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Making Sense Of The New Standards

- K-12 Alliance Staff Developer Training
- January 25, 2013

New Opportunities for All Learners

California Common Core State Standards (ELA and

Math)

Next Generation Science Standards

21st Century Skills

Prior Knowlege

- With your group discuss what you know about 21st

Century Skills, CCSS, and NGSS - What connections do you see?
- Chart your ideas. You will return to your

thinking on Sunday.

In The Classroom

Math

Science

ELA

21st Century Skills

Activity

- Choose a secret number (dont say it aloud)
- add 5 to that number
- double that sum
- subtract 4 from that product
- divide the results by 2
- subtract your secret number from the quotient
- you have 3.

How Did That Happen?

- What is behind this trick?
- Is it foolproof?
- Discuss your thoughts at your table.

Explain this trick

- Use the tools at your table to explain what you

think is happening. - Remember
- You may all have had different secret numbers.
- No matter what number you selected, you all ended

up with 3.

Transfer to a Whiteboard

- Think about how to use the tools to demonstrate

how the trick was done. - Use the white board to depict your demonstration.

Connect action to a direct model with a specific

Secret choice

Instructions What I did My model

Choose a secret number I chose 2 beans (2 beans)

Add 5 I added 5 more

Double that sum I multiplied by two

Subtract 4 Subtracted 4 beans

Divide by 2 I pulled half away

Subtract secret number I pulled off 2 beans

You have three I was astonished!

Connect action to a model for any choice (A set

of all secret numbers)

Instructions What I did My model

Choose a secret number I chose a cup to represent any Cup

Add 5 I added 5 beans Cup

Double that sum I multiplied by two Cup Cup

Subtract 4 Subtracted 4 beans Cup Cup

Divide by 2 I pulled half away Cup

Subtract secret number I pulled off the cup

You have three Voila!

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5

Double that sum

Subtract 4

Divide by 2

Subtract secret number

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum

Subtract 4

Divide by 2

Subtract secret number

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum Cup Cup 2(n5) 2n 10

Subtract 4

Divide by 2

Subtract secret number

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum Cup Cup 2(n5) 2n 10

Subtract 4 Cup Cup 2n 10 4 2n6

Divide by 2

Subtract secret number

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum Cup Cup 2(n5) 2n 10

Subtract 4 Cup Cup 2n 10 4 2n6

Divide by 2 Cup (2n6)/2 n 3

Subtract secret number

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum Cup Cup 2(n5) 2n 10

Subtract 4 Cup Cup 2n 10 4 2n6

Divide by 2 Cup (2n6)/2 n 3

Subtract secret number N 3 n 3

You have three

Words Manipulatives Algebra Expressions/Result

Choose a secret number Cup n

Add 5 Cup N5

Double that sum Cup Cup 2(n5) 2n 10

Subtract 4 Cup Cup 2n 10 4 2n6

Divide by 2 Cup (2n6)/2 n 3

Subtract secret number N 3 n 3

You have three Yes, I do. 3

8th Grade Expectation

Words Results Cumulative Expression

Choose a secret number n n

Add 5 N5 N5

Double that sum 2(n5) 2n10 2(n5)

Subtract 4 2n 10 4 2n6 2(n 5) 4

Divide by 2 (2n6)/2 n 3 2

Subtract secret number N 3 n 3 2

You have three 3 2(n 5) 4 -n 3 2

2(n 5) 4

2(n 5) 4 -n

Language Of Doing Math

- Which of these words best describes what I asked

you to do - Represent
- Solve
- Evaluate
- Simplify
- Determine
- Compare
- Find
- Explain

Instructional Words implication for process

- Represent To portray in another abstract way.
- Solve Finding an unknown quantity or

expression. - Evaluate To find the value of by substituting

values in an expression or function. - Simplify To make a math expression simpler.
- Determine Find or choose
- Compare Relate values of 2 or more expressions
- Explain Describe a process.
- Justify Support the logic of a process or

solution

Standards for Mathematical Content K-8

- How the grade level standards are organized

Standards Clusters Domains

7th Grade Common Core Standard Connection

- 7.EE.4. Use variables to represent quantities

in a real-world or mathematical problem, and

construct simple equations and inequalities to

solve problems by reasoning about the quantities.

