making sense of the new standards k-12 alliance staff developer training january 25, 2013

Making SenseOf 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

21st Century Skills

ELA

Activity

• Choose a secret number (don’t 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


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 •••


I pulled off the cup •••

You have three Voila!

Words Manipulatives Algebra Expressions/Result


Cup n

Add 5

Double that sum

Subtract 4

Divide by 2


You have three



Cup n

Add 5 Cup • • • • • N+5

Double that sum

Subtract 4

Divide by 2


You have three



Cup n

Add 5 Cup • • • • • N+5

Double that sum Cup •••••Cup •••••

2(n+5) = 2n + 10

Subtract 4

Divide by 2


You have three



Cup n

Add 5 Cup • • • • • N+5


2(n+5) = 2n + 10

Subtract 4 Cup•••Cup•••

2n + 10 – 4= 2n+6

Divide by 2


You have three



Cup n

Add 5 Cup • • • • • N+5


2(n+5) = 2n + 10


2n + 10 – 4= 2n+6

Divide by 2 Cup••• (2n+6)/2 = n + 3


You have three



Cup n

Add 5 Cup • • • • • N+5


2(n+5) = 2n + 10


2n + 10 – 4= 2n+6

Divide by 2 Cup••• (2n+6)/2 = n + 3


••• N + 3 – n = 3

You have three



Cup n

Add 5 Cup • • • • • N+5


2(n+5) = 2n + 10


2n + 10 – 4= 2n+6

Divide by 2 Cup••• (2n+6)/2 = n + 3


••• N + 3 – n = 3

You have three Yes, I do. 3

8th Grade Expectation

Words Results Cumulative Expression


n n

Add 5 N+5 N+5

Double that sum 2(n+5) = 2n+10 2(n+5)

Subtract 4 2n + 10 – 4 = 2n+6

2(n + 5) – 4

Divide by 2 (2n+6)/2 = n + 3 2


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 Connections7 ------> 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 Back5—4—3—2—1—Kinder!

• 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

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

Which of These Describe your work on the “Trick”?

Common Core Math Standards

1997 CA. Math Standards

29

CCSS Requires Three Shifts in Mathematics

1. Focus: Focus strongly where the standards focus.

2. Coherence: Think across grades, and link to major topics

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

30

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.

31

GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2Addition and subtraction - concepts, skills, and problem solving and place value

3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

Key Areas of Focus in Mathematics

Grade Shifts: Examples

Concept1997

Standards

CCSS

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

Grade2

K

Introduction to ProbabilityGrade

3Grade

7

Introduction of fractions as numbers

Grade2

Grade3

Add and subtract simple fractions

Grade3

Grade4

33

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

34

• 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)

35

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

36

37

Required Fluencies in K-6

GradeStandard

Required Fluency

K K.OA.5 Add/subtract within 51 1.OA.6 Add/subtract within 10

22.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

33.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,0005 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3Multi-digit divisionMulti-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.38

making sense of the new standards k-12 alliance staff developer training january 25, 2013

Documents