5 Day Unit Plan. Algebra/Grade 9. JenniferJohnston

Size: px
Start display at page:

Download "5 Day Unit Plan. Algebra/Grade 9. JenniferJohnston"

Transcription

1 5 Day Unit Plan Algebra/Grade 9 JenniferJohnston Geometer s Sketchpad Graph Explorer Algebra I TI-83 Plus Topics in Algebra Application Transform Application

2 Overall Objectives Students will use a variety of technologies and resources to expand their knowledge of graphing ordered pairs and equations. They will become efficient in working with calculators and computers for mathematical purposes. The students will help each other throughout the unit by presenting their ideas, working together as groups, and assessing one another. NYS Standards Covered: Number and Numeration Operations Modeling/Multiple Representation Measurement Patterns/Functions NCTM Standards Covered: Algebra Data Analysis and Probability Problem Solving Reasoning and Proof Communications Connections 2

3 Resources Algebra I. Simon & Schuster, Chapter 5; pgs Doody, Cecelia. Hands-on Activities For your Mathematics Classroom. I2T2 Workshop. November 17, 2001 Larson, Ron, Laurie Boswell, Timothy Kanold, and Lee Stiff. Algebra I. Evanston, IL: McDougal Littell, Inc., Chapter 4; pgs Chapter 5; pgs Schoaff, Dr. Eileen. Introduction to Lines 3

4 Materials Day 1: Geometer s Sketchpad Computer Projection Device (In-Focus) Opening handout Handout for Main Activity File saved on Geometer s Sketchpad for students to open Homework Assignment Day 2: Opening handout Graph Explorer Algebra I: Equation Match Graph Explorer handout Homework Assignment Day 3: TI-83 Plus Transform Application Topics in Algebra Application Calculator Links Handout for Closing Activity Homework Assignment 4

5 Day 4: Opening handout Algebra I Handout for Main Activity Closing handout Homework Assignment Day 5: TI-83 Plus Opening handout Calculator Links Stop watch Handouts for Main Activity Homework Assignment 5

6 Overview of Graphing Linear Equations Day 1: Graphing Ordered Pairs The students will be reviewing graphing ordered pairs on the coordinate plane by doing activities on Geometer s Sketchpad. Day 2: Graphing Equations of Lines They will use basic reasoning to conclude patterns between sets of ordered pairs. Graph Explorer will help them see the graphs of the equations, while Algebra I will force them to draw the graph on their own. Day 3: Slope of a Line The graphing calculator will help the students make conjectures about the connection between steepness and an equation of a line. Topics in Algebra will show the students an animated lesson about the slope formula along with a game to help them practice using the formula. Day 4: Graphs Using Intercepts Students will use Geometer s Sketchpad and Algebra I to graph a line by using the intercepts. They will be using the slope-intercept form to write equations. Also, they will use graphs of equations to find the intercepts. Day 5: Scatter Plot and Best-Fit Lines The TI-83 Plus will be helpful to plot data and make conjectures about the data. They will look at the line regression and slope-intercept form on the calculator involving best-fit lines. 6

7 Day 1: Graphing Ordered Pairs Objectives: Ninth grade students will use their knowledge to graph ordered pairs on the coordinate plane. They will use Geometer s Sketchpad to plot sets of ordered pairs that make up pictures by connecting line segments. They students will test their peers on the knowledge they have of graphing ordered pairs. They will work together in groups to make a presentation at the end of the class. Opening Activity: Students will be given a handout with a set of ordered pairs. They will need to label the x- and y-axis and the point of origin on the coordinate plane. Each student is required to plot each ordered pair, label its coordinates, and label the number of that particular point. Main Activity: Students will open Geometer s Sketchpad on their computer and use the program to plot another set of ordered pairs. After the students have graphed their points; have them discuss with each other the different ways they plotted the points. They should be able to see that it can be done more than one way. Let the students connect the points to form the picture. Two volunteers can present to the class the different ways to connect the points on the computer that is connected to the overhead projector. Students need to print out their work to hand in. 7

8 Closing Activity: Students will be given a more difficult picture on Geometer s Sketchpad. They are asked to label the points with a letter and label the coordinates of each point. Students will need to print out their work to hand in. They can discuss the different methods they used to get the coordinates of the set of ordered pairs that makes up this picture. Homework: Students will be given a worksheet with instructions on their assignment and what is required of them for tomorrow. 8

9 Teachers Notes Opening Activity: Plotting ordered pairs should be a review for this class. This worksheet will tell me if there are any students who might need more instruction for this lesson. Make time to go over a few examples of plotting ordered pairs with (x,y) coordinates if it seems like some students do not understand. Main Activity: The students should be discussing two main ways of plotting points on GSP. First, using the arrow and clicking on the point. Second, going under graph and plot points. In the small presentation, students should be able to show that after using plot points, if nothing else is clicked on, you can go to construct; segments and the fish is formed. You should have your overhead screen ready for this in case a student presents in this way. The similar way to construct segments is by highlighting each point in the order you want the segment to appear and go to construct; segment. Another way to construct segments is to go to the tool bar on the left and choose the line segment box. The students can connect points by clicking on the particular point and dragging the line to the next point. Closing Activity: The students will need to open this file through GSP to begin. The students can highlight each point and go to measure; coordinates. They can also make a text cell for each ordered pair and label its coordinates. 9

10 Homework: Read over the homework assignment with the class and make sure everyone understands. If there are no questions, explain to them that the assignment is easiest if they look through a coloring book or children s book. The pictures are creative and you can add points to make it a connect the dots picture.

