UNIVERSITY OF ALASKA ANCHORAGE
ALASKA DEPARTMENT OF EDUCATION & EARLY DEVELOPMENT
Naked Math Gets a CTE Cover-upUAA
Partnered in 2011 & 2012 Research by National Research Center for Career & Technical Education
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?
Lets Look at Some Trends1.7 Math Credits3.6 math credits3.8 math credits3.4 math creditsSource: NAEP Trends in Academic Progress
NAEP Math Scores vs. Average # of High School Math Credits
How Can We Increase Math Achievement?One way not THE ONLY way to help increase math achievementA 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 AccuplacerFor complete research results, see NRCCTE
Core Principles of the ModelCommunity of practice is criticalBegin with the CTE curriculum NOT the math curriculumMath is an essential workplace skillMaximize the math in the CTE curriculumCTE teachers are teachers of math-in-CTE they are not math teachers
What is the Model?1 CTE Teacher + 1 Math Teacher = 1 TeamEach teamMaps the CTE curriculumIdentifies embedded math concepts Creates math-enhanced lessonsCTE teacher delivers the lessonsCTE teacher and math teacher continue to collaborate before and after each math-enhanced lesson is delivered
What is a Math-Enhanced CTE Lesson ?Introduce the CTE lessonAssess students math awarenessWork through the math example embedded in CTE lesson using standard math vocabularyWork through related, contextual math-in-CTE examplesWork through naked math examplesFormative assessment Summative assessment includes math questions
Sample Curriculum Map Healthcare
CTE Course or UnitCTE Concepts or ApplicationsEmbedded Math ConceptsDiseasesWork-place safety, body mechanics and disease prevention practicesBasic human anatomy and physiology, growth, development, wellness and disease.Relationship between diseases /disorders to the environmental or genetic causes.StatisticsWhole numbersInterpreting dataTemperatureCharts and graphsPercentagesGraphingProbabilityGrowth and Develop-mentBasic human anatomy and physiology, growth, development, wellness and disease.ProportionCharts and graphsEstimationWeightsPercentsReading interpreting dataWhole numbersHealth CareersPotential health science careers required education, and opportunities.Measure and perform calculations.U.S health care system and the interdependence of careers and professionals.StatisticsCost/benefit ratioComputationRatiosDecimalsConversionTrendsCharts/ graphs
CTE Course or UnitCTE Concepts or ApplicationsEmbedded Math ConceptsBody StructuresBasic human anatomy and physiology, growth, development, wellness and disease.Basic anatomy and physiology of body systems and topographic terms.QuadrantsPlanesMeasuringRatiosSkeletal SystemBasic anatomy and physiology of the skeletal system.MeasurementsAnglesFormulasPositive and negative numbersEstimationIntegu-mentary SystemBody surface areaWound AreaPercentSurface areaAreaRespiratory SystemMajor structures of the respiratory systemManaging the airway.VolumeEstimationDilation
Sample Curriculum Map Construction
CTE Course or UnitCTE Concepts or ApplicationsEmbedded Math ConceptsConstructionFloor systemsArea perimeterMeasurementEstimationRatioWhole numbersInterpret tablesTwo dimensional drawingsScalingConstructionScaling/ conversionsRatios/ proportionsFractions & DecimalsMeasurementFactorsInverse fractionsTwo and three dimensional drawingsPoint of referenceLinear equationsQuadratic equationsAreaConstructionElectricityUnitsDirect variationIndirect variationSolve equationsSchematicsFormulasPercentAverage
CTE Course or UnitCTE Concepts or ApplicationsEmbedded Math ConceptsConstructionDoors and windowsRatiosTolerancesFormulasWhole numbers & FractionsMeasurementConstructionSquaringPythagorean theoremCongruenceMeasurementWhole numbers & FractionsConstructionMeasurementLinear measurementAreaAngle measurementFractionsRatios/ proportionsConstructionWallsMeasurement- linearAreaWhole number operationsFractions & DecimalsPythagorean theoremConstructionRoofingSlopesTrigAreaConversionFractionsPythagorean theoremLinear equations
The Model does NOT . . .Force extra math into the CTE programCreate a mentoring or coaching relationship the teachers are partnersInclude developing or re-designing curriculumUse team-teaching, i.e., math teacher does not teach in the CTE classAbove all, it does NOT make the CTE class into a math class
Statewide Participants in Math-in-CTE2010-2011AnchorageDenaliFairbanksKetchikanMat-Su
* 8 Construction Teams* 4 Health Careers Teams
Alaska Team ReactionsCTE teachers:Now I know why my construction students cant subtract 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!
A Sample Math-Enhanced LessonSCALINGDRAWINGSDeveloped by Dave Oberg and Jen Nelson, Service High School, Anchorage School District, 2010
What would you need to know before you begin your drawing?What are standard paper sizes? A: 8.5 X 11B: 11 X 17C: 18 X 24D: 24 X 36
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?
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?
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 = 1?
= 1; therefore the ratio is 1/4.
Set up a proportion for each dimension:Inches 1 = L and 1 = W Feet 4 120 4 40Cross multiply to create an equation4L = 120 and 4W = 404 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.
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 first:1 = W and 1 = L 4 40 4 200Cross multiply to create an equation,4W = 40 and 4L= 2004 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 200Cross 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.
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 280Cross Multiply to get the equation: 10x = 28010 10 Divide by 10 to solve. x = 28 pounds of food per day
Naked Math Problems
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).