1. California’s Common Core State Standards (CCSS Extending Textbook Problems
Presented by:
Courtney Fox – Project Facilitator – Desert Sands Unified School District
Sally Miller – Project Facilitator – Desert Sands Unified School District

2. Standards for Mathematical Practice SMP’s
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of the others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning 2 3
Sally

3. Standards for Mathematical Practice . . .
College instructors rate the Mathematical Practices as being of higher value for students to master in order to succeed in their courses than any of the CCSS content standards.
If a student becomes proficient at the SMPs, he/she can learn any content.
To change students’ ways of thinking, we must first change how we teach.
We need to ask ourselves . . .in my math class, who is doing the talking? Who is doing the math?
The value of the common core is only as good as the implementation of the mathematical practices.
Once you show them how, you cannot find out how they are thinking.
When a child makes a mistake, they are showing a way of thinking that needs to be addressed to the whole class.
When you’re planning, think about “what task can I give to build understanding, rather than how can I explain clearly so they will understand.”

4. Going to the Zoo
32 children and 4 teachers are taking a mini-bus to the San Diego Zoo. The teachers will sit 2 to a seat and the students will have to sit either 2 or 3 to a seat. The bus has 16 seats. How many children will have to sit two to a seat, and how many children will have to sit three to a seat?
Sally

5. Solving It Algebraically
x = # of seats of students sitting 2 to a seat
y = # of seats of students sitting 3 to a seat
x + y = 14
2x + 3y = 32
Sally

6. 5 minute video on precision from a 5th grade classroom – I don’t think the grade level matters. How do will follow up after the video (if we use it).

7. SMP #2 Reason abstractly and quantitatively
DECONTEXTUALIZE
Represent the problem using charts, graphs, equations, expressions, number lines, manipulatives, pictures, etc.
How might you solve it?
Tallies
Picture
Multiplication
Division
Mathematical Problem
CONTEXTUALIZE
Pause as needed to refer back to the situation to make sure your answer makes sense.
Courtney
Reason Abstractly and Quantitatively

8. SBAC Example of SMP 2 – Grade 3
Contextualize to
Sally
Decontextualize
Example#1

9. SBAC Example of SMP 2 – Grade 5
Contextualize
Decontextualize
Sally
Example#2

10. SBAC Example of SMP 2 – Grade 6
Contextualize to
Decontextualize
Sally
Example#3

11. SBAC Example of SMP 2 – Grade 6
Decontextualize to
Contextualize
Sally
Example#4

12. 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.
Sally 12
California’s Common Core State Standards: Toolkit | Content and Curriculum, | Mathematics

13. Construct Viable Arguments Critique the reasoning of others
SMP #3: Construct viable arguments and critique the reasoning of others.
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
Courtney

14. SBAC Example of SMP 3 – Grade 4
Pablo solved a multiplication problem using two different methods. He made a mistake in either Method W or Method Z.
Sally
Identify the method where Pablo made a mistake and explain what he should do to correct it.
Example#5
Explain flawed logic of others

15. SBAC Example of SMP 3 – Grade 5
Explain your answer by relating the information in the table to the given equation.
Example#6

16. SBAC Example of SMP 3 – Grade 6
Justify your answer
Which measure of center, the mean or the median, is best to use when describing this data? Thoroughly explain your reasoning for choosing one measure over the other measure.
Sally
Example#7

17. SBAC Example of SMP 3 – Grade 7
Sally
Use a counter-example to justify your reasoning
Example#8

18. SBAC Example of SMP 3 – Grade 8
Sally
Example#9
Explain flawed logic of others

19. 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.
Sally 19
California’s Common Core State Standards: Toolkit | Content and Curriculum, | Mathematics

20. Extending a Text Problem
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 # _____
Courtney 20
Curriculum & Instruction
Steering Committee 20

21. HM Textbook – Elementary
SMP #2
Write a number sentence for this problem.
Solve the problem and show your work. (Don’t forget to label your answer.)
Did the farmer sell more or less than 700 pumpkins and squash. Write a number sentence to illustrate your answer.
Courtney

22. HM Textbook – Elementary
SMP #3
A teacher gave her students the following problem to solve:
A farmer sold 434 pumpkins and 226 squash. How many pumpkins and squash did he sell?
Sylvia said the answer is 660 and Caleb said the answer is 208.
Which student is correct?
Explain how you know.

23. Holt Textbook – Middle School
SMP #2
Write 2 different equations that could be used to find the perimeter of the horse pen. Explain why both equations solve the problem.
Courtney

24. Holt Textbook – Middle School
SMP #3
If Karen decides to make the pen 3 feet longer, how much more fencing will she need? Justify your answer with words and a picture.

25. Extending a Text Problem
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 # _____
Courtney 25
Curriculum & Instruction
Steering Committee 25

26. Extending a Text Problem
Courtney 26
Curriculum & Instruction
Steering Committee 26

27. Extending a Text Problem
Courtney 27
Curriculum & Instruction
Steering Committee 27

28. “The greatest sign of a success for a teacher...is to be able to say,
The children are now working as if I do not exist.”
-- Maria Montessori