11 Name: Math 9 Label the x-axis and the y-axis. Label the origin and its coordinates. Plot these ordered pairs. Label the number of the ordered pair and label its coordinates. 1. ( 1, 2 ) 2. ( -1, 6 ) 3. ( 0, 3 ) 4. ( 4, 0 ) 5. ( 1, -4 ) 6. ( 4, 1 ) 7. ( -2, 5 ) 8. ( -5, -3 ) 9. ( -6, -1 ) -. ( 6, -5 ) - (Handout for Opening Activity) 11

12 Name: KEY Math 9 Label the x-axis and the y-axis. Label the origin and its coordinates. Plot these ordered pairs. Label the number of the ordered pair and label its coordinates. 11. ( 1, 2 ) 12. ( -1, 6 ) 13. ( 0, 3 ) 14. ( 4, 0 ) Y-axis 15. ( 1, -4 ) 2 (-1, 6) 16. ( 4, 1 ) 7 (-2, 5) 17. ( -2, 5 ) 3 (0, 3) 18. ( -5, -3 ) 1 (1, 2) 19. ( -6, -1 ) 20. ( 6, -5 ) 9 (-6, -1) Origin (0, 0) 6 (4, 1) 4 (4, 0) X-axis 8 (-5, -3) 5 (1, -4) (6, -5) (Handout for Opening Activity) 12

13 GSP Activity Math 9 Make sure you put your name on your GSP worksheet with a text cell. Make text cells on your page to answer the questions below. I. Plot the following set of ordered pairs. 1. ( 8, 1 ) 2. ( 7, 2 ) 3. ( 4, 4 ) 4. ( 1, 5 ) 5. ( -2, 4 ) 6. ( -5, 1 ) 7. ( -6, 2 ) 8. ( -8, 4 ) 9. ( -8, -5 ). ( -6, -3 ) 11. ( -5, -2 ) 12. ( -2, -3 ) 13. ( 2, -4 ) 14. ( 5, -3 ) 15. ( 7, -1 ) II. III. What type of command or method did you use to plot your points? Are there any alternative ways to plot this set of ordered pairs? Discuss with your neighbor the method they used to plot their set of points. IV. What picture is made when you connect the points with the line segments? V. Which method did you use to connect the points with line segments? (Handout for Main Activity) 13

14 Student's Sample Worksheet II. I went to Graph; Plot Points...I then typed in the ordered pairs and clicked on plot. This plotted the set of ordered pairs. III. You can individually click on the point with the arrow. IV. A fish V. After I plotted the points, I went directly to Construct; Segment. Since I went in the order of 1 through 15 when I plotted my ordered pairs, I could use only one command to get my entire picture. 5 F J G E I D H C Q M L N P O K -5 14

15 GSP Activity Math 9 Label each point with a capital letter. Label the coordinates of each point. There are 17 ordered pairs. - - (Open this file through GSP for Closing) 15

16 GSP Activity Math 9 Label each point with a capital letter. Label the coordinates of each point. There are 17 ordered pairs. C: (0.0,.0) C D: (-2.0, 7.0) D S: (2.0, 7.0) S E: (-3.0, 4.0) E R R: (3.0, 4.0) F: (-4.0, 0.0) F Q - Q: (4.0, 0.0) G: (-7.0, -4.0) G H H: (-4.0, -4.0) I: (-2.0, -4.0) I L: (2.0, -4.0) L O O: (4.0, -4.0) P: (7.0, -4.0) P J J: (-3.0, -6.0) K M M: (1.0, -6.0) K: (-1.0, -6.0) N N: (3.0, -6.0) - (Open this file through GSP for Closing) 16

17 Graphing Ordered Pairs: Homework Assignment Your assignment for tonight is to create a picture of your choice. It must consist of a set of at least ordered pairs with connecting line segments, like we did in class today. Be as creative as you would like. On one sheet of graph paper, draw your picture with its points, but do not label the coordinates of the points. On a separate sheet of graph paper, state the set of ordered pairs of your picture. The assignment is due at the beginning of class tomorrow. You will give the first sheet to one student and the second to another student. It is their job to find the set of ordered pairs for your picture for the first sheet. For the second sheet, they are to plot the ordered pairs and connect the dots, like we did in class. They will do your assignment for homework and give it back to you the next day. It is your job to then correct the assignment and turn both papers in to the teacher. (Homework Handout) 17

18 Day 2: Graphing Equations of Lines Objectives: Ninth grade students will use a table of values to determine an equation of a line. They will use Graph Explorer to graph sets of ordered pairs and lines. Students will practice graphing linear equations on Algebra I by using a game. Opening Activity: Students are given a table of values with four ordered pairs. It is their job to determine two more ordered pairs that follow the same pattern. X Y Students are asked to state how they concluded that the two points follow the same pattern as the other four. State in words the pattern of these ordered pairs. Write an algebraic expression for these ordered pairs. Main Activity: On Graph Explorer, students are going to determine whether or not this set of ordered pairs satisfies the algebraic statements they have come up with. Students will enter their ordered pairs into a table. They can plot these points and enter their equation into y1. If all of these ordered pairs lie on this line, they are correct. If they are wrong, they need to examine their ordered pairs and line before moving on. Make a print out of the correct graph. 18

