Standards For Mathematical Practice
Standard for
Mathematical Practice
Make sense of problems and persevere in
solving them
Mathematically proficient students start by
explaining to themselves the meaning of a
problem and looking for entry points to its
solution. They analyze givens, constraints,
relationships, and goals. They monitor and
evaluate their progress and change course if
necessary.
Reason abstractly and quantitatively
Mathematically proficient students make
sense of quantities and their relationships in
problem situations. They have the ability to
decontextualize (represent problems
abstractly or symbolically) and
contextualize (create representation of a
problem while attending to the meanings of
the quantities).
Construct viable arguments and critique
the reasoning of others
Mathematically proficient students
understand and use stated assumptions,
definitions, and previously established
results in constructing arguments. They
make and critique conjectures and build a
logical progression of statements to explore
the truth of these conjectures.
Model with mathematics
Mathematically proficient students can
apply the mathematics they know to solve
problems arising in everyday life, society,
and the workplace.
ST Math
Ten Marks
ST Math engages students in learning
through problem solving. Students are
easily challenged with 50 or more complex
problems during a single session, building
mastery through the development of
strategic thinking, conceptual
understanding, perseverance and practice.
Teachers can evaluate how students interact
and respond to combo questions, which
consist of two parts, where the response to
the second part is dependent on the
response to the first. Ten Marks also has a
variety of items where students can practice
their procedural skills as well as their
conceptual knowledge. Hints and videos
help students make additional sense of
problems.
ST Math content objectives are designed
around learning paths that begin with basic
concepts but end in rigorous applications
where students use abstract, quantitative,
and creative reasoning to solve non-routine
problems.
Through multiple choice and “choose all
that apply” items students have to use their
reasoning skills to select statements that fit a
given condition.
Using teacher mode, ST Math software
provides teachers the opportunity to bring
the games into the classroom and use them
as a vehicle for classroom discussion, asking
students to make conjectures, discuss
problem-solving strategies in groups, and
clearly explain and justify their reasoning.
Ten Marks allows teachers to use preview
mode in order to explicitly teach and
generate class discussions around concepts.
Like ST Math, teachers can ask students to
make conjectures, discuss problem-solving
strategies in groups, and clearly explain and
justify their reasoning.
Learning paths guide students’ progress
from visual!to symbolic to contextual
problem solving, using mathematics to
model and describe complex situations.
During practice within Ten Marks, students
have the option to see mathematical models
with help videos, hint explanations, and
solution justifications.
Use appropriate tools strategically
Mathematically proficient students consider
the available tools when solving a
mathematical problem. Students are
sufficiently familiar with tools appropriate
for their grade or course to make sound
decisions about when each of these tools
might be helpful, recognizing both the
insight to be gained and their limitations.
Attend to precision
Mathematically proficient students try to
communicate precisely to others. They are
careful about specifying units of measure,
and labeling axes to clarify the
correspondence with quantities in a
problem. They calculate accurately and
efficiently, express numerical answers with
a degree of precision appropriate for the
problem context.
Look for and make use of structure
Mathematically proficient students look
closely to discern a pattern or structure.
They can see complicated things, such as
some algebraic expressions, as single objects
or as being composed of several objects.
Look for and express regularity in repeated
reasoning
Mathematically proficient students notice if
calculations are repeated, and look both for
general methods and for shortcuts. They
continually evaluate the reasonableness of
their intermediate results.
Through new touch technology integration,
ST Math bridges the gap between visual and
physical manipulatives, enabling students to
choose real world tools and strategically use
them to solve problems.
Graphic representations of tools (ie:
protractors, graph paper, and base 10
blocks) connect students with real-world
tools needed to solve problems. Teachers
create opportunities for students to interact
between paper/pencil and technology tasks
choosing appropriate tools as needed.
Students directly experience precision in
mathematics, connecting the precision
inherent in symbolic representations to
precision in measuring and using tools.
Students will practice with precision
through assignments and playlists. Students
lacking precision will have opportunities to
redo problems and will be automatically
assigned amplifiers to gain necessary
content knowledge. Teacher view of error
analysis provides additional opportunities
to direct students’ attention to precision.
Each game in ST Math is based on a visual
schema. Students internalize these
interactive representations, connecting the
structure of the models with the symbols,
and using this structure to solve problems.
Hints in Ten Marks specifically help
students break apart complex problems to
be able to look more closely at patterns and
structures within problems. Teacher mode
allows teachers the ability to engage
students in discussion around this practice.
Students can also utilize hints through
independent practice.
Each key concept is presented in multiple
games with different representations,
allowing students to identify ideas and
reasoning strategies that enable them to
solve problems in different forms.
Ten Marks provides a 20,000-item question
bank for instruction and practice, which
include:
• Constructed response (fill-ins)
• Multi-part constructed response
• Multiple choice
• Multi-part multiple choice
• Select-all-that-apply
• Multi-part combination items