California’s Common Core State Standards (CCSS Extending Textbook Problems 1 [email protected] Presented by: Courtney Fox – Project Facilitator – Desert Sands Unified School District Sally Miller – Project Facilitator – Desert Sands Unified School District [email protected]
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California’s Common Core State
Standards (CCSS
Extending Textbook Problems
1
Presented by:
Courtney Fox – Project Facilitator – Desert Sands Unified School District
Sally Miller – Project Facilitator – Desert Sands Unified School District
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of the others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
3
2
Standards for Mathematical Practice SMP’s
SMP #2 Reason abstractly and
quantitatively
SBAC Example of SMP 2 – Grade 6
4
Grade 6
Claim 2
DOK 2
Contextualize
Decontextualize
Go back to the
Context of the
problem
SBAC Example of SMP 2 – Grade 6
5
Grade 6
Claim 1
DOK 1
Contextualize
to
Decontextualize
SBAC Example of SMP 2 – Grade 6
6 Grade 6 Claim 1 DOK 1
Decontextualize
to
Contextualize
Next Steps
• Think about what you learned in regards
to SMP #2.
• Decide on one thing you will do
differently in your classroom to create
opportunities for your students to
practice SMP #2.
• Share your ideas with a partner.
7
SMP #3: Construct viable arguments
and critique the reasoning of others.
8
Construct Viable
Arguments
Analyze problems to make
conjectures
Justify answers Explain with
examples and non-examples
Explain
Why Critique the reasoning of others
Listen to and ask questions
of others Compare the arguments of
others
Identify and explain flawed logic of others
Ask
Why
SBAC Example of SMP 3 – Grade 6
9
Grade 6
Claim 3
DOK 3
Justify your
answer
SBAC Example of SMP 3 – Grade 7
10
Grade 7
Claim 3
DOK 3
Use a counter-
example to justify
your reasoning
SBAC Example of SMP 3 – Grade 8
11
Grade 8
Claim 3
DOK 3
Explain flawed logic of others
SBAC Example of SMP 3 – Grade 8
12
Grade 8
Claim 3
DOK 2
Explain flawed logic with a counter
example
Next Steps
• Think about what you learned in regards
to SMP #3.
• Decide on one thing you will do
differently in your classroom to create
opportunities for your students to
practice SMP #3.
• Share your ideas with a partner.
13
Big Ideas of the SMP’s
14
Students justify their answer using academic
vocabulary (verbally and in writing).
Students look for multiple ways to solve a problem.
Students work in collaboration (listening to others,
questioning others and presenting with others).
Students continually ask “Does my answer/process
make sense?”
Students apply their math skills to real world
situations.
Talking Math = Learning Math
Quotes from Phil Daro . . .
15
In reference to the SMPs . . .”these are
definitions of math expertise and
expertise develops over time in
complex ways, it is not just something
you learn.”
“These are practices of students, not
teaching practices, yet they have direct
implications for teaching practices.”
Extending a Text Problem
16
Extending a Text Problem to Access a Mathematical Practice
Grade ____
1. Choose a problem from a lesson that typifies computational practice-a routine problem in most lessons. 2. Describe how you might extend it to access a specific practice. 3. Using the same problem, extend it again to access a different practice.
Problem Extension Modification for
Practice # _____
Extension Modification for
Practice # _____
Grade 7 Page 8 Question 20
17
x + 4.3 for x = 6 SMP 3
After evaluating the expression shown above:
Martin got the answer x = 10.3
Lucia got the answer x = 4.9
Which answer is correct and explain how you know.
or
Which answer is incorrect and explain the mistake
that was made.
Scaffold opportunity: Sentence Frame
I know ___________ answer is correct because
when I substitute _______ in for x, I get the answer
_____.
I know ______ answer is correct because ________.
and/or
Differentiate the math task by changing the difficulty
of the math expression.
* When the focus of the problem is the justification or
explanation, keep the “math” simple.
Holt Textbook – Grade 7
18
SMP 2
Write a word problem that could be solved using the
expression x + 4.3
Solve the expression and explain how the value of
the expression changes as the value for x changes in
relation to your problem.
Scaffold opportunity (conceptual):
Change the 4.3 to a whole number (4)
Holt Textbook – Grade 6
19
Extension for SMP #2
In order to solve the problem, will you
change the fraction to a decimal or the
decimal to a fraction? Explain why. Solve
the problem and show your work.
Extension for SMP #3
Miles filled two bags with old toys when
he cleaned the attic. The first bag weighs
5.40 pounds and the second weighs
Which bag weighs more? (work from Learner
A is provided.)
Look at the work from learner A and
answer the following questions:
Do you understand how Learner A worked
the problem? If so, explain his/her work.
If not, what questions would you ask
Learner A.
SMP 3 Questions from SBAC Samples
20
Extending a Text Problem – on your own . . .
21
Problem Extension Modification for
Practice # _____
Extension Modification for
Practice # _____
Select a “textbook problem” from the handout and extend it for
SMP #2 and/or SMP #3.
Selling a Mobile App
22
Proportional Relationships in Selling a Mobile App
23
“The greatest sign of a success for a teacher...is to be able to say,
The children are now working as if I did not exist.”
-- Maria Montessori
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