19 Students will do the same activity for the worksheet given to them. They will find the pattern and come up with two new ordered pairs. The students will use Graph Explorer to plot their data and sketch a graph. Closing Activity: Students will use Algebra I to play a game that involves the same type of reasoning. To start the game from Algebra I, they can use the following commands: Open Algebra I; File; Open; Equation Match. The students are required to match their equation to the target equation by moving the graph with the mouse arrow. They do not Your Equation m b y = -x+4 Target Equation m b y = 3x-1 New Go! Help - - Your Equation m b y = 3x-1 Target Equation m b y = 3x-1 New Go! Help - know y = mx + b form for an equation of a line. They can make conjectures about the form of the equation after they play the game a few times. They should be able to conclude, for example, the slope is 3 for this graph and it crosses the y-axis at 1. This - 19

20 will help them understand the slope-intercept form much better when we work with the equation later in the unit. They will do 3 different trials and make a printout of each of the 3 screens. Homework: Students will be doing a worksheet that involves substituting ordered pairs into an equation to verify the ordered pairs lie on that particular line. This process is the opposite from what they did in class. 20

21 Teachers Notes Opening Activity: If the students are having a hard time determining the relationship, have them tell you the pattern in words. They might understand the equation if it is said in a complete sentence. The setup of the table of values should be a review. Main Activity: Make sure each student makes a print out of the correct version of this problem before doing the worksheet. Have them leave their printouts on their desk. You want to be able to walk around and see that their printouts are correct so you know they understand the lesson. Closing Activity: These are a bit more difficult so offer help to the students who are struggling. Conduct a class discussion on the conjectures that you want the students to realize. If they are having trouble getting motivated to think about this, encourage them with questions that have hints. Do not give them the answers. You should let them think on their own. Homework: Make sure they know that there is no difference between y = (3x + 2)/4 and 4y 3x = 2. They should see that, by algebra, these are equivalent. 21

22 Graphing Equations of Lines Math 9 This is a table of values, or ordered pairs. There is a pattern and two ordered pairs are missing. Can you fill in the blanks with two ordered pairs.? X Y How did you conclude that these were the missing ordered pairs? 2. State in a complete sentence the pattern you found in this table of values. 3. Write an algebraic expression for the pattern of this table of values. 4. Before we move on, write down your ideas on how we could check to see if your expression is the correct equation of the line made up of these values. (Handout for Opening Activity) 22

23 Sample Student Worksheet Graphing Equations of Lines Math 9 This is a table of values, or ordered pairs. There is a pattern and two ordered pairs are missing. Can you fill in the blanks with two ordered pairs.? X Y How did you conclude that these were the missing ordered pairs? The right side is three times the left side for each pair. 6. State in a complete sentence the pattern you found in this table of values. The pattern is that y is 3 times bigger than x. 7. Write an algebraic expression for the pattern of this table of values. Y = 3*x 8. Before we move on, write down your ideas on how we could check to see if your expression is the correct equation of the line made up of these values. Graph the ordered pairs and draw a line. If all of the points are on the line, they are correct. (Handout for Opening Activity) 23

24 Graph Explorer Activity Math 9 Name: Add the 2 missing ordered pairs. Write an algebraic expression for each of the tables. Plot the points on Graph Explorer. Enter your equation into y1. Make a sketch of the graph with the ordered pairs on the coordinate plane to the right X Y X Y

25 3. 15 X Y (Handout for Main Activity) 25

26 Graph Explorer Activity Math 9 Name:Sample Student Worksheet_ Add the 2 missing ordered pairs. Write an algebraic expression for each of the tables. Plot the points on Graph Explorer. Enter your equation into y1. Make a sketch of the graph with the ordered pairs on the coordinate plane to the right. 1. X Y y = x X Y y = x

27 3. X Y y = 2x (Handout for Main Activity) 27

28 Homework Handout Math 9 Name: Verify each ordered pair works for the given equation by substituting the values for x and y. Sketch the graph of the equation and plot the points. Are each of these ordered pairs solutions for these equations? 1. y = 2 3x ( 0, 2 ) ( 3, -7 ) 15 ( 1, -5 ) ( -1, 5 ) ( -2, 8 ) ( -3, -3 ) 2. y = -x/ ( 3, -3 ) ( 2, -6 ) ( -3, 4 ) ( 0, -2 ) ( -6, 0 ) ( 9, -4 )

29 3. 2y = x 3 ( 0, 3 ) ( 5, 1 ) 15 ( -3, -3 ) ( 1, -1 ) ( 2, 0 ) ( 6, 1 ) 4. 4y 3x = 2 5 ( 1, 5/4 ) ( -1, -1/4 ) ( 0, 1/2 ) ( 2/3, 1 ) ( -1, 0 ) ( -1/3, 1 ) 5. 2x + 5y = 1 ( 2, 1 ) ( 0, 5 ) ( 0, 1/5 ) ( 5/2, -4/5 ) ( 1/2, 0 ) ( -1/2, 2/5 ) (Homework Handout) 29

30 Homework Handout Math 9 Name:KEY Verify each ordered pair works for the given equation by substituting the values for x and y. Sketch the graph of the equation and plot the points. Are each of these ordered pairs solutions for these equations? 1. y = 2 3x ( 0, 2 ) * ( 3, -7 ) * ( 1, -5 ) ( -1, 5 ) * ( -2, 8 ) * ( -3, -3 ) 2. y = -x/3 2 ( 3, -3 ) * ( 2, -6 ) ( -3, 4 ) ( 0, -2 ) * ( -6, 0 ) * ( 9, -4 )

