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NYU Steinhardt EMAT Teaching Residency
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Here slope is calculated through picture design


Art, Math  


9, 12, 11, 10  

Title – Calculating Slope through Picture Design
By – Dolores Bencivengo
Primary Subject – Math
Secondary Subjects – Art
Grade Level – 9-12

Concept / Topic To Teach:

    Slope, rate of change

Standards Addressed:

    3 Mathematics

Specific Objectives:

    Students will be able to evaluate slope using the slope formula. Students justify their answer showing positive, negative, zero, or undefined slopes calculated.

Required Materials:

    Graph paper, pencils, rulers

Step-By-Step Procedures:

      Define slope as a rate of change and when given two ordered pairs, evaluate slope using the slope formula. Write formula on board:

Y2-Y1 / X2-X1

      Model with (1,1) and (2,3) as the x and y values:

(3-1) / (2-1) = 2/1

      Note that positive slope correlates to line pointed upward and right.
      Model with (-3,-1) and (2,-4):

(-4 – -1) / (2 – -3) = -2/6

      Note that negative slope correlates to line pointed upward left
      Model with (2,0) and (2,2) resulting with

zero in denominator: undefined; vertical line

      Model with (1,3) and (0,3)resulting with

zero in numerator; horizontal line

      Teacher draws an x,y axis and makes a large picture of a square labeling each corner a, b, c, d
      List the coordinates of each point:

        a =

        b =

        c =

        d =
      Teacher then uses line segment ab and calculates the slope using the slope formula.

    The process is continued until slope is calculated for each line segment. Model which is positive, negative, zero or undefined.

Plan For Independent Practice:

      Students are given a sheet of graph paper and asked to create any picture they want using a minimum of 10 points.

      They may use only straight lines (no smiley faces allowed!)
    Students label each point, then use the formula to evaluate the slope of each line. Students label the lines as positive, negative, zero, or undefined slope.

Closure (Reflect Anticipatory Set):

    Have students restate in their own words how to evaluate slope using the slope formula.

Assessment Based On Objectives:

    On-going assessment as students are working, as well as on the completed project turned in.

Extensions (For Gifted Students):

  • More picture points and choices
  • Evaluate area of picture
  • Picture in picture – shade first one – find area of shaded region only

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