Grade 8

Course Sequence and Options for TUSD Middle Schools

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

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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.

Focus

• Places strong emphasis on the new grade-level and course-level standards (Shift in content)

Coherence

• Think across grades and link major topics in each grade

Rigor

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

Focus

Coherence Rigor

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

• Extending operations with fractions to rational numbers

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

Focus

• Mathematics that students need for success in college and careers

Coherence

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

Rigor

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

Progression of Mathematics Courses K-5

6–8

Higher Math (9 – 12)

Advanced Math

• Kindergarten

• Grade 6

• Algebra I

AP Probability & Statistics

• Grade 1

• Grade 7

• Geometry

Calculus

• Grade 2

• Grade 8

• Algebra II

TUSD Additional Offerings:

• Grade 3

Intermediate Algebra II Pre-Calculus

• Grade 4

AP Calculus AB

• Grade 5

AP Calculus BC Applied Calculus IB Math SL

1997 Framework

2013 CCSS Framework

• On Grade Level: • Grade 6 - Math • Grade 7 - Pre-Algebra • Grade 8 - Algebra I

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

• Not On Grade Level: • Grade 8 - General Math

• Algebra I moved to high

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

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

Two Course Pathways for Students

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

Packs Algebraic skills over 3 years to build strong conceptual skills.

• Grade 8 - Algebra I

Why take this path?

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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)

1997 Algebra I – 2.0

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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.

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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.

New CCSS Standard

Corresponding 1997 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.

• 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.

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

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Algebra I (26) Geometry (11)

Statistics, Data Analysis, and Probability (5) moved from Grade 7 Math Plus 6 Completely New Math Standards

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

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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

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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)

57% of TUSD’s 2013-14 students in Grade 12 are currently enrolled in their 4th year of high school math.

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)

Two Pathways – Four Years of High School Math 5th Grade Year

6th Grade Year

7th Grade Year

8th Grade Year

Freshmen Year

Sophomore Year

Junior Year

Senior Year IB Math SL

Accelerated Path Math 6A*

Math 7A*

Honors Option Courses Algebra 1*

Geometry

Algebra 2

Pre-Calc

AP Calc AB AP Calc BC Applied Calculus

Math 5* AP

Statistics

Math 6

Math 7

Math 8

Algebra 1

Traditional Path

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Signifies a course with an end of year mastery exam.

Geometry

Algebra 2

Finite Math Pre-Calc

1 2 3

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

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

• 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).

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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).

Two Course Pathways for Students

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

Packs Algebraic skills over 3 years to build strong conceptual skills.

• Grade 8 - Algebra I

1

• 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.

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• Develop assessments (placement, interim, and endof-course).

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• Rename courses and update Course Catalog for 2014-15.

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• Communicate and elicit feedback from our community.