31 3. 2y = x 3 ( 0, 3 ) ( 5, 1 ) * ( -3, -3 ) * ( 1, -1 ) * ( 2, 0 ) ( 6, 1 ) 4. 4y 3x = 2 ( 1, 5/4 ) * ( -1, -1/4 ) * ( 0, 1/2 ) * ( 2/3, 1 ) * ( -1, 0 ) ( -1/3, 1 ) 5. 2x + 5y = 1 ( 2, 1 ) ( 0, 5 ) ( 0, 1/5 ) * ( 5/2, -4/5 ) * ( 1/2, 0 ) * ( -1/2, 2/5 ) * (Homework Handout) -8-31

32 Day 3: Slope of a Line Objectives: Ninth grade students will use the TI-83 Plus to review the steepness of a line as rise/run. They will look at an overview on the Topics In Algebra Application. Students will use the application to play two different games on their own and with a partner. Opening Activity: Students will look at Transform ; an application on their TI-83 Plus. They will use this to evaluate the steepness of a line and set of lines. They will enter Ax + 2 into y1. We will look at a slide show that starts with A = 0 and ends with A =. We can see by the example below there is a big difference in A = 1 and A = 5. The first graph is less steep than the second graph. 32

33 The students will see the same graphs on their calculators for 11 different values of A. If they would like to stop the slide show at any time, they can press enter. We will have a class discussion about what happens to the graphs as A gets closer to. We will talk about what A represents in this equation of a line. Students will choose another equation example and we will observe the slide show again. We can discuss the similarities and differences to the first slide show. They are encouraged to use negative numbers for the value of A in order to see an important change in the graph. There should be another class discussion about the representation of A. The students should make the conclusion that the constant in front of x represents the steepness of a line. They can be told that this steepness is a line s slope. Main Activity: Students will use their TI-83 Plus applications to look at an overview of slope as rise/run. They will play a game in Topics in Algebra, Chapter 3. In order to look at the overview and play the game, they have to use the following commands: APPS; ALG1CH3 (ENTER); ENTER; 3:LINEAR FUNCTIONS (ENTER); 1:SLOPE WITH GRID (ENTER); 1:OVERVIEW (ENTER). They can use the arrows to go through the slide show. After they see the slide show, they can press 2 nd : QUIT. This will take them back to the menu screen. They can choose 3:ACTIVITIES and this will get them started on the game. 33

34 Students will look at the same game and are asked to think about the picture being displayed on the coordinate plane. The starting point would represent something and the ending point would represent something similar. They are to consider what type of algebraic expression can be used to find the slope of a line that connects these points. They can record any ideas they have on this expression and save them for later in the activity. Students will continue evaluating slope of a line by looking at another overview in Topics in Algebra, Chapter 3. The students will see the formula for slope is (change in y)/(change in x) = (y 2 - y 1 )/(x 2 -x 1 ). They can compare their algebraic expression with the one given by the calculator overview. This calculator overview can be found in a similar way. For the first overview, the students chose 1:SLOPE WITH GRID. For this overview, we want them to choose 2:SLOPE USING COORD. All of the other steps are the same. Closing Activity: Students will link their calculators with a partner and play the game that involves the slope formula. 34

35 The game can be found under the following commands: Apps (ENTER); ALG1CH3 (ENTER); ENTER; LINEAR FUNCTIONS (ENTER); 2:SLOPE USING COORD (ENTER); 3:ACTIVITIES (ENTER); > (ARROW); 2:SCREEN CROSS (ENTER); NEXT (F4); NEXT (F4); PLAY (F4). The object of the game is to get the correct slopes for each line segment before your partner. The first person to get from the left side of the screen to the right side is the winner. They should play against two different people. Homework: Finish the questions about your observations that you made about the game you played with a partner. Do the worksheet involving the slope formula. 35

36 Teachers Notes Opening Activity: Remind the students that a line has steepness, we call this slope. The variable we are using to express slope is a constant. We can use any constant. So although we used, A, they should know we can use any letter to represent the slope. We can conclude from the slide show that as our constant gets larger, our line gets steeper. Main Activity: Make sure the students review what rise/run is. They should see what the relationship is to slope. The problems on the game should be fairly simple with the help of scrap paper. Let them discuss the algebraic expression amongst each other. Write down any expressions that they feel are correct. After looking at the next overview, have the class discuss what is wrong, if anything, with the expressions they gave. Closing Activity: They may need scrap paper to do their arithmetic. 36

37 TI-83 Plus Math 9 Name: Definition: A set of points that are located on the same line are called COLLINEAR POINTS. 1. Is any set of three points collinear? Give some examples to justify your answer. 2. What type of line has a negative slope? Make a sketch of the line What does the line that has undefined slope look like? - - After playing the slope game with at least two different partners, write a short paragraph ( 4 to 5 complete sentences ) about anything that interested you while playing that game. Are there any other observations that can be made? (Handout for Closing) 37

38 TI-83 Plus Math 9 Name: KEY Definition: A set of points that are located on the same line are called COLLINEAR POINTS. 4. Is any set of three points collinear? Give some examples to justify your answer. No Ex: 5. What type of line has a negative slope? Make a sketch of the line What does the line that has undefined slope look like? - After - playing the slope game with at least two different partners, write a short paragraph ( 4 to 5 complete sentences ) about anything that interested you while playing that game. Are there any other observations that can be made? (Handout for Closing) 38

