1. UNIVERSITY OF ALASKA ANCHORAGE ALASKA DEPARTMENT OF EDUCATION & EARLY DEVELOPMENT Naked Math Gets a CTE Cover-up UAA Dr. Sally Spieker sally.spieker@uaa.alaska.edu 907-786-6498 EED Marcia Olson marcia.olson@alaska.gov 907-465-8704 Research by National Research Center for Career & Technical Education

2. Questions to think about... Do math and CTE teachers collaborate at your school or district? Do math teachers know what math concepts kids need in CTE courses? Do CTE teachers use the same math vocabulary and algorithms that are used in math class?

3. Lets Look at Some Trends 1.7 Math Credits 3.6 math credits 3.8 math credits 3.4 math credits Source: NAEP Trends in Academic Progress

4. How Can We Increase Math Achievement? One way – not THE ONLY way – to help increase math achievement A model of curriculum integration and pedagogy to increase CTE students math achievement while maintaining technical skill attainment. Students showed significantly higher math achievement on Terra Nova and Accuplacer For complete research results, see NRCCTENRCCTE

5. Core Principles of the Model Community of practice is critical Begin with the CTE curriculum – NOT the math curriculum Math is an essential workplace skill Maximize the math in the CTE curriculum CTE teachers are teachers of math-in-CTE – they are not math teachers

6. What is the Model? 1 CTE Teacher + 1 Math Teacher = 1 Team Each team Maps the CTE curriculum Identifies embedded math concepts Creates math-enhanced lessons CTE teacher delivers the lessons CTE teacher and math teacher continue to collaborate before and after each math-enhanced lesson is delivered

7. What is a Math-Enhanced CTE Lesson ? Introduce the CTE lesson Assess students math awareness Work through the math example embedded in CTE lesson – using standard math vocabulary Work through related, contextual math-in-CTE examples Work through naked math examples Formative assessment Summative assessment includes math questions

8. Sample Curriculum Map – Healthcare CTE Course or Unit CTE Concepts or ApplicationsEmbedded Math Concepts Diseases Work-place safety, body mechanics and disease prevention practices Basic human anatomy and physiology, growth, development, wellness and disease. Relationship between diseases /disorders to the environmental or genetic causes. Statistics Whole numbers Interpreting data Temperature Charts and graphs Percentages Graphing Probability Growth and Develop- ment Basic human anatomy and physiology, growth, development, wellness and disease. Proportion Charts and graphs Estimation Weights Percents Reading interpreting data Whole numbers Health Careers Potential health science careers required education, and opportunities. Measure and perform calculations. U.S health care system and the interdependence of careers and professionals. Statistics Cost/benefit ratio Computation Ratios Decimals Conversion Trends Charts/ graphs CTE Course or Unit CTE Concepts or Applications Embedded Math Concepts Body Structures Basic human anatomy and physiology, growth, development, wellness and disease. Basic anatomy and physiology of body systems and topographic terms. Quadrants Planes Measuring Ratios Skeletal System Basic anatomy and physiology of the skeletal system. Measurements Angles Formulas Positive and negative numbers Estimation Integu- mentary System Body surface area Wound Area Percent Surface area Area Respiratory System Major structures of the respiratory system Managing the airway. Volume Estimation Dilation

9. Sample Curriculum Map – Construction CTE Course or Unit CTE Concepts or Applications Embedded Math Concepts ConstructionFloor systems Area perimeter Measurement Estimation Ratio Whole numbers Interpret tables Two dimensional drawings Scaling ConstructionScaling/ conversions Ratios/ proportions Fractions & Decimals Measurement Factors Inverse fractions Two and three dimensional drawings Point of reference Linear equations Quadratic equations Area ConstructionElectricity Units Direct variation Indirect variation Solve equations Schematics Formulas Percent Average CTE Course or Unit CTE Concepts or Applications Embedded Math Concepts ConstructionDoors and windows Ratios Tolerances Formulas Whole numbers & Fractions Measurement ConstructionSquaring Pythagorean theorem Congruence Measurement Whole numbers & Fractions ConstructionMeasurement Linear measurement Area Angle measurement Fractions Ratios/ proportions ConstructionWalls Measurement- linear Area Whole number operations Fractions & Decimals Pythagorean theorem ConstructionRoofing Slopes Trig Area Conversion Fractions Pythagorean theorem Linear equations

