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Integrating Common Core Math into CTE Courses

2012 CTE Summer ConferenceDr. Mary A. Steltz

Presenter

July 25, 2012

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Common Core State Standards for Mathematics

“For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in theUnited States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise ofcommon standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.” These Standards are a substantial answer to thatchallenge” (http://www.corestandards.org/the-standards/mathematics)

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Agenda

• Who Am I? Who are you?

• Explanation of 8 Mathematical Practices

• Understanding the Common Core Standards

• Purpose of Session• Look at Mathematical

Vocabulary for Common Core

• Discussion, Fears and Anxiety about Common Core Implementation

• Take Away Activities, Strategies and Resources

• Assessment of Common Core and how CTE can help?

• Question and Answer Session

• Contact Information

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Who Am I? Who Are You?

• Doctorate in Curriculum & Instruction from GWU.

• Expansive training in Mathematics, Literacy, Business Education, Classroom Management, and Facilitative Leadership.

• 10-year teacher and resident of NC – from Arkansas.

• Wife, mother and grandmother.

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Mathematical Practices

• Video: http://www.youtube.com/watch?v=vJyZgeDeynM

• Understanding the Common Core Mathematical Standards (handout)

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Purpose

• Implementation of Common Core Standards for Mathematics in CTE Courses– What are the mathematical standards?

• http://www.corestandards.org/the-standards

• Implementation of Common Core Standards for Mathematics in CTE Courses– What are the mathematical standards?

• http://www.corestandards.org/the-standards

• Implementation of Common Core Standards for Mathematics in CTE Courses– What are the mathematical standards?

• http://www.corestandards.org/the-standards

• Implementation of Common Core Standards for Mathematics in CTE Courses– What are the mathematical standards?

• http://www.corestandards.org/the-standards (p.58)

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Mathematics Vocabulary:Middle School: 6th Grade

• Ratio• Unit rate• Tape diagram• Double number line• diagram• Percent• Greatest Common• Factor• Least Common• Multiple• Distributive Property• Integer• Positive Number• Negative Number• Opposite• Zero pair• Absolute value• Inequality

• Exponents• Term• Coefficient• Order of operations• Substitution• Dependent variable• Independent variable• Nets• Median• Mode• Range• Mean• Dot plot• Histogram• Box plot• Interquartile range• Mean absolute deviation

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Mathematics VocabularyMiddle School: 7th Grade

• Proportion• Simple Interest• Tax• Markup• Markdown• Percent of increase• Percent of decrease• Gratuities• Commissions• Percent error• Additive inverse• Multiplicative inverse• Scale drawing• Plane sections• Circumference

• Supplementary angles• Complementary angles• Vertical angles• Adjacent angles• Surface area• Sample population• Random sampling• Variability• Probability• Frequency• Simple event• Compound events• Tree diagram• Simulation

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Mathematics VocabularyMiddle School: 8th Grade

• Terminating decimal• Repeating decimal• Irrational number• Integer exponent• Square root• Cube root• Radical• Scientific notation• Slope• y-intercept• slope-intercept form• linear equation• like terms• simultaneous linear• equations• function• input• output• non-linear functions• rate of change• rotation

• Reflection• Translation• Congruent• Dilation• Similar figures• Transversal• Corresponding angles• Interior• Exterior• Pythagorean theorem• Cone volume formula• Cylinder volume• formula• Sphere volume• formula• Scatter plot• Outlier• Positive association• Negative association• Line of best fit• Bivariate measurement data

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Mathematics Vocabulary High School: Number and Quantity

• Fundamental theorem of Algebra• Vector• Initial point• Terminal point• Velocity• Parallelogram rule• Scalar multiplication• Matrices• Zero matrix• Identity matrix• Determinant

• Rational exponent• Complex number• Conjugate• Moduli• Imaginary number• Real number• Rectangular form• Polar form• Quadratic equation• Polynomial

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Mathematics VocabularyHigh School: Algebra

• Complete the square• Maximum• Minimum• Exponential function• Geometric series• Remainder Theorem• Binomial Theorem• Pascal’s Triangle• Logarithmic Function

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Mathematics VocabularyHigh School: Functions

• Domain• Range• Function notation• Fibonacci sequence• Recursive process• Intercepts• Increasing intervals• Decreasing intervals• Positive intervals• Negative intervals• Relative maximum• Relative minimum• Symmetries• End behavior• Periodicity• Rate of change• Step function• Absolute value function• Asymptote

• Exponential function• Logarithmic function• Trigonometric function• Period• Midline• Amplitude• Exponential growth• Exponential decay• Constant function• Arithmetic sequence• Geometric sequence• Invertible function• Radian measure• Arc• Sine• Cosine• Tangent

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Mathematics VocabularyHigh School: Geometry

• Angle• Circle• Perpendicular lines• Parallel lines• Line segments• Point• Line• Arc• Rigid motion• Congruent• Angle-Side-Angle• (ASA)• Side-Angle-Side (SAS)• Side-Side-Side (SSS)• Inscribed• Scale factor• Dilation• AA similarity Theorem• Law of Sines• Law of Cosines

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Mathematics VocabularyHigh School: Statistics and Probability

• Dot plot• Histogram• Box plot• Interquartile range• Standard deviation• Outlier• Frequency table• Relative frequency• Joint relative frequency• Marginal relative frequency• Conditional relative frequency• Residuals• Correlation• Causation• Correlation coefficient

• Sample survey• Experiment• Observational studies • Margin of effort• Simulation models• Subsets• Unions• Intersections• Complements• Independent• Conditional probability• 2-way frequency table• Addition Rule• Multiplication Rule• Permutations• Combinations• Theoretical probability

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Break Time (5 minutes)

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Vocabulary Test Anyone???