39 Slope Homework Math 9 Name: Find the slope of the line that contains each pair of points. 1. ( 5, 7 ) and ( 3, 4 ) 2. ( 7, 6 ) and ( 4, 3 ) 3. ( -1, 3 ) and ( 2, -2 ) 4. ( 0, -2 ) and ( 4, 3 ) 5. ( 6, 0 ) and ( -3, 5 ) 6. ( -4, -1 ) and ( 1, 3 ) 7. ( 1, 3 ) and ( -4, -5 ) 8. ( -5, -6 ) and ( -1, -5 ) Find the slope of each line from its graph. 1. (the scale goes by 1) (Homework Handout) 39

40 Slope Homework Math 9 Name:KEY Find the slope of the line that contains each pair of points. 1. ( 5, 7 ) and ( 3, 4 ) m = 3/2 2. ( 7, 6 ) and ( 4, 3 ) m = 1 3. ( -1, 3 ) and ( 2, -2 )m = -5/3 4. ( 0, -2 ) and ( 4, 3 ) m = 5/4 5. ( 6, 0 ) and ( -3, 5 ) m = -5/9 6. ( -4, -1 ) and ( 1, 3 ) m = 4/5 7. ( 1, 3 ) and ( -4, -5 ) m = 8/5 8. ( -5, -6 ) and ( -1, -5 ) m = 1/4 Find the slope of each line from its graph. 1. (the scale goes by 1) 2. m = 0 m = (Homework Handout)

41 Day 4: Graphs Using Intercepts Objectives: Ninth grade students will be using their problem solving skills as groups to find the x-intercepts and y-intercepts of equations. They will use Algebra I to make tables of values, graph the equations, and check their solutions. Opening Activity: Students are given some basic vocabulary by looking at a graph on the computer overhead. They are told the definitions of x- and y-intercepts and are able to look at a picture on GSP. They will discuss the values, or coordinates, of these points. Students will eventually come to the conclusion that the x-intercept has coordinates of (x, 0), and the y-intercept has coordinates of (0, y). They will be given an equation and are asked to find the x- and y-intercepts. They can discuss, in groups of 3 or 4, how they can find the intercepts given the equation and realization they just made about the coordinates. Main Activity: Students will use the information from the previous activity to graph this equation using Algebra I. On their handout, they can plot their two points and draw the line that goes through each of the points. On Algebra I, they can set up a table of values by choosing the command from the left side of the screen. They should enter their two ordered pairs, or two intercepts, into their table of values on Algebra I. They will make a graph box and connect the two boxes by clicking on the double arrow from the table and dragging it to the double arrow on the graph box. Students can click on the table and press enter to get their graph. They should answer the questions on the handout. They 41

42 can graph the equations from the worksheet by using similar steps, which are the following: determine the slope; find the x-intercept and the y-intercept; enter the values into the table; graph the equation; and make a sketch of the graph from the computer onto your paper. They should make a y= box for each graph to check their answer and make sure it is the correct equation with graph. The opening handout has the students write down the x- and y-intercepts for the beginning equation, so they do not need to rewrite them on the main handout. Closing Activity: Students will be given a variety of graphs and they are asked to find the x-intercepts and y-intercepts by looking at the graph. Homework: Students will be doing a handout that has a variety of questions. The questions will be like the activities we did today in class. One part of the assignment asks the students to write an equation of a line given its graph. The students will need to determine the x- and y-intercepts. They will need to find the slope between these two points by using the slope formula. They will then write the equation of this line by using the formula: y = mx + b. Students know that m can stand for the slope of the line. They are told that the y-coordinate of the y-intercept can be substituted for b. The x and y are part of the equation of the line, which they should remember from writing and graphing equations the other day. 42

43 Teachers Notes Opening Activity: The overhead screen should show an axis with grid. Draw any line on the grid that crosses the x- and y-axis. The y-intercept is the value of y when x = 0. The x-intercept is the value of x when y = 0. Explain the definition and point to each of these points. The students should be able to write their own definition of these two terms. When they work in groups, they should see that 0 can be substituted in for y then the same for x. For example, 2x + 3y = 6. Let x = 0, we have 2(0) + 3y = 6. This gives us 3y = 6 and we can solve for y to get its intercept. The y-intercept is 2. The opposite can be done for the x-intercept. Main Activity: The students should be able to follow the handout and answer the questions without any problems. Closing Activity: The students should have no problem doing this worksheet. The graphs are very easy to understand. All they have to do is determine ordered pairs. Homework: Let the students know that they can still look up the slope formula in their calculator applications if they forget the formula. If any of the students are having difficulty understanding the assignment, they should work together to discuss their problems. Also, they can stay after to go over an example or ask questions. If there is time after the closing activity, it would be beneficial to do an example of one of these problems. I think it will help them greatly if they try it on their own first. The main 43

44 objective of this activity is to let the students think for themselves about writing the equation of a line. 44

45 Intercepts Opening Math 9 Name: 1. Define, in your own words, the following terms: X-intercept - Y-intercept - 2. Find the x-intercept and the y-intercept of the graph of the equation 2x + 3y = 6. What should you do first to find the x-intercept? X-intercept: What should you do next to find the y-intercept? Y-intercept: (Opening Handout) 45

