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Standards
of
Student
Practice
in
Mathematics
Proficiency
Matrix
Students:
(I)
=
Initial
(IN)
=
Intermediate
(A)
=
Advanced
1a
Make
sense
of
Explain
their
thought
processes
in
Explain
their
thought
processes
in
Discuss,
explain,
and
demonstrate
problems
solving
a
problem
one
way.
solving
a
problem
and
representing
it
solving
a
problem
with
multiple
in
several
ways.
representations
and
in
multiple
ways.
(Question/Wait
time)
(Grouping/Engaging)
(Pair
–
Share)
1b
Persevere
in
solving
Stay
with
a
challenging
problem
for
Try
several
approaches
in
finding
a
Struggle
with
various
attempts
over
them
more
than
one
attempt.
solution,
and
only
seek
hints
if
stuck.
time,
and
learn
from
previous
(Question/Wait
time)
(Grouping/Engaging)
solution
attempts.
(Show
Thinking)
2
Reason
abstractly
and
Reason
with
models
or
pictorial
Are
able
to
translate
situations
into
Convert
situations
into
symbols
to
quantitatively
representations
to
solve
problems.
symbols
for
solving
problems.
appropriately
solve
problems
as
well
(Grouping/Engaging)
(Grouping/Engaging)
as
convert
symbols
into
meaningful
situations.
(Encourage
Reasoning)
3a
Construct
viable
Explain
their
thinking
for
the
Explain
their
own
thinking
and
Justify
and
explain,
with
accurate
arguments
solution
they
found.
thinking
of
others
with
accurate
language
and
vocabulary,
why
their
(Show
Thinking)
vocabulary.
solution
is
correct.
(Question/Wait
time)
(Grouping/Engaging)
3b
Critique
the
reasoning
Understand
and
discuss
other
ideas
Explain
other
students’
solutions
and
Compare
and
contrast
various
of
others.
and
approaches.
identify
strengths
and
weaknesses
of
solution
strategies
and
explain
the
(Pair
–
Share)
the
solution.
reasoning
of
others.
(Question/Wait
time)
(Grouping/Engaging)
©
LCM
2011
Hull,
Balka,
and
Harbin
Miles
mathleadership.com
4
Model
with
Use
models
to
represent
and
solve
a
Use
models
and
symbols
to
represent
Use
a
variety
of
models,
symbolic
Mathematics
problem,
and
translate
the
solution
and
solve
a
problem,
and
accurately
representations,
and
technology
to
mathematical
symbols.
explain
the
solution
representation.
tools
to
demonstrate
a
solution
to
a
(Grouping/Engaging)
(Question/Prompt)
problem.
(Show
Thinking)
5
Use
appropriate
tools
Use
the
appropriate
tool
to
find
a
Select
from
a
variety
of
tools
the
Combine
various
tools,
including
strategically
solution.
ones
that
can
be
used
to
solve
a
technology,
explore
and
solve
a
(Grouping/Engaging)
problem,
and
explain
their
reasoning
problem
as
well
as
justify
their
tool
for
the
selection.
selection
and
problem
solution.
(Grouping/Engaging)
(Show
Thinking)
6
Attend
to
precision
Communicate
their
reasoning
and
Incorporate
appropriate
vocabulary
Use
appropriate
symbols,
vocabulary,
solution
to
others.
and
symbols
when
communicating
and
labeling
to
effectively
(Show
Thinking)
with
others.
communicate
and
exchange
ideas.
(Allowing
Struggle)
(Encourage
Reasoning)
7
Look
for
and
make
use
Look
for
structure
within
Compose
and
decompose
number
See
complex
and
complicated
of
structure
mathematics
to
help
them
solve
situations
and
relationships
through
mathematical
expressions
as
problems
efficiently
(such
as
2
x
7
x
observed
patterns
in
order
to
simplify
component
parts.
5
has
the
same
value
as
2
x
5
x
7,
so
solutions.
instead
of
multiplying
14
x
5,
which
is
(2
x
7)
x
5,
the
student
can
mentally
calculate
10
x
7.
(Allowing
Struggle)
(Encourage
Reasoning)
(Question/Prompt)
8
Look
for
and
express
Look
for
obvious
patterns,
and
use
Find
and
explain
subtle
patterns.
Discover
deep,
underlying
regularity
in
repeated
if/
then
reasoning
strategies
for
relationships,
i.e.
uncover
a
model
or
reasoning
obvious
patterns.
equation
that
unifies
the
various
aspects
of
a
problem
such
as
(Grouping/Engaging)
(Allowing
Struggle)
discovering
an
underlying
function.
(Encourage
Reasoning)
©
LCM
2011
Hull,
Balka,
and
Harbin
Miles
mathleadership.com
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