9-2-14
Name of Teacher:
School:
HCPSS Student Learning Objective
Mathematical Practices 4: Model with mathematics (Practice Focus)
Component
Student Learning
Objective (SLO)
Population
Learning Content
Description
100% of students will demonstrate growth in Common Core State Standards for
Mathematics in the learning behaviors defined by the Standards for Mathematical
Practice 4: Model with mathematics, as evidenced by performance on worthwhile
mathematical tasks and/or high quality formative assessment items and
participation in effective classroom discourse.
Of the ______ (number) students selected for this SLO:
 ______ performed at the (low/high) basic level on the previous year’s (M/H)SA
 ______ performed at the (low/high) proficient level on the previous year’s
(M/H)SA
 ______ performed at the (low/high) advanced level on the previous year’s
(M/H)SA
 ______ were below grade level at the end of the previous year
 ______ were on grade level at the end of the previous year
 ______ were above grade level at the end of the previous year.
The Standards for Mathematical Practice describe varieties of expertise that
mathematics teachers should seek to develop in their students.
1.
2.
3.
4.
5.
6.
7.
8.
Instructional
Interval
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
The practices describe ways in which developing student practitioners of the
discipline of mathematics increasingly ought to engage with the subject matter as
they grow in mathematical maturity and expertise throughout the elementary,
middle and high school years. The mathematical practices are not skill‐based
content that students should learn through direct teaching methods. Instead, the
student behaviors develop over time and often emerge during certain learning
activities and through the study of specific, critical mathematics topics and
standards. These learning activities, coordinated by mathematics teachers, must
include challenging problems, student collaborative groups, interactive discourse,
and adequate time.
School year 2013-14 (one year)
Mathematics classes are 50 minutes per day, 5 days per week. (Seminar periods
provide an additional 50 minutes per day, 5 days per week.)
This SLO is a sample. Targets need to be adjusted based on your students’ data. Student growth should be
achieved for all students.
9-2-14
Evidence of Growth To monitor student progress, the following data/measures will be used:
 Analysis of student work samples to identify the proficiency level of engagement
in the mathematical practices
 Analysis of student behaviors and dispositions during classroom learning
experiences.
It should be noted that the mathematical practices are interdependent, and do not
develop in isolation from one another. While the focus of this SLO is on student
engagement with practice 4 during learning experiences, mathematics teachers
need to continually assess student progress on the practices in a holistic fashion.
Furthermore, in using the Standards of Student Practice in Mathematics Proficiency
Matrix, mathematics teachers and leaders need to apply their knowledge of grade
appropriate content and pedagogy to adjust the indicators of progress.
Baseline
Of the ______ (number) students selected for this SLO baseline levels of engagement
with mathematical practice 4: Model with mathematics, as measured using the
Standards of Student Practice in Mathematics Proficiency Matrix:
 ______ % demonstrated a baseline level of engagement of Absent
 ______ % demonstrated a baseline level of engagement of INitial
 ______ % demonstrated a baseline level of engagement of Intermediate
 ______ % demonstrated a baseline level of engagement of Advanced.
(Attach class roster to share students’ scores on Beginning-of-the-Year
Assignment/Performance Task/Assessment.)
Rationale for
Student Learning
Objective
The abilities and mathematical dispositions of students develop as opportunities to
learn are provided and are described in the Standards of Student Practice in
Mathematics Proficiency Matrix. As a means to help students continue in a pattern of
growth with mathematical proficiency, the matrix is a tool to help consider and
gauge students’ progress with engagement with the practices. With teacher
guidance, students’ proficiency will progress from the baseline levels to more
advanced proficiency levels.
Target
The target for the _____ students identified for this SLO will be to demonstrate an
increase in mathematical practice proficiency level(s), with a focus on practice 4
using the Standards of Student Practice in Mathematics Proficiency Matrix.
*Please note: Students identified by IEP teams as having significant cognitive
disabilities will have individual targets.
Criteria for
Effectiveness
Full Attainment of
Target
More than 90% of
students meet agreed
upon learning targets
consistent with
Partial Attainment of
Target
Between 75% and 90% of
students demonstrated
growth with consistent
proficiency in Math
Insufficient Attainment
of Target
Less than 75% of students
meet agreed upon
learning targets
consistent with
This SLO is a sample. Targets need to be adjusted based on your students’ data. Student growth should be
achieved for all students.
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proficiency in Math
Practice #4: Model with
mathematics.
Strategies
Practice #4: Model with
mathematics.
proficiency in Math
Practice #4: Model with
mathematics.
 The teacher, working with a collaborative teacher team, should collect data
through informal observation, student work samples on worthwhile
mathematical tasks and formative items, and other learning artifacts (including
digital recordings, student responses to higher order thinking questions).
