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Here slope is calculated through picture design
9, 10, 11, 12
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
- 3 Mathematics
- Students will be able to evaluate slope using the slope formula. Students justify their answer showing positive, negative, zero, or undefined slopes calculated.
- Graph paper, pencils, rulers
- 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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