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# Here slope is calculated through picture design

Subjects:

Art, Math

Grades:

9, 10, 11, 12

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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