Second Grade
How Not What
With the adoption of Common Core Standards for Math, the focus during this first year of
implementation in the Great Falls Public Schools will be on a shift in HOW we teach Mathematics skills
and concepts.
This focus is based on the 8 Mathematical Practices that are a part of the Common Core Standards.
1. Make sense of problems and persevere in solving them
I can try many times to understand and solve a math problem.
Ways to Infuse
 Suggest students use pictures, numbers,
and words to begin working their problem.
 Students brainstorm ways to begin solving
and list suggestions on the board for all
students to see.
 If students find their pathway is a dead
end, discuss with other students how they
started. Do not erase old work to refer
back to later.
 Reconsider the question that was asked to
them. Decide if their solution matches.
 Challenge students to find the most
number of ways to find a solution.
 Have students reflect, “Is there more than
one solution?”
 Use formative assessment and openended questions to guide instruction.
 Students justify if their answer is
reasonable.
 Start with a small amount of time to work
on problems and for sharing problems and
build to a greater amount of time.
What to Look For In Students
 Use multiple entry points for solution.
 Analyze information.
 Plan a solution pathway.
 Use objects, drawings, and diagrams to
solve problems.
 Monitor learning and change course as
necessary.
 Asks, “Does this make sense?”
2. Reason abstractly and quantitatively
I can think about the math problem in my head, first.
Ways to Infuse
 Give students wait time and have them
independently write down ideas first.
 Share their ideas with others.
 Use manipulatives to express values and
understand their meaning.
 Illustrate a situation with a graph, chart, or
equation.
 Choose various methods to communicate
findings.
 Students write a rule for what is
happening and have others check it or try
it.
 Students check their theory with other
numbers.
 Students check generalized statements by
completing at least 3 samples.
What to Look For In Students
 Make sense of quantities.
 Represents abstract situations
symbolically.
 Represent the problem accurately.
 Translates from contextualized to
generalized and vice versa.
 Flexibly use properties of operations.
3. Construct viable arguments and critique the reasoning of others
I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies
too.
Ways to Infuse
 Students write out their work in pictures,
numbers, and words.
 Teacher records all possible ways students
are going to/will find solutions on the
board for all to see.
 Discuss methods listed that are most
efficient, effective, or appropriate for the
situation.
 Students give examples and non-examples
to prove their point.
 Use questioning strategies and encourage
students to do that of their peers. (Ex.
Explain how you did that. How do you
know? Etc.)
 Discuss methods and solutions with
various students.
 Students have the flexibility to
change/modify their solutions after
discussion.
What to Look For In Students
 Use definitions and previous results in
constructing arguments.
 Make conjectures and use counterexamples to support their ideas.
 Listen to or read the arguments of others.
 Ask probing questions to other students.
4. Model with mathematics
I can use math symbols and numbers to solve problems.
Ways to Infuse
What to Look For In Students
 Record student thinking on the board.
 Write an equation that represents a
Insert math operations when necessary to
situation.
model writing an equation.
 Illustrate mathematical relationships with
 Students develop their own equations to
diagrams, two-way tables, graphs, flow
solve mathematical concepts.
charts and formulas.
 Students write out their work in pictures,
 Make a problem simpler.
numbers, and words.
 Check to see if an answer makes sense.
 Put large amounts of related data into
 Change a model when necessary.
graphs, charts, flow charts, or diagrams.
 Students use smaller/easier numbers to
test a theory and move to larger/more
complex numbers.
 Break a problem down into more
manageable parts. Solve one piece at a
time.
 Students decide the most efficient,
accurate, or conceptual way to solve
problems.
 Reconsider the question being asked to
check if the solution is reasonable.
 Check your solution with a partner or small
group, justifying your own reasoning and
critiquing the reasoning of others.
 If students find their pathway is a dead
end, discuss with other students how they
started. Do not erase old work to refer
back to later.
 Whole class discussion on solutions.
Students decide which methods were
more efficient, effective, or appropriate
for the problem.
 Reflect on what they might do differently
or give them the option to rework their
solution.
5.
Use appropriate tools strategically
I can use math tools, pictures, drawings, and objects to solve the problem.
Ways to Infuse
 Students need to choose and justify their
tools without prompting. i.e. ruler,
drawings, manipulatives, etc.
 Record student strategies on the board
putting stars next to those that were most
efficient, effective, and/or appropriate for
the problem.
 Discuss whole-class, before solving
problems, which tools would be best
suited for the task.
What to Look For In Students
 Choose tools that are appropriate for the
task.
 Use technological tools to visualize the
results of assumptions, explore
consequences, and compare predictions
with data.
 Identify relevant external math resources
and use them to pose or solve problems.
6. Attend to precision
I can check to see if my strategy and calculations are correct.
Ways to Infuse
 Have a vocabulary word
bank/wall/glossary and have students
justify thinking using appropriate
terminology.
 When there is more than one term for a
mathematical concept use the terms
interchangeably. i.e. plus/addition.
 Enforce the use of correct terminology
when students write in mathematics.
 Do not accept answers without
appropriate labels.
 Although the method chosen is critical and
varied, students should get a correct
answer.
 Student can justify their solutions in a
variety of ways.
 Students can communicate their solutions
effectively to others.
What to Look For In Students
 Communicate precisely using appropriate
terminology.
 Specify units of measure and provide
accurate labels on graphs.
 Express numerical answers with
appropriate degree of precision.
 Provide carefully formulated explanations.
7. Look for and make use of structure
I can use what I already know about math to solve the problem.
Ways to Infuse
 Help students become proficient in
decomposing numbers. i.e. Number of the
Day.
 Label for students when they are correctly
using the properties.
 Help students use the properties to
become more efficient mathematicians.
 Show students that there are multiple
ways to represent a quantity.
(decomposition)
What to Look For In Students
 Look for patterns or structure, recognizing
that quantities can be represented in
different ways.
 Use knowledge of properties to efficiently
solve problems.
 View complicated quantities as single
objects or as a composition of several
objects.
8. Look for and express regularity in repeated reasoning
I can use a strategy that I used to solve another math problem.
Ways to Infuse
What to Look For In Students
 After students have built a conceptual
 Notice repeated calculations and look for
understanding of a concept, encourage the
general methods and shortcuts.
use of the standard shortcut for solving
 Continually evaluate the reasonableness
problems, only if it is common core grade
while attending to details.
level appropriate.
 Reconsider the question to check if the
solution is reasonable.
 Check your solution with a partner or small
group, justifying your own reasoning and
critiquing the reasoning of others.
Considerations
Using Harcourt
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Start each lesson with an open-ended question from the bottom of the student page to
generate discussion.
Change the questions/problems in the book to facilitate deeper student thinking and infuse the
cultural context.
Do selected practice problems last and the problem solving first.
Utilize the Alternative Teaching Strategy, Writing and Math, Early Finisher, ESOL/ESL/ELL
options.
Pay attention to margins and use a critical eye to find good questioning prompts, formative
assessment opportunities, and writing prompts.
Alternative Resources
Many Standards will require the use of other materials to support instruction. If you are unsure of
where to find alternative resources to support the Common Core Standards, refer to the list below.