Common Core Connections 7 ------gt 6

- 7th Grade (p. 31) 7.EE.4. Use variables to

represent quantities in a real-world or

mathematical problem, and construct simple

equations and inequalities to solve problems by

reasoning about the quantities. - 6TH (P. 26) 6.EE.6. Use variables to represent

numbers and write expressions when solving a

real-world or mathematical problem understand

that a variable can represent an unknown number,

or, depending on the purpose at hand, any number

in a specified set.

Follow the Standard Back 54321Kinder!

- Keep track of the standards you determine to be

in the line from Kindergarten to 5th grade and on

to Middle school. - Remember the key idea is representing (modeling)

a mathematical idea in a manner chosen by the

student.

Common Core Standards for Mathematics

- Two Types of Standards
- Mathematical Practice (recurring throughout the

grades) - Mathematical Content (different at each grade

level)

Standards for Mathematical Practice

- Make sense of problems and persevere in solving

them. - Reason abstractly and quantitatively.
- Construct viable arguments and critique the

reasoning of 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

Which of These Describe your work on the Trick?

Common Core Math Standards

1997 CA. Math Standards

CCSS Requires Three Shifts in Mathematics

- Focus Focus strongly where the standards focus.
- Coherence Think across grades, and link to major

topics - Rigor In major topics, pursue conceptual

understanding, procedural skill and fluency, and

application

Shift 1 Focus Strongly where the Standards Focus

- Significantly narrow the scope of content and

deepen how time and energy is spent in the math

classroom. - Focus deeply on what is emphasized in the

standards, so that students gain strong

foundations.

Key Areas of Focus in Mathematics

Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K2 Addition and subtraction - concepts, skills, and problem solving and place value

35 Multiplication and division of whole numbers and fractions concepts, skills, and problem solving

6 Ratios and proportional reasoning early expressions and equations

7 Ratios and proportional reasoning arithmetic of rational numbers

8 Linear algebra

Grade Shifts Examples

Concept 1997 Standards CCSS

Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle) Grade 2 K

Introduction to Probability Grade 3 Grade 7

Introduction of fractions as numbers Grade 2 Grade 3

Add and subtract simple fractions Grade 3 Grade 4

Shift 2 Coherence Think Across Grades, and

Link to Major Math Topics Within Grades

- Carefully connect the learning within and across

grades so that students can build new

understanding on foundations built in previous

years. - Begin to count on solid conceptual understanding

of core content and build on it. Each standard is

not a new event, but an extension of previous

learning.

Shift 3 Rigor Expect fluency, deep

understanding, and application

- The CCSSM require a balance of
- Solid conceptual understanding
- Procedural skill and fluency
- Application of skills in problem solving

situations - Pursuit of all threes requires equal intensity in

time, activities, and resources.

Solid Conceptual Understanding

- Teach more than how to get the answer and

instead support students ability to access

concepts from a number of perspectives - Students are able to see math as more than a set

of mnemonics or discrete procedures - Conceptual understanding supports the other

aspects of rigor (fluency and application)

Fluency

- The standards require speed and accuracy in

calculation. - Teachers structure class time and/or homework

time for students to practice core functions such

as single-digit multiplication so that they are

more able to understand and manipulate more

complex concepts

Required Fluencies in K-6

Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100

3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit division Multi-digit decimal operations

Application

- Students can use appropriate concepts and

procedures for application even when not prompted

to do so. - Teachers provide opportunities at all grade

levels for students to apply math concepts in

real world situations, recognizing this means

different things in K-5, 6-8, and HS. - Teachers in content areas outside of math,

particularly science, ensure that students are

using grade-level-appropriate math to make

meaning of and access science content.