GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?


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1 GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2. What types of correlations may exist on a scatter plot? 3. How do you find missing coordinates of an ordered pair? 3. Find the missing coordinate of an ordered pair solution, given one coordinate of the pair Plot ordered pairs of numbers on the rectangular coordinate system Why is a pair of coordinates called an ordered pair? How do you use this order to graph a point? How do you determine which quadrant a point lies in without graphing? Graph paired data to create a scatter diagram Provide real world data (or have students collect) for a scatter plot. How do you determine which variable is dependent/independent? What determines the scale used when graphing data? What does the trend of the points tell you about the data? Find the missing coordinate of an ordered pair solution, given a table of values and one coordinate of the pair. Model using input/output diagrams to create tables of values. How can you find y given x? Will this work if you are given y instead of x? Why or why not? How can you find x if given y?
2 Graphing Linear Equations 1. Graph a linear equation by finding and plotting ordered pair solutions 1. How do you graph linear equations by plotting ordered pairs? 2. What do the points on the graph of a linear equation represent? 3. In a linear equation, which variable represents the input? Which variable represents the output? Graph a linear equation by finding and plotting ordered pair solutions Have students create tables of values (from previous lesson, using input/output if needed). From geometry, how many points determine a straight line? How many points should you graph to ensure your graph of the line is probably correct? Intercepts 1. Identify intercepts of a graph 2. Graph a linear equation by finding and plotting intercept points 1. What are xand yintercepts of a line and how do you find them? 2. How do you graph a line using intercepts? Activities and Questions to ask student: Identify intercepts of a graph Display graph of line intersecting the axes and give equation. Name the coordinates of the yintercept. What is the xcoordinate of a point on the yaxis? Using this fact and what you learned about making tables of values, how can you find y when x = 0 without using graph? Name the coordinates of the x intercept. What is the ycoordinate of a point of the xaxis? Using this fact, how could you find x when given y = 0 without using the graph?
3 How is graphing a linear equation using the x & yintercepts similar/different from graphing a line using a table of values? Graph a linear equation by finding and plotting intercept points Is there an advantage of using x & yintercepts to graph a line as opposed to using a table of values? Explain. What steps do you need to take to graph a linear equation using the intercepts? Does is matter what form the equation is in? What is the easiest form to use when graphing using intercepts? Slope and Rate of Change 1. Find the slope of a line given two points of the line 2. Find the slope of a line given its equation. 1. What is the slope of a line and how do you find it? 2. Give realworld examples of slope as a rate of change. 3. Find the slopes of horizontal and vertical lines 4. Slope as a rate of change Find the slope of a line given two points of the line What is meant by the slope of a line? Where have you seen slope used in the real world? Sketch 2 different lines with positive slopes. How are lines similar? How are the different? How can you find rise/run from the graph? Show that rise = difference in ycoordinates and run= difference in xcoordinates. Using this fact, how can you find rise/run or slope without using a graph? Introduce slope formula. Find the slope of a line given its equation (slopeintercept form) Illustrate a line with two marked points & its equation and let students calculate slope. Do you see this slope represented in the equation? Where is it located? Find the slopes of horizontal and vertical lines How are horizontal and vertical lines different from the lines we have discussed so far?
4 Given a horizontal line with two marked points, let students calculate the slope. What is the rise of a horizontal line? What does having zero as rise in the fraction simplify to? What does this mean the slope of a horizontal line is? Repeat for vertical lines. Slope as a rate of change Using real world data (with a linear relationship), plot points or have students plot points and calculate the slope. What does the rise represent in this data if rise = change in y values? What does run represent in this data if run = change in xvalues? Equations of Lines 1. Use the slopeintercept form to write an equation of a line 2. Use the slopeintercept form to graph a linear equation 3. Find distance between two points 4. Find the midpoint Use the slopeintercept form to write an equation of a line (given slope, m, and yintercept, b) 1. How do you write equations of lines? 2. How do you graph linear equations? 3. How do you find distance and midpoint between 2 points? 4. What is the relationship between the Pythagorean Theorem and the Distance Formula In y=mx+b, what does m represent? What does b represent? Given slope and yintercept, how can you write the equation of the line? Use the slopeintercept form to graph a linear equation Why is y=mx+b called slopeintercept form? What does m stand for? What does b stand for? Which variable is a point on the line that we can start our graphing with? How can we use the slope to create more points? Find distance between two points Students draw 2 given points on a grid and instruct them to make a right triangle with given points as vertices. How can you find the length between the two points using the
5 Pythagorean formula? Show that the legs of the triangle can be expressed as the difference in xcoordinates and ycoordinates and substituted into the Pythagorean formula, solve for the hypotenuse, d. Introduce distance formula. Find the midpoint What is meant by midpoint of a segment? Using a horizontal line segment on the xaxis, with endpoints (2,0) & (6,0), ask students to locate midpoint. How did you come up with (4,0)? Using a vertical line segments on yaxis with endpoints (0,2) & (0,8), ask students to locate midpoint. How did you come up with (0,5)? Discuss the connection between averaging xcoordinates and ycoordinates and finding the midpoint of a line segment. Ask students to graph two points that are not horizontally or vertically lined up. Using what you learned from finding midpoints of horizontal and vertical segments, find the midpoint of your two points. Graph the point to visually estimate if you are correct. Ask students to write a formula to find the x and y coordinates of the midpoint of two points on a coordinate plane.
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