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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

[email protected]

Presented by:

Courtney Fox – Project Facilitator – Desert Sands Unified School District

Sally Miller – Project Facilitator – Desert Sands Unified School District

[email protected]

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