Creating a Transition
CCSSM Unit
Example of a unit on
expressions and equations
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Think in Terms of Units
Phil Daro has suggested
that it is not the lesson or
activity, but rather the
unit that is the “optimal
grain-size for the
learning of mathematics”.
Hence that was the
starting point for our
Scope and Sequence.
Developers of High
School: Patrick Callahan,
Dick Stanley, David
Foster, Brad Findell,
Phil Daro, and Marge
Cappo
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New K-12 Math Curriculum Inspired by
The Common Core State Standards
The Gates Foundation and the Pearson
Foundation are funding a large scale project to
create a system of courses to support the ELA
and Mathematics CCSS. These will be a
modular, electronic curriculum spanning all
grade levels. A Santa Cruz based company,
Learning In Motion, is working to write the
lessons.
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Middle School Curriculum
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A Mathematical Big
Idea
Expression and
Equations
3x – 5
-2x + 7 = y
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The Big Idea of the Unit
The seventh grade unit “Expressions and Equations” addresses the
mathematical concepts of variables, expressions and equations.
Students learn that variables can represent unknown quantities. An
algebraic expression is a generalization of number(s), operation(s)
and/or variable(s) that represents one or more quantities. An
algebraic equation is a statement that indicates two expressions are
equal. Students represent real situations or mathematical
relationships with expressions and equations. Students solve
equations using mathematical methods such as, guess and check,
using tables, graphs, deductive reasoning, and algebraic methods.
Student use properties of operations to change expressions and
equations into different forms. They model real life situations with
expressions and equations. Algebraic methods of solving equations
are learned and applied to everyday and mathematical situations.
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Unit of Study
Around a Big Idea
Preassessment
MARS Task
1 day
Instruction
POM or Expert
Investigation
Instruction
5 - 10 days
Math Talks
CC
FAL
Instruction
Final
Assessment
MARS Task
2 days
1 day
We are
Here
Unit of Study
Around a Big Idea
Preassessment
MARS Task
1 day
Instruction
POM or Expert
Investigation
Instruction
5 - 10 days
Math Talks
CC
FAL
Instruction
Final
Assessment
MARS Task
2 days
1 day
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LESSONS
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Unit of Study
Around a Big Idea
Preassessment
MARS Task
Instruction
POM or Expert
Investigation
Instruction
CC
FAL
Instruction
Final
Assessment
MARS Task
We are
Here
1 day
5 - 10 days
Math Talks
2 days
1 day
MATH TALKS
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Math Talks
•
A daily ritual with the entire class for the purpose of developing
conceptual understanding of and efficiency with numbers,
operations and other mathematics such as geometry and
algebra. (no more than 10 minutes per day)
Math Talks are used to:
• Support active student engagement through signaling
• Review and practice procedures and concepts
• Introduce a concept before diving into the lesson of the day
• Support students in deepening their understanding of the
Properties of Arithmetic and our Place Value System
• Explore mathematical connections and relationships
• Encourage students to construct viable arguments and critique
the reasoning of others
• Support students in using precise mathematical language in
sharing their different strategies and approaches
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Math Talk
If the lime and cherries are single digits,
what are their values?
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Math Talk
If the grape is a single digit, what values
could the grape be?
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Math Talk
If the plum and orange are single digits
What are their values?
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Unit of Study
We are
Here
Preassessment
MARS Task
1 day
Instruction
Around a Big Idea
POM or Expert
Investigation
Instruction
5 - 10 days
Math Talks
CC
FAL
Instruction
Final
Assessment
MARS Task
2 days
1 day
Month
A program
to foster
school-wide
participation
in math and
problem
solving.
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REASONING AND EXPLAINING
1. Make sense of problems and persevere in
solving them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical Practices
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
How are the POM be used?
• The POM are used school wide to
promote problem solving.
• Each problem is divided into five
levels, A-E, to meet the learning
development needs of all students.
• A great tool for Differentiated
Instruction.
• Students, teachers and parents
learn to ask questions and
persevere in solving non-routine
problems.
• The whole school celebrates doing
mathematics at school.
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It’s better to solve one
problem five different
ways than to solve five
different problems.
George Polya
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“A problem is
not a problem if
you can solve it
in 24 hours.”
George Polya
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Creating a Poster
Your concluding thoughts on an
explanation poster for a level you feel
you have completed
AND
Your current thoughts on a status
poster for a level you are still
exploring.
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Explanation Poster: The focus of your poster
should be on how your findings can be justified
mathematically and how your findings make
sense. Include words and visuals (such as
drawings) as a part of your justification.
