Vertical AlignmentProfessional Development

February 8, 2012Northern Vance High School

Where We’ve Been

Introduction to Common Core/NC Essential Standards

Mathematical Practices

CLOSE Reading Technique

What’s Next

Today’s PurposeTo explore the format of the Common Core State Standards for Mathematics

To examine the vertical alignment of instruction and assessments to ensure that course expectations (2012-2013) are appropriately aligned to Common Core State Standards.

Key ideas

Common core state standards are research based.

The sequence of topics respects what is known about how children learn and develop over time.

The intent is for students to “understand”, not just do.

All students must have the opportunity to learn the same high standards.

Naming the standardsWhat does 7.G.3 tell you?

Grade level Standard number

7.G.3

Domain

This is the third 7th grade Geometry standard.

High school standards (math 1)These standards have a slightly different naming

convention.

Conceptual category Standard number

A-CED.3

Domain

This standard is from the Algebra category and the Creating Equations domain. It is standard #3.

Accessing YOUR Standards Go to the VCS Moodle site

Click on Instructional Technology from the Course Categories

Click on Common Core & NC Essential

Standards

Select Common Core State

Standards for Math from the

Mathematics section

CLOSE Read

Closely read p. 5 of the CCSS, “How to read the grade level standards”.

List 3 key ideas from the page.

Share your ideas with others at your table.

Each table will report 2 ideas.

Key fact!!!!

“These standards are not intended to be new names for old ways of doing business.”

The standards for mathematical practice are crucial here.

Our standards are organized into FIVE Conceptual Categories:

• Number and Quantity• Algebra

• Functions• Geometry

• Statistics and Probability

Modeling Standards Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a

Standard for Mathematical Practice, and specific modeling standards appear the high school standards indicated by

a star symbol (★).

A Close Look at the

Knowing where to find information is just as

important as knowing the information.

Using the Common Core State Standards in

Mathematics, search with others around you to navigate through the conceptual categories and answer the questions on

the handout provided

A Close Look at the

HIGH SCHOOL INTRODUCTION

Approximately

5 mins.

High School Introduction p.57 1. What symbol indicates the mathematics that

students need to take advanced courses? The symbol, “+”

2.  What does a * symbolize in the standards? Modeling standard

 3. What does it mean if a cluster heading has a *? All standards in that cluster are modeling

standards

A Close Look at the

NUMBER AND QUANTITY

Approximately

13 mins.

Number & Quantity p.58 – 59  

4. …how will the numbers systems be extended for high school students?

Imaginary and complex numbers are introduced 5. …what are the two ways that number systems remain the same?

They all have communicative, associative, and distributive properties

Their new meanings are consistent from before.

  6. Read the subsection Quantities and explain the process of quantification.

The analysis of attributes of interests by determining their quantity (value) as determined by the context of

the problem.

Number & Quantity cont. p.58 – 59 7.

Domain Cluster No. of Standards

No. of Advanced Standards

The Real Number System

N-RN

• Extend the properties of exponents to rational exponents 2 0

• Use properties of rational and irrational numbers. 1 0

QuantitiesN-Q • Reason quantitatively and use units to solve problems 3 0

The Complex Number System

N-CN

• Perform arithmetic operations with complex numbers 2 1

• Represent complex numbers and their operations on the complex plane 0 3

• Use complex numbers in polynomial identities and equations 1 2

Vector and Matrix Quantities

N-VM

• Represent and model with vector quantities. 0 3

• Perform operations on vectors. 0 2

• Perform operations on matrices and use matrices in applications. 0 7

Number & Quantity p.58 – 59 8. List one standard or cluster that indicates a strong correlation to

the MODELING standard.

N-Q #1-3 (Quantities Cluster)

ALGEBRA

Approximately

17 mins.

