COMMON CORE STANDARDS – MATHEMATICS

Course Sequence and Options for TUSD Middle Schools

Presentation Outline Switch Shifts in the Common Core Recommendations for TUSD Why take this path? Addressing acceleration Moving forward with next

steps

Making the Switch

Background The implementation of the Common

Core State Standards in Math (CCSSM) requires rethinking not only course content, but also course sequencing.

The CCSSM are greatly accelerated, more rigorous, and contain more content than the 1997 Content Standards.

Common Core Standards Mathematics

Three Major Shifts• Places strong emphasis on the

new grade-level and course-level standards (Shift in content)

Focus

• Think across grades and link major topics in each grade

Coherence

• Higher order thinking and application to real-world situations and problems

Rigor

Common Core Standards Mathematics

Grades 6 – 8 • Algebraic concepts, geometric

concepts, ratio, proportion, rates, percent, and statistics and probability within a spiral curriculum

Focus

• Extending operations with fractions to rational numbers

Coherence

•Foundational concepts of Algebra•Expectations of fluency with expressions and linear equations

Rigor

Common Core Standards Mathematics

Higher Mathematics (9 – 12)

• Mathematics that students need for success in college and careers

Focus

• Extending from algebraic concepts to calculus, trigonometry, and advanced probability and statistics

Coherence

• Expectation that students are college and career ready and able to utilize mathematics in their lives

Rigor

2013 California Framework

Progression SequenceProgression of Mathematics Courses

K - 5

• Kindergarten

• Grade 1

• Grade 2

• Grade 3

• Grade 4

• Grade 5

6 – 8

• Grade 6

• Grade 7

• Grade 8

Higher Math (9 –

12) • Algebra I

• Geometry

• Algebra II

Advanced Math

AP Probability & Statistics

Calculus

TUSD Additional Offerings:

Intermediate Algebra II

Pre-Calculus

AP Calculus AB

AP Calculus BC

Applied Calculus

IB Math SL

Comparing Old to New

1997 Framework• On Grade Level:

• Grade 6 - Math• Grade 7 - Pre-

Algebra• Grade 8 - Algebra I

• Not On Grade Level:• Grade 8 - General

Math (for students not enrolled in Algebra I, penalty on API for General Math test)

2013 CCSS Framework

• On Grade Level:• Grade 6 Math• Grade 7 Math• Grade 8 Math

• Algebra I moved to high school

• Grade 8 students in Algebra I take the Grade 8 Math SBAC test

Recommendation for TUSD

Traditional Course

Pathway

•Grade 6 Math•Grade 7 Math•Grade 8 Math

Accelerated Course

Pathway• Grade 6

• Grade 6 Math• First 1/2 of Grade 7

Math • Grade 7

• Second 1/2 of Grade 7 Math

• Grade 8 Math• Grade 8 - Algebra I

Two Course Pathways for Students

Packs Algebraic skills over 3 years to build strong

conceptual skills.

Why take this path?

Math Subject Area Council – Standards Analysis

Teacher representatives from all schools, grade levels, and math courses participated

Examined the CCSS standards and compared them to the 1997 standards

Found great differences in the CCSS, particularly in middle school grades

Differences were noted in an expanded curriculum, greater depth and complexity, significant content shifts, emphasis on literacy, and first instances of spiral curriculum for high school Geometry (6th grade)

CST vs. CCSS Standards

1997 Algebra I – 2.0 Students understand and use such operations as

taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

CCSS Algebra I - N-RN.1 Explain how the definition of the meaning of rational

exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

Rigor

New CCSS Standard

•Algebra I – IF-F.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Corresponding 1997 Standard

•Trigonometry - 2.0 Students know the definition of sine and cosine as y-and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.•Calculus - 9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

Grade 8 CCSS Mathematics

The Grade 8 CCSS Math contain a large number of accelerated 1997 Content Standards:

Algebra I (26) Geometry (11)

Statistics, Data Analysis, and Probability (5) moved from Grade 7 Math

Plus 6 Completely New Math Standards

Algebra 1 Analysis Results

The CCSS for Algebra I contain a large number of accelerated 1997 Content Standards:

Algebra II (15) AP Probability and Statistics (6) Probability and Statistics (5) Pre-Calculus (1) Calculus (2) Trigonometry (3) Algebra I (60)

Plus 19 Completely New Algebra I Standards

Addressing acceleration

Goals

Increase the number of students taking four years of high school mathematics.

Maintain or increase the number of students taking Advanced Placement and other advanced high school mathematics courses.

Any acceleration should take into consideration a commitment of four years of high school mathematics.

• Successful transitions beyond high school, without the need for remediation, are in part dependent on students’ consistent math enrollment throughout high school. (WestEd, 2013)

• Irrespective of students’ math performance, taking four years of high-school math strengthens their postsecondary and employment opportunities in STEM-related fields. (WestEd, 2013)

Challenges to Acceleration

42%of TUSD’s 2013-14 students in Grade 12 are currently

enrolled in

an advanced math course in their 4th year of high school math.

(AP Calculus AB/BC, IB Math SL, Applied Calculus, AP Statistics, Pre-Calculus)

57%of TUSD’s 2013-14 students in Grade 12 are currently

enrolled in

their 4th year of high school math.

Senior Year

Junior Year

Sophomore Year

Freshmen Year

8th GradeYear

7th Grade Year

6th Grade Year

5th GradeYear

Math 5*

Math 6A*

Math 6

Math 7A*

Math 7 Math 8 GeometryAlgebra 1

Algebra 1*

* Signifies a course with an end of year mastery exam.

Geometry Algebra 2 Pre-CalcAP Calc

BC

Algebra 2

Pre-Calc

AP Calc AB

AP Statistics

IB Math SL

Finite Math

Applied Calculus

Accelerated Path

Traditional Path

Two Pathways – Four Years of High School Math

Honors Option Courses

Is Middle School Acceleration Possible?

1 •Advancing students through the sequence requires compacted courses without omitting content.

2 •Skipping standards is not recommended, as students will miss foundational skills.

3 •The creation of compacted courses must include all standards (i.e. covering and mastering content for more than one grade level in one school year).

Challenges to Acceleration

42-minute class periods in middle school equate to one lost class period per week as compared to high school length periods.

More content needs to be covered in these 42 minutes.

Acceleration may require a two-period math structure to accommodate the sheer amount of content involved with compacting 1.5 years of content into one school year.

Although accelerated Grade 8 students may take Algebra I, at this time Grade 8 students will take the Grade 8 Mathematics Smarter Balanced Assessment.

Decisions to accelerate students, especially in middle school, should be carefully considered.

• Solid evidence of mastery of prerequisite standards should be required; diagnostic testing can help identify strengths and challenges in particular areas of math content (WestEd, 2013).

Recommendation

Traditional Course

Pathway

•Grade 6 Math•Grade 7 Math•Grade 8 Math

Accelerated Course

Pathway• Grade 6

• Grade 6 Math• First 1/2 of Grade 7

Math • Grade 7

• Second 1/2 of Grade 7 Math

• Grade 8 Math• Grade 8 - Algebra I

Two Course Pathways for Students

Packs Algebraic skills over 3 years to build strong

conceptual skills.

Our Plan for 2013-141 • Obtain Board direction.

2• Create bridge course

support for 2013-14 to close the gaps.

3• Create curriculum for grades 6/7

and 7/8 combined classes to support acceleration for the 2014-15 school year.

4• Develop assessments

(placement, interim, and end-of-course).

5• Rename courses and update

Course Catalog for 2014-15.

6• Communicate and elicit

feedback from our community.