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 courtney.fox@dsusd.us sally.miller@dsusd.us

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

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. https://www.teachingchannel.org/videos/class-warm-up-routine 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.”

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

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

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).

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 http://www.pd360.com/index.cfm?ContentId=7298

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

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

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

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

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, 6-12 | Mathematics

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 http://www.pd360.com/index.cfm?ContentId=7289

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

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

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

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

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

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, 6-12 | Mathematics

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

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

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.

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

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.

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

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

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

“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