1. 3rd
Grade
Agenda
&
Goals
• Update
the
Training
&
Implementa7on
Plan
• Iden7fy
strategies
for
math
learning
difficul7es
• Explore
3rd
grade
content
and
pedagogy
in
Math
in
Focus

2. Math
Learning
Difficul7es
1. ESTIMATE
how
many
of
your
students
demonstrate
each
math
learning
difficulty
2. DISCUSS
which
learning
difficul7es
do
you
see
most
oIen?

3. Strategies
for
Math
Learning
Difficul7es
✭ the
strategies
that
you
associate
with
Singapore
Math

4. Pedagogy:
C-­‐P-­‐A
Jerome
Bruner’s
research
proved
that
instruc7onal
strategies
build
understanding
for
students
when
they
move
from…
• Concrete
(manipula7ves)
to
• Pictorial
(visual
models
or
drawings)
to
• Abstract
representa7ons
(numbers,
symbols)

5. Pedagogy:
Rela7onal
Understanding
Richard
Skemp’s
research
proved
that
for
long
term
learning
to
occur
rela(onal
understanding
is
more
successful
than
instrumental
learning.
Rela(onal
Understanding
Instrumental
Understanding
Conceptual
Procedural
WHY
before
HOW
How
One
to
One
Correspondence
Oral
Coun7ng
Quan77es
and
Values
Wri7ng
numbers,
Spelling
numbers
Each
piece
RELATES
to
all
others
Isolated
steps
or
steps
without
meaning
Reading
with
understanding
Phone7c
or
word
calling

6. Pedagogy:
Perceptual
Variability
Zoltan
Diene’s
research
proved
that
children
gain
the
most
conceptual
understanding
when
they
are
exposed
to
a
concept
through
a
variety
of
materials
or
experiences.
Perceptual
Variability
?
z! ;!
p! /!
"
q!

7. Reflec7ng
On
Pedagogy
Select
one
strategy
for
addressing
math
learning
difficul7es.
Discuss
how
it
connects
to
Singapore
Math
Pedagogy…
v Concrete-­‐Pictorial-­‐Abstract
(Bruner)
v Rela7onal
Understanding
(Skemp)
v Mul7ple
Representa7ons
(Dienes)

8. Place
Value
Strips
1.
Find
a
partner
to
compose
one
of
these
numbers:
61
42
23
14
35
56
2.
With
your
partner
say
these
about
your
number:
a.
____
tens
and
____
ones
make
_____
b._____
+
_____
=
_______

9. Place
Value
Strips
3.
Find
another
pair
to
add
these
numbers
mentally:
61
+
35
=
42
+
23
=
56
+
14
=
4.
Find
another
pair
to
add
these
numbers
mentally:
14
+
35
=
23
+
56
=
42
+
61
=

10. Place
Value
Strips
5.
Exchange
cards
with
anyone
in
your
foursome.
6.
Use
the
hundreds
around
the
room
(and
a
partner)
to
make
these
numbers…
142
361
523
614
435
256

11. Place
Value
Strips
7. Come
to
the
front
of
the
room
and
put
the
3-­‐digit
numbers
in
order
from
least
to
greatest.
8.
Find
another
pair
to
add
these
numbers
mentally:
256
+
361
=
523
+
142
=
435
+
614
=

12. Mental
Math
7. Use
the
same
strategy
you
used
with
place
value
strips
to
add
these
numbers
mentally.
47
+
52
=
29
+
74
=
251
+
638
=

13. Mental
Math
Decomposing
to
Friendly
Numbers
64
+
35
=
56
+
53
=

14. Mental
Math
8. Now
use
branching
(number
bonds)
to
add
these
numbers.
47
+
52
=
29
+
74
=
251
+
638
=

15. Base
Ten
Blocks:
+
-­‐
x
~
Solve
these
problems
using
base
ten
blocks…
267
423
+645
-­‐
265
33
69
~ 3
=
x
4
(3
equal
groups)

16. Introducing
Place
Value
Discs
•
Relate
to
Place
Value
Strips
(what
they
know)
•
Relate
to
Base
Ten
Blocks
(what
they
know)
•
Represent
numbers
using
two
representa7ons
at
the
same
7me
(strips
with
chips)
(base
ten
with
chips)
•
Represent
numbers
on
a
place
value
chart
first
(before
doing
computa7on)

17. Place
Value
Chips:
+
-­‐
x
~
Solve
these
problems
using
place
value
chips…
267
423
+645
-­‐
265
33
69
~ 3
=
x
4
(3
equal
groups)