Creating a Transition CCSSM Unit Example of a unit on
expressions and equations SVMI Slide 2 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
Slide 3 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. Slide
4 Middle School Curriculum Slide 5 Slide 6 Expression and Equations
-2x + 7 = y 3x 5 A Mathematical Big Idea Slide 7 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. Slide 8 Unit of Study Around a Big Idea Pre- assessment
MARS Task Instruction Final Assessment MARS Task Instruction POM or
Expert Investigation CC FAL 1 day2 days1 day5 - 10 days Math Talks
Slide 9 Unit of Study Around a Big Idea Pre- assessment MARS Task
Instruction Final Assessment MARS Task Instruction POM or Expert
Investigation CC FAL 1 day2 days1 day5 - 10 days Math Talks We are
Here Slide 10 Slide 11 Unit of Study Around a Big Idea Pre-
assessment MARS Task Instruction Final Assessment MARS Task
Instruction POM or Expert Investigation CC FAL 1 day2 days1 day5 -
10 days Math Talks We are Here Slide 12 MATH TALKS Slide 13 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 Slide 14 Math Talk If the
lime and cherries are single digits, what are their values? Slide
15 Math Talk If the grape is a single digit, what values could the
grape be? Slide 16 Math Talk If the plum and orange are single
digits What are their values? Slide 17 Unit of Study Around a Big
Idea Pre- assessment MARS Task Instruction Final Assessment MARS
Task Instruction POM or Expert Investigation CC FAL 1 day2 days1
day5 - 10 days Math Talks We are Here Slide 18 Problems of the
Month A program to foster school-wide participation in math and
problem solving. Slide 19 CCSS Mathematical Practices OVERARCHING
HABITS OF MIND 1. Make sense of problems and persevere in solving
them 6. Attend to precision REASONING AND EXPLAINING 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 Slide 20 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.
Slide 21 Its better to solve one problem five different ways than
to solve five different problems. George Polya Slide 22 Slide 23
Slide 24 Slide 25 Slide 26 Slide 27 A problem is not a problem if
you can solve it in 24 hours. George Polya Slide 28 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. Slide 29
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. *Remember to
justify or explain your processes you have used so far and why they
make mathematical sense as clearly as you can. Slide 30 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. Slide 31 Unit of Study Around a
Big Idea Pre- assessment MARS Task Instruction Final Assessment
MARS Task Instruction POM or Expert Investigation CC FAL 1 day2
days1 day5 - 10 days Math Talks We are Here Slide 32 P-32 Slide 33
P-33 Slide 34 P-34 Slide 35 P-35 Slide 36 Writing Algebraic
Expressions P-36 Area of rectangle = _ _ _ _ _ _ _ _ _ _ _ _ Slide
37 Writing Algebraic Expressions P-37 Perimeter of rectangle = _ _
_ _ _ _ _ _ _ _ _ _ Slide 38 Writing Algebraic Expressions P-38
Which two expressions are equivalent? Slide 39 Which Equations
Describe The Story? P-39 A pencil costs $2 less than a notebook. A
pen costs 3 times as much as a pencil. The pen costs $9 Which of
the four equations opposite describe this story? Let x represent
the cost of notebook. Slide 40 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 Slide 41
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 P-41 Slide 42 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. P-42
Slide 43 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. P-43 Slide 44 Matching Stories and Equations (Class) P-44
Slide 45 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 P-45 Slide 46 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 side- by-side in the
appropriate quadrant. Write an explanation to show how you arrived
at the equation match to your story situation. P-46 Slide 47
Showing Steps to Solving Equations Once youve 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 side- by-side in the appropriate quadrant. Write an
explanation to show how you arrived at the equation match to your
story situation. P-47 Slide 48 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. P-48 Slide 49 P-49 Slide 50 Unit
of Study Around a Big Idea Pre- assessment MARS Task Instruction
Final Assessment MARS Task Instruction POM or Expert Investigation
CC FAL 1 day2 days1 day5 - 10 days Math Talks We are Here Slide 51
Apprentic e Task Slide 52 Slide 53 Slide 54 2013-2014 SVMI TASKS,
TOOLS, TALK54
