Presentation on theme: "California’s Common Core State Standards (CCSS Extending Textbook Problems Presented by: Courtney Fox – Project Facilitator – Desert Sands Unified School."— Presentation transcript:
1 California’s Common Core State Standards (CCSS Extending Textbook Problems Presented by:Courtney Fox – Project Facilitator – Desert Sands Unified School DistrictSally 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 quantitativelyConstruct viable arguments and critique the reasoning of the othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoning23Sally
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. https://www.teachingchannel.org/videos/class-warm-up-routineWhen 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 Zoo32 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 seaty = # of seats of students sitting 3 to a seatx + y = 142x + 3y = 32Sally
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 DECONTEXTUALIZERepresent the problem using charts, graphs, equations, expressions, number lines, manipulatives, pictures, etc.How might you solve it?TalliesPictureMultiplicationDivisionMathematical ProblemCONTEXTUALIZEPause as needed to refer back to the situation to make sure your answer makes sense.CourtneyReason Abstractly and Quantitatively
8 SBAC Example of SMP 2 – Grade 3 ContextualizetoSallyDecontextualizeExample#1
9 SBAC Example of SMP 2 – Grade 5 ContextualizeDecontextualizeSallyExample#2
10 SBAC Example of SMP 2 – Grade 6 ContextualizetoDecontextualizeSallyExample#3
11 SBAC Example of SMP 2 – Grade 6 DecontextualizetoContextualizeSallyExample#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.Sally12California’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 ArgumentsAnalyze problems to make conjecturesJustify answersExplain with examples and non-examplesExplainWhyCritique the reasoning of othersListen to and ask questions of othersCompare the arguments of othersIdentify and explain flawed logic of othersAskWhyCourtney
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.SallyIdentify the method where Pablo made a mistake and explain what he should do to correct it.Example#5Explain 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 answerWhich 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.SallyExample#7
17 SBAC Example of SMP 3 – Grade 7 SallyUse a counter-example to justify your reasoningExample#8
18 SBAC Example of SMP 3 – Grade 8 SallyExample#9Explain 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.Sally19California’s Common Core State Standards: Toolkit | Content and Curriculum, | Mathematics
20 Extending a Text Problem Extending a Text Problem to Access a Mathematical PracticeGrade ____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.ProblemExtension Modification forPractice # _____Courtney20Curriculum & InstructionSteering Committee20
21 HM Textbook – Elementary SMP #2Write 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 #3A 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 #2Write 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 #3If 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 PracticeGrade ____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.ProblemExtension Modification forPractice # _____Courtney25Curriculum & InstructionSteering Committee25
26 Extending a Text Problem Courtney26Curriculum & InstructionSteering Committee26
27 Extending a Text Problem Courtney27Curriculum & InstructionSteering Committee27
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
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