Status Poster: The focus of your poster should
be on your processes so far and where you
think you want to go next and/or
questions/wonderings you have about this level.
Include words and visuals as a part of your
justification.
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*Remember to justify or explain your processes you
have used so far and why they make mathematical
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Gallery Walk
• Each group will display their
poster.
• Each group selects a group
member to be the docent to
answer questions or provide
clarifications/explanations.
• The other group members
examines, explores, reviews
the other groups’ posters.
• There will be time for your
group to re-assemble and
discuss the information shared
in the groups’ posters.
• Please mind gallery walk norms
and be respectful of the work
and information shared.
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Unit of Study
Around a Big Idea
Preassessment
MARS Task
1 day
Instruction
POM or Expert
Investigation
Instruction
5 - 10 days
Math Talks
We are
Here
CC
FAL
Instruction
Final
Assessment
MARS Task
2 days
1 day
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P-32
LESSONS
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P-33
LESSONS
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P-34
LESSONS
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P-35
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Writing Algebraic Expressions
Area of rectangle = _ _ _ _ _ _ _ _ _ _ _ _
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P-36
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Writing Algebraic Expressions
Perimeter of rectangle = _ _ _ _ _ _ _ _ _ _ _ _
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P-37
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Writing Algebraic Expressions
Which two expressions are equivalent?
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P-38
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Which Equations Describe The
Story?
A pencil costs $2 less than a
notebook.
A pen costs 3 times as much as
a pencil.
The pen costs $9
Let x represent the cost of notebook.
A:
3x  6  9
B:
C:
x6 9
3x  2  9
D:
3( x  2)  9
Which of the four equations
opposite describe this story?
P-39
Writing Equations To Describe A Story?
• Write an equation for Story 1 (S-1).
• Let x represent the number you are trying to find.
• (Solo, Partner, Class)
P-40
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Writing Equations To Describe A Story?
• Write equations for
Stories 2-6 (S-2S-6).
• Let x represent the
number you are trying
to find.
• Individual Think Time
• Partner Talk
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P-41
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Matching Stories and Equations
• Work together to match
each story with an
equation.
• Be sure to check to see
whether any of the
equations you and your
partner have written down
“match” the equations on
the cards.
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P-42
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Sharing Matched Stories and Equations
Docent/Data Collector Protocol
Before we begin sharing our work, have one
partner write down the agreed upon
matches on the dry/erase board.
• Docent (Remains)
• Data Collectors (Visits)
• Discuss, revise, edit, and extend your
mathematical thinking to create a
Presentation Poster.
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P-43
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Matching Stories and Equations (Class)
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P-44
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Showing Steps to Solving
Equations
Material Management
• Divide your construction paper into four
quadrants.
– Glue cards E1 to E4 on the front of your
poster
– Glue cards E5 and E6 on the back of your
poster
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P-45
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Showing Steps to Solving
Equations
• Matching “E1-E4” with “Steps to Solving”
• Select the steps needed to solve each of the
equation cards E1-E4.
• Write a description of the process involved for
each step in solving; e.g., “divide both sides by 2”
or “add 6 to both sides”.
• Do this for each step in the solving process.
• If you find that there is more than one method for
solving an equation, glue the two solutions sideby-side in the appropriate quadrant.
• Write an explanation to show how you arrived at
the equation match to your story situation.
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P-46
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Showing Steps to Solving
Equations
• Once you’ve finished matching E1-E4, begin
showing the steps and justifications for E5
and E6.
• Write a description of the process involved for
each step in solving; e.g., “divide both sides by 2”
or “add 6 to both sides”.
• Do this for each step in the solving process.
• If you find that there is more than one method for
solving an equation, glue the two solutions sideby-side in the appropriate quadrant.
• Write an explanation to show how you arrived at
the equation match to your story situation.
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P-47
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Follow-Up Lesson
• Original pre-assessment, “Express
Yourself”
• Carefully look over your original work.
• Please write about what you have learned
since you did this task.
• “Express Yourself (Re-visited)”
• Please use what you have learned to answer
these questions.
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P-48
LESSONS
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P-49
LESSONS
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We are
Here
Unit of Study
Around a Big Idea
Preassessment
MARS Task
1 day
Instruction
POM or Expert
Investigation
Instruction
5 - 10 days
Math Talks
CC
FAL
Instruction
Final
Assessment
MARS Task
2 days
1 day
Apprentic
e Task
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© SVMI
TASKS, TOOLS, TALK
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LESSONS
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RE-ENGAGEMENT