46 Intercepts Opening Math 9 Name:KEY 1. Define, in your own words, the following terms: X-intercept the point where a line crosses the x-axis Y-intercept the point where a line crosses the y-axis 3. Find the x-intercept and the y-intercept of the graph of the equation 2x + 3y = 6. What should you do first to find the x-intercept? Let y = 0 X-intercept: 3 What should you do next to find the y-intercept? Let x = 0 Y-intercept: 2 (Opening Handout) 46

47 Algebra I Math 9 Name: Answer the questions and then graph the following equations. For questions # 1, use the x- and y-intercept from the opening handout to find the slope since the equations are the same. 1. 2x + 3y = 6 a. What is the slope of this line? b. Sketch the graph of the equation c. Using Algebra I, enter your coordinates - into the table of values. Press enter to get the graph of your equation. To check if this is the right graph for the equation, make a y = box by choosing it from the tool bar on the left of the screen. Connect the y= box with your graph box. Press enter on your table to get the equation and the graph. d. Does your sketch match the picture on the computer? x + 7y = 14 a. X-intercept: b. Y-intercept: c. Find the slope: d. Make a sketch of the graph after you have done the graph on Algebra I

48 3. y = 4x + 8 a. X-intercept: b. Y-intercept: c. Find the slope: 15 d. Make a sketch of the graph. 4. x 2y = 6 a. X-intercept: b. Y-intercept: c. Find the slope: d. Make a sketch of the graph (Main Handout) 48

49 Algebra I Math 9 Name:KEY Answer the questions and then graph the following equations. For questions # 1, use the x- and y-intercept from the opening handout to find the slope since the equations are the same. 5. 2x + 3y = 6 b. What is the slope of this line? m = -2/3 b. Sketch the graph of the equation. c. Using Algebra I, enter your coordinates into the table of values. Press enter to get the - graph of your equation. To check if this is the right graph for the equation, make a y = box by choosing it from the tool bar on the left of the screen. Connect the y= box with your graph box. Press enter on your table to get the equation and the graph. d. Does your sketch match the picture on the computer? x + 7y = 14 e. X-intercept: 4 f. Y-intercept: 2 5 g. Find the slope: m = -1/

50 h. Make a sketch of the graph after you have done the graph on Algebra I. 7. y = 4x + 8 e. X-intercept: -2 f. Y-intercept: 8 g. Find the slope: m = 4 h. Make a sketch of the graph. 8. x 2y = 6 e. X-intercept: 6 f. Y-intercept: g. Find the slope: 1/2 h. Make a sketch of the graph (Main Handout) 50

51 Intercepts Closing Math 9 Name: Use the graph to find the x-intercept and the y-intercept of the line. 1. Window: (-7.5, 7.5) x (-5, 5) X-intercept: Y-intercept: 2. Window: (-7.5, 7.5) x (-5, 5) X-intercept: Y-intercept: 3. Window: (-9.5, 5.5) x (-5.5, 4.5) X-intercept: Y-intercept: 4. Window: (-40, 20) x (-20, 50) X-intercept: Y-intercept: Scale is by 51

52 5. Window: (-0, 0) x (-0, 0) X-intercept: Y-intercept: Scale is by Window: (-.5,.5) x (-7, 7) X-intercept: Y-intercept: (Closing Handout) 52

53 Intercepts Closing Math 9 Name:KEY Use the graph to find the x-intercept and the y-intercept of the line. 1. Window: (-7.5, 7.5) x (-5, 5) X-intercept: 2 Y-intercept: 3 2. Window: (-7.5, 7.5) x (-5, 5) X-intercept: -2 Y-intercept: 4 3. Window: (-9.5, 5.5) x (-5.5, 4.5) X-intercept: -4 Y-intercept: Window: (-40, 20) x (-20, 50) X-intercept: - Y-intercept: 40 Scale is by 53

54 5. Window: (-0, 0) x (-0, 0) X-intercept: 25 Y-intercept: 50 Scale is by Window: (-.5,.5) x (-7, 7) X-intercept: -3 Y-intercept: 6 (Closing Handout) 54

55 Homework Handout Math 9 Name: Find the x-intercept of the graph. 1. x + 3y = x + 2y = x + 4y = x y = x + 3y = x 20y = 60 Find the y-intercept of the graph. 7. y = -2x y = 3x 4 9. y = 8x x 5y = x 9y = x + 12y = -84 Choose two of the equations from 1 6. Make sketches of the two that you have chosen

56 Choose two of the equations from Make sketches of each that you have chosen Follow each step in order to do the following problems. -15 Example 1 Step 1: Given these two intercepts, find the slope. (0, 5) and (, 0) m = Step 2: Substitute m into y = mx + b Step 3: Substitute the y-intercept in for b. This is the equation of the line. Problems: 1. (0, 9) and (3, 0) 4. (0,.01) and (.5, 0) 2. (4, 0) and (0, 8) 5. (-35, 0) and (0, 5) 3. (-1/2, 0) and (0, 3/4) 6. (.7, 0) and (0, -2.1) (Homework Handout) 56

57 Homework Handout Math 9 Name:KEY Find the x-intercept of the graph. 13. x + 3y = x + 2y = x + 4y = x y = x + 3y = x 20y = 60-5 Find the y-intercept of the graph. 19. y = -2x y = 3x y = 8x x 5y = x 9y = x + 12y =