Teachers should record baseline levels of proficiency of student engagement with
mathematical practice 4 using the Standards of Student Practice in Mathematics
Proficiency Matrix.
 In planning learning opportunities for students to engage in the mathematical
practices, teacher teams should:
o Identify content to be taught.
o Consider what mathematics students are to know and how students can
best demonstrate understanding.
o Select mathematical tasks that provide students with opportunities to
engage in collaborative critical thinking, multiple solution pathways and
representations, the selection and use of a variety of mathematical tools,
and modeling real-world situations in abstract terms.
o Carefully consider the strategies needed to help students engage in
productive reasoning and sense making. (e.g., initiating think-pair-share,
think-aloud, questioning and wait time, grouping and engaging
problems/tasks, using questions and prompts with groups, allowing
students to struggle, etc.)
o Formulate several questions they can pose to students to promote
reasoning, sense making and communication. Consider possible student
responses and common student understandings and approaches for
addressing student misunderstandings.
o Clarify, define and develop formative/summative assessment activities.
o Sequence lesson experiences to maximize opportunities to model with
mathematics. Strategically plan supports offered to students so that
students engage in productive struggle without becoming overly frustrated.
 For selected cluster, collect evidence and data throughout the school year to
reflect on individual student growth with mathematical practice 4 and document
levels of proficiency. Evidence should be collected at least quarterly. Evidence
could include, but is not limited to: student work samples, digital recordings, and
feedback from peer observation, and/or a teacher’s classroom observations.
This SLO is a sample. Targets need to be adjusted based on your students’ data. Student growth should be
achieved for all students.
Standards of Student Practice in Mathematics Proficiency Matrix
Mathematical
Practice
Students:
Initial (IN)
Make sense of
problems
Explain their thought
processes in solving a
problem one way.
Persevere in
solving them
Stay with a challenging
problem for more than one
attempt.
Reason with models or
pictorial representations to
solve problems.
1
2
3
Reason
abstractly and
quantitatively
Construct
viable
arguments
Critique the
reasoning of
others.
Explain their thinking for
the solution they found.
Model with
Mathematics
Use models to represent
and solve a problem, and
translate the solution to
mathematical symbols.
Use
appropriate
tools
strategically
Use the appropriate tool to
find a solution.
Attend to
precision
Communicate their
reasoning and solution to
others.
Look for and
make use of
structure
Look for structure within
mathematics to help them
solve problems efficiently
(Seeing 5 – 3(x – y)2 as 5
minus a positive number
times a square and use that
to realize that its value
cannot be more than 5 for
any real numbers x and y).
Look for obvious patterns,
and use if/ then reasoning
strategies for obvious
patterns.
4
5
6
7
8
Look for and
express
regularity in
repeated
reasoning
Understand and discuss
other ideas and
approaches.
Intermediate (I)
Advanced (A)
Explain their thought
processes in solving a
problem and representing
it in several ways.
Try several approaches in
finding a solution, and
only seek hints if stuck.
Are able to translate
situations into symbols for
solving problems.
Discuss, explain, and demonstrate
solving a problem with multiple
representations and in multiple
ways.
Struggle with various attempts
over time, and learn from previous
solution attempts
Convert situations into symbols to
appropriately solve problems as
well as convert symbols into
meaningful situations.
Justify and explain, with accurate
language and vocabulary, why
their solution is correct.
Compare and contrast various
solution strategies and explain the
reasoning of others.
Explain their own thinking
and thinking of others
with accurate vocabulary.
Explain other students’
solutions and identify
strengths and weaknesses
of the solution.
Use models and symbols
to represent and solve a
problem, and accurately
explain the solution
representation.
Select from a variety of
tools the ones that can be
used to solve a problem,
and explain their
reasoning for the
selection.
Incorporate appropriate
vocabulary and symbols in
others.
Compose and decompose
number situations and
relationships through
observed patterns in order
to simplify solutions.
Find and explain subtle
patterns.
Use a variety of models,
symbolic representations, and
technology tools to demonstrate
a solution to a problem.
Combine various tools, including
technology, explore and solve a
problem as well as justify their tool
selection and problem solution.
Use appropriate symbols,
vocabulary, and labeling to
effectively communicate and
exchange ideas.
See complex and complicated
mathematical expressions as
component parts.
Discover deep, underlying
relationships, i.e. uncover a model
or equation that unifies the various
aspects of a problem such as a
discovery of an underlying
function.
From Hull, T., Harbin Miles, R. and Balka, D. (2012). The common core mathematics standards: Transforming practice though team leadership.
Corwin and the National Council of Teachers of Mathematics. Thousand Oaks: CA.