• Define Polynomial– www.spellingcity.com (specifically for

Common Core) review spelling, vocabulary, create activities and exams; and create word lists to help students learn or review vocabulary.

• Other Resources– www.mathwords.com

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HOW?

WHY?

Gaps in student knowledge between the current standard course of study and Gaps in student knowledge between the current standard course of study and common core will need to be addressed.common core will need to be addressed.

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http://www.youtube.com/watch?v=wtmZKy_XXVU

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CTE CAREER CLUSTERS (16)http://www.dpi.state.nc.us/docs/cte/standards/2012cteessentialstandards.pdf

• Agriculture, Food & Natural Resources

• Architecture & Construction

• Arts, A/V Technology & Communications

• Business Management & Administration

• Education &Training • Finance • Government & Public

Administration • Health Science

• Hospitality & Tourism • Human Services • Information Technology • Law, Public Safety,

Corrections & Security • Manufacturing • Marketing • Science, Technology,

Engineering & Mathematics

• Transportation, Distribution & Logistics

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20th Century vs. 21st Century

 20th Century Classrooms 

21st Century Classrooms

Time-based • Outcome-based

• Focus on memorization of discrete facts

• Focus on what students KNOW, CAN DO and ARE LIKE after all the details are forgotten

• Lessons focus on lower level of Bloom’s Taxonomy – knowledge, comprehension and application

• Learning is designed on upper levels of Bloom’s – synthesis, analysis and evaluation

• Textbook-driven • Research-driven• Passive learning • Active learning

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Take-Aways

• Know your Crosswalks and Plans– http://www.ncpublicschools.org/acre/standards/

common-core-tools/#crmath

• Collaborate with core teachers’ curriculum, vocabulary and word lists, teach thematic units, plan pacing together and recommended novels

• Network with other counties• Stay current and up-to-date

– Visit DPI website or Common Core website– Surf other state’s websites about Common Core and

Essential Standards implementation

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Content-Specific Take Aways

• Computer Applications, Accounting – Use Excel formulas to teach algebra, PEMDAS, solving equations, etc.

• Principles of Business, Marketing – Teach Simple Interest, Tax, Sales Commission, Percent of Increase/Decrease

• FACS, Construction – Use cooking measurements to teach measures, fractions, decimals, and percents

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Activities and Strategies

• http://www.wordle.net/show/wrdl/http://www.wordle.net/show/wrdl/4396395/CommonCoreMath4396395/CommonCoreMath

• WORDOWORDO

• CLOCK BUDDIESCLOCK BUDDIES

• PEER PARTNERSPEER PARTNERS

• CONTENT FRAMESCONTENT FRAMES

• 4-3-2-1 STRATEGY4-3-2-1 STRATEGY

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Middle School Common Core Assessment 2012-2013

• Non-calculator section first, and it will be Non-calculator section first, and it will be approximately 1/3 to 1/2 of the testapproximately 1/3 to 1/2 of the test

• Includes grid in response questionsIncludes grid in response questions

• Designed for paper and pencil Designed for paper and pencil administration, for now (technology administration, for now (technology enhanced program later) Knox MS\6-8 enhanced program later) Knox MS\6-8 Updates.pdfUpdates.pdf

• THIS YEARTHIS YEAR

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High School Common Core Assessment 2012-2013

Year Standards Taught Standardized

Test(s)

2012-2013 Math 1

CCSS **Geometry/Algebra 2

Math 1 (NC)

2013-2014 Same as above Math 1 (NC)

2013-2014 Same as above Math 1 (NC), *SBAC after junior year

*Smarter Balanced Assessment Consortium

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Resources

www.ncdpi.wikispaces.net www.ncdpi.wikispaces.net www.corestandards.org www.corestandards.org www.brightstorm.comwww.brightstorm.com www.studyjams.comwww.studyjams.com www.onlinemathlearning.comwww.onlinemathlearning.com www.mathwords.comwww.mathwords.com www.spellingcity.comwww.spellingcity.com www.youtube.comwww.youtube.com www.google.com www.google.com

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Personal (Contact) Information

• Dr. Mary A. Steltz– steltzma@rss.k12.nc.us or– psychdr68@gmail.com

• 10-year veteran with Rowan–Salisbury Schools• Undergraduate of HBCU – UAPB• Graduate School at UALR• Doctoral Program at GWU