10. The Model does NOT... Force extra math into the CTE program Create a mentoring or coaching relationship – the teachers are partners Include developing or re-designing curriculum Use team-teaching, i.e., math teacher does not teach in the CTE class Above all, it does NOT make the CTE class into a math class

11. Statewide Participants in Math-in-CTE 2010-2011 Anchorage Denali Fairbanks Ketchikan Mat-Su Bering Strait Craig Fairbanks Kenai Ketchikan Mat-Su Unalaska Valdez UAA 2011-2012 * 5 Construction Teams * 5 Health Careers Teams * 1 Transportation Team * 8 Construction Teams * 4 Health Careers Teams

12. Alaska Team Reactions CTE teachers: Now I know why my construction students cant subtract ¼ from 15 in their heads! Now I know the correct math vocabulary for the 3-4-5 stair riser lesson. You mean a ratio is not the same as a proportion? Math teachers: I had no idea there was so much math in the CTE class. I see that my students need practice in performing mental math for use in real life. Now I know why we really do teach this stuff!

13. A Sample Math-Enhanced Lesson SCALING DRAWINGS Developed by Dave Oberg and Jen Nelson, Service High School, Anchorage School District, 2010

14. What would you need to know before you begin your drawing? 1. Dimensions of the building. 2. Size of the paper you are going to print the plans on. What are standard paper sizes? A: 8.5 X 11 B: 11 X 17 C: 18 X 24 D: 24 X 36

15. What is the relationship between the size of the building and the size of the paper? How many times larger is the building footprint than the paper it must fit on? What units would be used on the drawing? The building?

16. What does the term scale mean? The fraction used to represent the ratio making the drawing and building proportional. A ratio is a comparison of two things expressed as a fraction. In drafting, the drawing measure is always given first, followed by the measurement of the actual building. So, what is meant by ratio? A proportion is an equation showing that 2 ratios are equivalent. Then, what is a proportion?

17. Lets say we have a building whose floor plan footprint is 120 X 40. What size paper would we need to use if our drawing is to be done at a scale of ¼ = 1? ¼ = 1; therefore the ratio is 1/4. Set up a proportion for each dimension: Inches 1 = L and 1 = W Feet 4 120 4 40 Cross multiply to create an equation 4L = 120 and 4W = 40 4 4 4 4 Divide by 4 to solve. L = 30 inches and W = 10 inches Therefore, we would need to use D-size (36 X 24) paper.

18. Your client wants you to design a warehouse that is 40 x 200. What size paper should be used, and what scale should be used, for the blueprints of the building? Trying the ratio of ¼ first: 1 = W and 1 = L 4 40 4 200 Cross multiply to create an equation, 4W = 40 and 4L= 200 4 4 4 4 Divide by 4 to solve. W = 10 inches and L = 50 inches The width at this scale is too large for D-size paper. Trying the ratio of 1/8: 1 = W and 1 = L 8 40 8 200 Cross multiply to create an equation, 8W = 40 and 8L = 200 8 8 8 8 Divide by 8 to solve. W = 5 inches and L = 25 inches At this scale the size would fit on D-size paper, but would not fit on C-size paper. Therefore, the drawing must be at 1/8 = 1 on D-size paper.

19. Each day, the seals at an aquarium are each fed 1 pound of food for every 10 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day? One pound of food per 10 pounds of body weight is equivalent to a ratio of 1/10. Set up a proportion using food to body weight. Pounds of food 1 = _x_ Body weight of seal 10 280 Cross Multiply to get the equation: 10x = 280 10 10 Divide by 10 to solve. x = 28 pounds of food per day

20. Naked Math Problems

21. In teams of 2-3 students, use a tape measure to find the dimensions of this classroom (wall to wall). Determine the appropriate scales to use for each common paper size (if possible).

22. Questions? UAA Dr. Sally Spieker sally.spieker@uaa.alaska.edu 907-786-6498 EED Marcia Olson marcia.olson@alaska.gov 907-465-8704 Research by National Research Center for Career & Technical Education