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Naked Math Gets a CTE Cover-up. UAA Dr. Sally Spieker 907-786-6498. University of Alaska Anchorage Alaska Department of Education & Early Development. EED Marcia Olson 907-465-8704.

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naked math gets a cte cover up

Naked Math Gets a CTE Cover-up


Dr. Sally Spieker


University of Alaska Anchorage

Alaska Department of Education & Early Development


Marcia Olson


Research by National Research Center for Career & Technical Education

questions to think about
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?
let s look at some trends
Let’s Look at Some Trends

3.8 math credits

3.4 math credits

3.6 math credits

1.7 Math Credits

Source: NAEP Trends in Academic Progress

how can we increase math achievement
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 NRCCTE
core principles of the model
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
what is the model
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
what is a math enhanced cte lesson
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, contextualmath-in-CTE examples
  • Work through “naked math” examples
  • Formative assessment
  • Summative assessment includes math questions
the model does not
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
statewide participants in math in cte
Statewide Participants in Math-in-CTE
  • 2010-2011
    • Anchorage
    • Denali
    • Fairbanks
    • Ketchikan
    • Mat-Su
  • 2011-2012
  • Bering Strait
  • Craig
  • Fairbanks
  • Kenai
  • Ketchikan
  • Mat-Su
  • Unalaska
  • Valdez
  • UAA

* 5 Construction Teams

* 5 Health Careers Teams

* 1 Transportation Team

* 8 Construction Teams

* 4 Health Careers Teams

alaska team reactions
Alaska Team Reactions
  • CTE teachers:
    • Now I know why my construction students can’t subtract ¼” from 15” in their heads!
    • Now I know the correct math vocabulary for the3-4-5 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 lesson

A Sample Math-Enhanced Lesson



Developed by Dave Oberg and Jen Nelson, Service High School, Anchorage School District, 2010


What would you need to know before you begin your drawing?

1. Dimensions of the building.

What are standard paper sizes?

2. Size of the paper you are going to print the plans on.

A: 8.5” X 11”

C: 18” X 24”

B: 11” X 17”

D: 24” X 36”


What is the relationship between the size of the building and the size of the paper?

What units would be used on the drawing? The building?

How many times larger is the building footprint than the paper it must fit on?


What does the term “scale” mean?

The fraction used to represent the ratio making the drawing and building proportional.

So, what is meant by “ratio”?

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.

Then, what is a proportion?

A proportion is an equation showing that 2 ratios are equivalent.


Let’s 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.


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.

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.

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


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


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).




Dr. Sally Spieker



Marcia Olson


Research by National Research Center for Career & Technical Education