Montana Council for Teachers of Mathematics (MCTM)- links to numerous useful resources
http://Tinyurl.com/mctm-pda
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GFPS Moodle Course:
http://courses.gfps.k12.mt.us
Course Name: Best Practices in Elementary Mathematics
Password: focus

National Council for Teaching Mathematics support website
http://illuminations.nctm.org/

Math Solutions website
http://mathsolutions.com/index.cfm?page=wp10&crid=3
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Math Perspectives
http://mathperspectives.com/tcenter.html
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K-5 Math Teaching Resources
http://www.k-5mathteachingresources.com/
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Math Problem Search Engine
http://Mathworld.wolfram.com
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Lesson Planning Resources
http://www.uen.org/Lessonplan/LPview?core=2
http://www.k-5mathteachingresources.com/
http://readtennessee.org
(K-3)
http://www.helpingwithmath.com/
http://www.graniteschools.org/depart/teachinglearning/curriculuminstruction/math/elementar
ymathematics/Pages/default.aspx
http://www.orecity.k12.or.us/staff/curriculum_resources/mathematics/grade_level
https://www.teachingchannel.org/videos?page=1&categories=topics_commoncore&gclid=CKr3gKKEk7ACFQF7hwodqGn6oA
http://illustrativemathematics.org/standards/k8
http://www.insidemathematics.org
http://thinkmath.edc.org/index.php/CCSS_Mathematical_Practices
http://letsplaymath.net/
http://www.billingsschools.org/Page/425
Remember to check both the curriculum library and your school library for the following books
containing supplemental lessons:
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Math Solutions/Marilyn Burns
AIMS
*If looking at standards only, it would appear that some mathematical concepts are not taught
(data/graphing, probability, measurement, time/money). However, these concepts could be
embedded in other content or in how you teach other skills. See your grade level implementation
guide for more support.