ELECTIVE 2: MATH B String Art and Algebraic Equations

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1 ELECTIVE 2: MTH B String rt and lgebraic Equations section of compass learning will be assigned to help the student research the topic. The student will complete sections in Compass and any tests or quizzes assigned. The student will investigate string art, and create 3 string art designs based on polygons and circles. The design is determined by the student, and must be school appropriate. The student will explain the math involved in each string art design in a research paper. For Example: string placed in the design the starts at (0,5) and goes to (1,0) will have an equation of y y 1 = m ( x x 1 ) where m = (y y 1 ) therefore y 0 = 5 0 ( x - 1) = y 0 = -5 (x 1) ( x x 1 ) 0-1 This is in point slope form. In slope intercept form this becomes y = -5x + 5 the elements of a research paper as directed by compass lessons the position of each line in a coordinate plane the use of point slope form or slope intercept form for equations. CRETE three string art designs of your own and label each line with the equation of the line. Each line in the design should have a label for the equation of the line. t the end of the course the student will turn in to the instructor: 1. three string art designs draw and then strung with string (Can be on poster board with yarn or embroidery floss. ) 2. a research paper about string art and the math involved in making them. 3. notes taken during research. 4. The pages in this packet LG 1 Rate of Change LG 1 The Slope Formula LG 1 Slope Intercept Internet sites to use: Read the diagrams and information on the second page. It explains how to write an equation for a line. The slope of line B is found by using the coordinates for as (x,y) and the coordinates of B as (x 1,y 1 ) (0, 5) B= (1,0) slope = 5-0 = The y intercept,b, is where the line hits the y axis, (0,5) B Use mx + b = y The equation is -5x + 5 = y

2 Label each line with its equation: mx ± b = y, where m is the slope and b is the y intercept. Use b to calculate the x intercept. The slope is rise = y2 y1 m run x2 - x1 x intercept. This point is (0,3). This is the point (0, 5). It is also the y intercept, 5 5x + 5 = y slope = y- int. is 5, x- int. is - 4 1x + 3 = y -5x + 5 = y slope = y-int. is 5, x- int. is 3-3 X + 3 = y -1x + 5 = y 2 This is (3, 0). This is (-3,0) This is (2, 0) This is (4, 0) This is (-4,0) -1x 4 = y is the equation of this line. y-int. is -4 and x int. is (-4,0) the slope is -1 1x 4 = y is the equation of this line. slope is 1, x-int. is (4,0) and y-int. is -4. This is (0,-4) Equations that start high on the left and -1x - 4 = y has a negative slope, the b is -4 and go low to the right have negative slopes. the x intercept is -b/ m = - - 4/ -1 = -4 the point would be (-4,0) Equations that start low on the left and 1x 4 = y has a positive slope, the b is -4 and go high to the right have positive slopes. the x intercept is -b/m = --4/ 1 = 4 so the point would be (4,0)

3 What are the equations for some of these lines on the coordinate plane? Label some points,b,c,d, E, F, G, H and give the equations for line B,CD,EF, and GH. B = EF = CD = GH =

4 What are the equations for some of these lines on the coordinate plane? Label some points,b,c,d, E, F, G, H and give the equations for line B,CD,EF, and GH. B = EF = CD = GH =

5 What are the equations for some of these lines on the coordinate plane? Label some points,b,c,d, E, F, G, H and give the equations for line B,CD,EF, and GH. B = EF = CD = GH =

6 Create a design of your own. Keep them simple and label the lines with their equations.

7 Create a design of your own. Keep them simple and label the lines with their equations.

8 Create a design of your own. Keep them simple and label the lines with their equations.

9 For example: Print the page above out on card stock, draw your design on, write the equations. Next, poke holes in the points that need string in colors and tape the ends to the back of the card. Here you would have a hole at each black dot. I F H D C G E B J Finally, write out the equation for each line drawn. B = 6x + 6 = y EF = 3/2 x + 3 = y IJ = -1x +0 =y or IJ = -x = y DC = 1/6x + 1 = y GH = 2/3 x + 3 = y