Common Core Standards ForMathematics

MATHEMATICAL PRACTICES

45 States and District of Columbia have adopted CCSS

Quick Update

FCUSD Implementation Plan (review)

Two Types of Math Standards Within Common Core

Standards for Mathematical Practice

Describe varieties of expertise that educators should seek to develop in

their students

Identify processes and proficiencies that are

hallmarks of mathematically proficient

students

Remain the same throughout all grades K-12

9-12 standards organized by

conceptual category

(NOT by course)

K-8 grade level standards

Common Core Standards Overview

Mathematical Practices

Domain

Standards

Standards for Mathematical Practice

HABITS OF

MIND

CCSS Mathematical Practices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of 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.

Standards for Mathematical Practice

PLAY

1. MAKE SENSE OF PROBLEMS AND PERSEVERE IN SOLVING THEM.

Students need to develop a “puzzler’s disposition” Give them a chance to puzzle things out using what

they know Remember: mysteries are fun but not if someone tells you

the answer before you even try to solve it!

Too often students jump in to attempt a solution too fast. They just want to “do” something to the numbers.

Modify questions so they ask for more thought and not only for a numeric “answer.”

Common type of fraction problem:

What fraction of the bar is shaded blue?

What kind of mathematical thinking was required?

• Procedural• Definitional

What fraction of the white strip is the pink strip?

Promoting Mathematical Thinking

What kind of mathematical PRACTICES did the fraction problems require?

Math Practice 1: Make sense of problems and persevere in solving them.

Math Practice 2: Reason abstractly and quantitatively.

Math Practice 3: Construct viable arguments and critique the reasoning of others.

Math Practice 5: Use appropriate tools strategically. Math Practice 6: Attend to precision.

Much more attention than “mathematical reasoning” standards

Finding Mathematical Practices in our current program

Transitioning to Mathematical Practices with our current resources

Look at a problem-solving lesson in your TE

Tweak the lesson to make it more aligned to the mathematical practices.

What if you let the students work on the problem before you showed them each step to take?

Question from our book:

What number do these base ten blocks represent?

Incorporating Math Practices

Can you find a way to make 124 using only tens and ones?

Can you find a different way?

Find as many ways as you can to make 124 using hundreds, tens, and ones.

If you think you have found all the ways, explain how you know your list is complete?

3. Construct viable arguments and critique the reasoning of others.

Students talk about math and explain their thinking.

They construct arguments using concrete referents such as objects, drawings, diagrams, actions.

Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

One kind of task that naturally “pulls” children to explain is a “How many ways can you…” task.

Textbook activity

• In your TE find a “Talk About It” exercise.

• Work with a partner: if necessary, how can you make it a more mathematically rich discussion?

Mathematical Practices 3:Construct viable arguments

and critique the reasoning of others.

“What are the factors for 12?”

Find two numbers whose factors include 2, 3, 4, 6.

How are the two numbers related?

Putting it into Practice

Work to develop new “habits of mind” Give kids the background necessary to puzzle

through problems Use the resources you have: tweak it here

and there Lots of information on the internet Continuing professional development through

district and Sacramento County Office of Education

For more information: Common Core State Standards initiative:

www.corestandards.org

California Common Core Standards:

www.cde.ca.gov/ci/cc/

Assessment:

www.smarterbalance.org

Mathematical Practices:

http://thinkmath.edc.org

Common Core State Standards

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