58 Choose two of the equations from 1 6. Make sketches of the two that you have chosen. r x = 5-x 3 27+x sx = x + 3y = 5 -x + 3y = 27 Choose two of the equations from Make sketches of e ach that you have chosen. ux = -2 x+5 vx = 3 x y = -2x + 5 y = 3x

59 Follow each step in order to do the following problems. Example 1 Step 1: Given these two intercepts, find the slope. (0, 5) and (, 0) m = -1/2 Step 2: Substitute m into y = mx + b y = -1/2x + b Step 3: Substitute the y-intercept in for b. This is the equation of the line. y = -1/2x + 5 Problems: 4. (0, 9) and (3, 0) y = -3x (0,.01) and (.5, 0) y =.02x (4, 0) and (0, 8) y = -2x (-35, 0) and (0, 5) y = 3x (-1/2, 0) and (0, 3/4) 6. (.7, 0) and (0, -2.1) y = 3x 2.1 y = 3/2x + 3/4 (Homework Handout) 59

60 Day 5: Scatter Plot and Best Fit Lines Objectives: Ninth grade students will be using their TI-83 Plus to do an activity that involves a scatter plot. They will be constructing the best-fit line of this scatter plot after doing a hands-on activity. Opening Activity: Students will be doing a quick review of the previous night s homework. The review will be a handout that asks them to write equations in slope-intercept form (y = mx + b). Main Activity: Students will be doing an activity with their TI-83 Plus using stat plot. For 20 seconds, they will put the first letter of their last name in one-inch squares of grid paper. They will be doing this with their dominant hand, or the hand they write with. They will count how many times they wrote the letter and record that number, along with their name, on the spreadsheet. For 20 seconds more, students will use the opposite hand and do the same activity. They should count and record their data. Name of Student Number of Letters - Dominant 1) 2) 3) 4) 5) 6) 7) 8) 9) ) X Number of Letters Non-Dominant Y 60

61 The next step in this activity is to graph the data. On a separate piece of graph paper, make a first quadrant graph of the data by plotting the points from the table. The dominant hand numbers go into the x values; they represent the x-axis. The nondominant hand represents the y-axis. The students will link their calculators with the calculator at the front of the classroom. The front calculator has two lists stored. The first list, DOM, and the second list, NON. The students will be receiving both of these lists. The students will need to use the following commands: 2 nd Link; Arrow over once to Receive; Press enter. The front calculator has to follow these commands in order to send the two lists: 2 nd Link; 4:List ; Arrow down to DOM; Press enter (there should be a little square next to the chosen list); Arrow up or down to NON; Press enter; Arrow over once to Transmit; Press enter. By choosing both of these lists, the students should receive both of them into their calculators as long as the little squares appeared next to both lists. The students will be using these lists to construct a scatter plot of the data. They will use the following commands: 2 nd y =; 1:Enter; Press enter when the cursor is blinking to ON; Arrow down to TYPE; Press enter on the graph that has a bunch of dots; Arrow down to Xlist; 2 nd Stat; Under NAMES, arrow down to DOM; Press enter (DOM should appear in the Xlist spot); Arrow down to Ylist; 2 nd Stat; Under NAMES, arrow down to NON; Press enter (this should appear in the Ylist); Arrow down to Mark; Press 61

62 enter on the box; ZOOM; 9:ZOOMSTAT. The scatter plot of the classes data should appear on their screen. Closing Activity: Students will be using this data to find a best-fitting line. They will use linear regression to find the best-fitting line. They will need to follow these steps: 2 nd Stat; CALC; 4:LinReg(ax+b); 2 nd LIST; Arrow down to DOM and press enter; comma; 2 nd LIST; Arrow down to NON and press enter; comma; VARS; Y-VARS; 1:FUNCTION; 1:Y1; Enter. The students should get a screen that gives them values for a, b, r^2, and r. If the students look at y =, they will see that they have an equation of a line in y = mx+b form. They can use GRAPH to graph the line along with their data. There will be a handout for this activity that the students will do together in groups of two or three. The students should notice that a represents the slope and b represents the y-intercept. The value for r tells us how well this line fits our set of data. In other words, how well is our line in accordance with our data? The closer the absolute value of r is to 1, the better the line fits the data. 62

63 Homework: Students are given a homework assignment that involves the same activity. However, the experiment they have to simulate involves a little twist. Instead of using dominant and non-dominant, the people doing the activity would use their right and left hands; it doesn t matter which hand they usually write with. 63

64 Teachers Notes Opening Activity: Since there wasn t much time spent on slope-intercept form yesterday, you should go over more examples at the beginning of today s class. It is not a good idea to go over every homework problem from yesterday. If a student didn t do their homework, then we would just be giving them the answer. New example questions will help them learn the concept. Also, if they did have a problem or did not do their homework, they can go back and try it again. Main Activity: This is a great way to teach the students how to plot data using their calculators. Also, the activity is fun so they will want to try it. Closing Activity: This will help us review slope-intercept form in a different context. It will reinforce what each of the variables represents. When the students do the linear regression, the diagnostics on their calculator must be on. They can go to 2 nd CATALOG; Press D; Arrow down to Diagnostics On; ENTER; ENTER. Homework: The homework is designed to show the students that an experiment can be done right, but it may look like there was an error. If the experiment had been done by just saying right- and left-handed, the students may have assumed that the whole class is right-handed. I think it is easier for them to see the differences in the way the activities are worded. 64