Algebra pg. 62 – 63

9. What are the three subsections highlighted in the introduction? Expressions Equations & inequalities Connections to Functions and

Modeling

Algebra cont. pg. 62 – 63

Domain ClusterNo. of

Standards

No. of Advanced Standard

s

Seeing Structure in ExpressionsA-SSE

• Interpret the structure of expressions 2 0

• Write expressions in equivalent forms to solve problems

2 0

Arithmetic with Polynomials and Rational Expressions

A-APR

• Perform arithmetic operations on polynomials 1 0

• Understand the relationship between zeros and factors of polynomials

2 0

• Use polynomial identities to solve problems 1 1

• Rewrite rational expressions 1 1

Creating EquationsA-CED

• Create equations that describe numbers or relationships

4 0

Reasoning with Equations and Inequalities

A-REI

• Understand solving equations as a process of reasoning and explain the reasoning 2 0

• Solve equations and inequalities in one variable 2 0

• Solve systems of equations 3 2

• Represent and solve equations and inequalities graphically 3 0

Algebra cont. pg. 62 – 63

11. List one standard or cluster that indicates a strong correlation to the MODELING standard.

A-SSE #1, 3, & 4 A-CED #1-4 A-REI #11

FUNCTIONSApproximatel

y 10 mins.

Domain Cluster No. of Standards

No. of Advanced Standards

Interpreting FunctionsF- IF

• Understand the concept of a function and use function notation 3 0

• Interpret functions that arise in applications in terms of the context 3 0

• Analyze functions using different representations 3 1 (#7d)

Building FunctionsF-BF

• Build a function that models a relationship between two quantities

2 1 (#1c)

• Build new functions from existing functions 22 (#4b-d

& 5)

Linear, Quadratic, and Exponential Models

F-LE

• Construct and compare linear, quadratic, and exponential models and solve problems

4 0

• Interpret expressions for functions in terms of the situation they model

1 0

Trigonometric FunctionsF- TF

• Extend the domain of trigonometric functions using the unit circle 2 2

• Model periodic phenomena with trigonometric functions 1 2

• Prove and apply trigonometric identities 1 1

12.

Functions cont. pg. 67 – 68

13. List one standard or cluster that indicates a strong correlation to the MODELING standard.

F – IF #4-7F – BF #1 & 2F – LE (all)

F – TF #5 & 7

MODELINGApproximatel

y 13 mins.

Modeling pg. 72 – 73

14. Complete the sentence from the first paragraph on pg. 72

Modeling is the process of CHOOSING _ and USING appropriate mathematics and statistics to

analyze EMPIRICAL situations.

15. Complete the sentence from the second paragraph on pg. 72Real-world situations are not ORGANIZED and

LABELED for analysis; formulating tractable MODELS , representing such MODELS , and analyzing them is appropriately a CREATIVE

process.

Modeling pg. 72 – 73

17. Compare descriptive modeling and analytic modeling as described on page 73

Descriptive – describes or summarizes existing phenomenaAnalytic – explain data based on theoretical ideas with

parameters based on the situational model.

PROBLEM

FORMULATE

COMPUTE INTERPRET

VALIDATE

REPORT

16.

DELING

GEOMETRYApproximatel

y 10 mins.

Domain ClusterNo. of

Standards

No. of Advanced Standards

CongruenceG-C

• Experiment with transformations in the plane 5 0

• Understand congruence in terms of rigid motions 3 0

• Prove geometric theorems 3 0

• Make geometric constructions 2 0

Similarity, Right Triangles, and Trigonometry

G-SRT

• Understand similarity in terms of similarity transformations

3 0

• Prove theorems involving similarity 2 0

• Define trigonometric ratios and solve problems involving right triangles

3 0

• Apply trigonometry to general triangles 0 3

CirclesG-C

• Understand and apply theorems about circles 3 1

• Find arc lengths and areas of sectors of circles 1 0

Expressing Geometric Properties with Equations

G-GPE

• Translate between the geometric description and the equation for a conic section

2 1

• Use coordinates to prove simple geometric theorems algebraically

4 0

Geometric Measurement and Dimension

G-GMD

• Explain volume formulas and use them to solve problems 2 1

• Visualize relationships between two-dimensional and three-dimensional objects

1 0

Modeling with GeometryG-MD • Apply geometric concepts in modeling situations 3 0

20.

Geometry cont. pg. 74 – 75

19.List one standard or cluster that indicates a strong correlation to the MODELING standard.

G – SRT #8G – GPE #7G – GMD #3G – MG #1-3

DELING

STATISTICS & PROBABILITY

Approximately

7 mins.

