a number is always
even, and explain why 4 times a number can
be decomposed into two equal addends.
Traditional flash cards or timed tests have not been proven
as effective instructional strategies for developing
fluency.
Rather, numerous experiences with breaking apart actual
sets of objects and developing relationships
between numbers help children internalize parts of number
and develop efficient strategies for fact retrieval.
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Burns. About Teaching Mathematics (2000).
Fosnot & Dolk. Young Mathematicians at Work. (2001).
Richardson. Assessing Math Concepts (2002).
Van de Walle & Lovin (2006). Teaching Student Centered Mathematics K-3.
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The seven partitions of the number 5:
5+0
4+1
3+2
3+1+1
2+2+1
2+1+1+1
1+1+1+1+1
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Term popularized by Fuson and Zantsky
(2000)
Pairs of numbers “hiding” inside a number
Break-apart partners for 5
 4 and 1
 2 and 3
Lots of exploration!
Concrete
Pictorial
Abstract
Don’t rush to introduce the number sentence or purely
symbolic representations for number.
For very young
children, focus on
only a single number
for the entire activity.
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Kindergarten students should see addition
and subtraction equations, and student
writing of equations in kindergarten is
encouraged, but it is not required.

Craft stick separates the line of counters into
break apart partners.
Draw line down middle
of ziplock bag.
 Place counters inside.
 Record the break-apart
partners.
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Three-section paper plate
Pick a card. Put the corresponding
number of counters in the large
section of the plate. Explore
different ways to move the
counters from the large section to
the two smaller sections. This
shows how the number may be
decomposed. It is not
unreasonable to expect students to
find six or more ways to break
apart a number. After lots of
exploration, have older children
record the break apart partner on
paper .
Name ___________________________________
A. I picked the number ________________
I can think of this number as …
___________ and ___________
___________ and ___________.
___________ and ___________
___________ and ___________.
Name McGregor
A. I picked the number 8
I can think of this number as …
5 and 3
4 and 4
6 and 2
1 and 7
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Place dominoes face down
on the table. Students take
turns drawing a domino,
adding the number of dots
on both sides of the
domino and placing it in
the correct “parking spot”
on the mat.
Each person takes ten
turns. At the end of ten
turns, the person with the
tallest stack on any parking
spot is the winner.
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Draw a large circle on paper.
Drop manipulatives on the
paper. Some may fall in the
circle and some out of the
circle. Students record how
many are in and how many
are out.
Each pair of students needs a
bowl with 10 bears in it. The
bowl is the cave. Player A
covers his eyes while Player B
turns the cup over and hides
bears under the cup. Player A
uncovers his eyes and counts
how many bears are "out" of
the cave. He then determines
how many bears must be in the
cave. Player B checks the
amount by revealing the bears
in the cave.
I Wish I Had …
Hold out a bar of connecting cubes, a dot strip or a dot
plate showing 6 or less. Say, “I wish I had six.”
Students respond with the part that is needed.
Ten Frames
VARIATIONS
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Say the number of spaces
on the card instead of the
number of dots
Say one more or two more
than the number of dots
Say the ten fact
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Both players turn up two ten-frame cards.
The winner is the one with the larger total
number. Children can use many different
number relationships to determine the
winner without actually finding the total
number of dots.
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Count out 50 counters.
Players each turn over one card as in War. The
player with the greater number of dots wins
as many counters from the pile as the
difference between the two cards. The
players keep their cards. The game is over
when the counter pile runs out. The player
with the most counters wins.
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Show a set number of counters. Ask what is 2
more or 1 less, etc. Add a filled ten-frame and
repeat the questions. Add more filled tenframes or take some away.
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Play with a partner. Each player has ten
counters. Turn all of the counters over so that
the yellow side is showing. Each player rolls
the die and turns over that number of
counters to the RED side. Continue until each
person has all of their RED sides showing.
Then start the game over again.
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Recording a number sentence is optional.
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Turn all cards over on table.
Match the numbers card to the correct dot card.
3 and 2
3 and 0
Play with a partner. Deal Uno cards. Players
lay cards face down. Player A flips top card
over. Player B flips his card over. If he can
make 10, he captures both cards and says
"Snappo!"
If he can't, he lays his card face
up on the table. Players keep
taking turns, flipping cards,
trying to make 10. A new card
that is turned over can be
matched with any card to make
10. Any player recognizing a
pair that makes 10 can call
“Snappo” and take the set.
Game ends when there are no
matches left. The player who
captured the most cards wins.
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Rules of Go Fish game except players ask one
another for the missing addend to complete
their sum of ten.
Use playing cards with face cards removed or
Uno cards.
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With a partner build a train 20 cubes long.
One partner rolls the die and removes exactly
that number of cubes from the train until
there are no cubes left. The other partner
keeps a record of how many rolls of the die it
takes to make the train disappear. He/she
writes a number sentence to show what
happens after each roll. Switch rolls and
repeat the activity several times.
3
5
2
1. Teach how numbers “go together.”
2. Create addition stories.
3. Create subtraction stories.
5
3
2
Number Bond Stories
2
3
1
+
=
+
=
-
=
-
=
Sentence Frame
There are ______ birds. ________ of
the birds are _______ and _______ of
the birds are _______.
Symbols-only Practice
7 + 9
6 1
8 + 5
2 3
6 + 10 = 16
10 + 3 = 13
Practice
9 + 6
10 + 5 = 15
26 + 8
Choose a Few for Practice
38 + 7
197 + 6
298 + 4
2,394 + 29
3,495 + 38