20. Why is there a star (*) in the title of this strand on page 79?

ALL STATISTICS AND PROBABILITY STANDARDS ARE ALSO MODELING STANDARDS

Domain Cluster No. of Standards

No. of Advanced Standards

Interpreting Categorical and Quantitative Data

S-ID

• Summarize, represent, and interpret data on a single count or measurement variable 4 0

• Summarize, represent, and interpret data on two categorical and quantitative variables 2 0

• Interpret linear models 3 0Making Inferences & Justifying Conclusions

S - IC

• Understand and evaluate random processes underlying statistical experiments 2 0

• Make inferences and justify conclusions from sample surveys, experiments and observational studies

4 0

Conditional Probability and the Rules of Probability

S-CP

• Understand independence and conditional probability and use them to interpret data 5 0

• Use the rules of probability to compute probabilities of compound events in a uniform probability model

2 2

Using Probability to Make Decisions

S-MD

• Calculate expected values and use them to solve problems 0 4

• Use probability to evaluate outcomes of decisions 0 3

21

FINAL SUMMATION TIME!

Domains Cluster No. of Standards

No. of Adv. Standards

Number and Quantity 4 9 9 18

Algebra 4 11 23 4

Functions 4 10 22 9

Geometry 6 15 37 6

Probability & Statistics 4 9 22 9

Grand Total! 22 54 113 46

Inch-deep

coverage

Lengthy

review

Definition of

insanity

Re-teaching at next level

The Current Dilemma

DAILY instructional

activities/lessons are aligned to state standards

The Solution

(Cohen, 1987; English & Steffy, 2001; Moss-Mitchell, 1998; Neidermeyer & Yelon, 1981; Porter et al., 1994; Porter & Smithson, 2001; Price-Braugh, 1997; Wishnick, 1989)

VERTICAL ALIGNMENTEstablishing and/or recognizing the scope and sequence

of course content to ensure…

An appropriate amount of time is devoted to instruction

Unnecessary repetitions are

removed

Gaps are indentified

Assessments are appropriate

Activity: Building a Map

• In two separate groups, remove the content of the envelope and place them on the table so that all members can read its statements

• Discuss what statements should be learned and/or mastered at each grade band (K-2, 3-5, 6-8 and 9-12) in regards to the Geometry Domain

Activity: Building a Map

• Have one group member keep notes of the conversations and/or questions that arise

• Once a group consensus has been made, arrange them on the table under the appropriate grade band

• Make note of how one statement may contribute to the understanding of another

Activity: Building a Map

• Have a group member share out the group’s progression map and discussions with the whole group

Compare your maps to the Common Core State Standards for Mathematics

K-2 Standards

K.G.2Correctly

name shapes regardless of

their orientations

or overall size.

1.G.3Partition

circles and rectangles into two and four equal shares, describe the shares using

the words halves, fourths, and quarters, and use the

phrases half of, fourth of, and

quarter of.

2.G.2Partition a

rectangle into rows and

columns of same-size

squares andcount to find

the total number of

them.

3-5 Standards

3.G.1Understand that shapes in different categories

4.G.1Draw points,

lines, line segments,

rays, angles

5.G.2Represent real world

and mathematical problems by

graphing points

in the first quadrant of

the coordinate plane, and interpret

coordinatevalues of

points in the context of the

situation

6-8 Standards

6.G.3Draw polygons

in the coordinate plane given

coordinates for the vertices

7.G.5Use facts

about supplementar

y, complementary, vertical,

and adjacentangles in a multi-step problem to write and

solve simple equations for an unknown angle in a

figure.

8.G.4Understand that a two-dimensional

figure is similar to another if

thesecond can be obtained from the first by a sequence of rotations,

reflections, translations, and dilations;

9-12 Standards

G.CO.3Given a

rectangle, parallelogram, trapezoid, or

regular polygon,

describe the rotations and

reflections that carry it onto

itself.

G.C.1Prove that all

circles are similar.

G.GPE.5Prove the slope

criteria for parallel and perpendicular lines and use them to solve geometric

problems

HOW DID YOUR GROUP DO?

Discuss your reactions and any misconceptions that

you/your group may have had.

Where We’re Going On next/last early release session will

be on Wednesday, March 21 at Northern

We will begin Unit/Assessment Planning and Locating Resources

There will be two days of Common Core/NC Essential Standards training for core teachers this summer – Dates TBA

Before you GO…

To submit an evaluation on today’s professional

development session:

• Return to the 1:1 Professional Development

VCS Moodle http://moodle.vcs.k12.nc/moodle

• Under the EVALUATION topic, select

“Professional Development (Feb. 8, 2012) EVALUATION”

*Hard copies are available for those

without laptops/internet

connection