65 Slope-Intercept Form Math 9 Name: Write an equation in slope-intercept form of the line that passes through the points. 1. (-3, 0) and (0, -1) 2. (-1, 0) and (0, -3) 3. (4, 2) and (-2, -4) (*HINT: After finding the slope, substitute it for m and use one of your points for your x and y. Use algebra to solve for b.) 4. (-6, -5) and (1, 4) 5. (2, 3) and (4, 3) 6. (5, -) and (12, -7) (Opening Handout) 65

66 Slope-Intercept Form Math 9 Name:KEY Write an equation in slope-intercept form of the line that passes through the points. 7. (-3, 0) and (0, -1) y = -1/3x (-1, 0) and (0, -3) y = -3x (4, 2) and (-2, -4) y = x - 2 (*HINT: After finding the slope, substitute it for m and use one of your points for your x and y. Use algebra to solve for b.). (-6, -5) and (1, 4) y = 9/7 x + 19/7 11. (2, 3) and (4, 3) y = (5, -) and (12, -7) y = 3/7 x 85/7 (Opening Handout) 66

67 X Y Name of Student 1) 2) 3) 4) 5) 6) 7) 8) 9) ) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) Number of Letters - Dominant Number of Letters - Non- Dominant (Main Activity) 67

68 First Quadrant Graph Paper

69 Homework Assignment Math 9 Name: We did the activity using dominant and non-dominant hands for writing. However, some people are left-handed and others are right-handed. For example, John is writes with his left hand. He writes the first letter of his last name on the worksheet for 20 seconds with his right hand. Then, he changes hands and writes the letter in the boxes with his left hand. What do you think would happen to the data if 29 students were righthanded and 1 student was left-handed? What would the scatter plot look like? Your job is to give an example of 5 students who are participating in the activity. Out of these five students, four are right-handed and one is left-handed. Fill in the table below with five students names. Fill out the table as if the experiment were conducted amongst these five students, remembering that one student is left-handed. Try to make your data as real as possible, like five of your friends did the experiment. Name of Number of Letters - Right Number of Letters - Left hand Student hand 1) 2) 3) 4) 5) Draw a first quadrant graph of the data by plotting the points above. 69

70 Draw the y = x line on your first quadrant graph. What is the meaning of this line? What do the points above the y = x line represent? What do the points below the y = x line represent? What is the significance of points near the y = x line? (Homework Handout) 70

71 Homework Assignment Math 9 Name: Student Sample Worksheet We did the activity using dominant and non-dominant hands for writing. However, some people are left-handed and others are right-handed. For example, John is writes with his left hand. He writes the first letter of his last name on the worksheet for 20 seconds with his right hand. Then, he changes hands and writes the letter in the boxes with his left hand. What do you think would happen to the data if 29 students were righthanded and 1 student was left-handed? What would the scatter plot look like? Your job is to give an example of 5 students who are participating in the activity. Out of these five students, four are right-handed and one is left-handed. Fill in the table below with five students names. Fill out the table as if the experiment were conducted amongst these five students, remembering that one student is left-handed. Try to make your data as real as possible, like five of your friends did the experiment. Name of Number of Letters - Right Number of Letters - Left hand Student hand 1)Karen )John )Megan )Shawn )Kristen

72 w x = x Draw a first quadrant graph of the data by plotting the points above. Draw the y = x line on your first quadrant graph. What is the meaning of this line? This is the line that represents people who are right and left handed. What do the points above the y = x line represent? The people who write more letters with their left hand. What do the points below the y = x line represent? The people who write more letters with their right hand. What is the significance of points near the y = x line? These people can write well with both hands. (Homework Handout) 72

Educator s Guide to Graphing y = mx + b

Educator s Guide to Graphing y = mx + b Educator s Guide to Graphing y = mx + b Overview: Using an ipad and Sketchpad Explorer, students will graph a linear equation using the y intercept and slope. Grades and Subject Areas: High School Algebra

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 T936 Mathematics Success Grade 8 [OBJECTIVE] The student will find the line of best fit for a scatter plot, interpret the equation and y-intercept of the linear representation, and make predictions based

More information

Lesson 17. Student Outcomes. Lesson Notes. Classwork. Example 1 (5 10 minutes): Predicting the Pattern in the Residual Plot

Lesson 17. Student Outcomes. Lesson Notes. Classwork. Example 1 (5 10 minutes): Predicting the Pattern in the Residual Plot Student Outcomes Students use a graphing calculator to construct the residual plot for a given data set. Students use a residual plot as an indication of whether the model used to describe the relationship

More information

Plotting Points in 2-dimensions. Graphing 2 variable equations. Stuff About Lines

Plotting Points in 2-dimensions. Graphing 2 variable equations. Stuff About Lines Plotting Points in 2-dimensions Graphing 2 variable equations Stuff About Lines Plotting Points in 2-dimensions Plotting Points: 2-dimension Setup of the Cartesian Coordinate System: Draw 2 number lines:

More information

Lesson 6.1 Linear Equation Review

Lesson 6.1 Linear Equation Review Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can

More information

Math Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure

Math Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure Math Labs Activity 1: Rectangles and Rectangular Prisms Using Coordinates Problem Statement Use the Cartesian coordinate system to draw rectangle ABCD. Use an x-y-z coordinate system to draw a rectangular

More information

Graphs of linear equations will be perfectly straight lines. Why would we say that A and B are not both zero?

Graphs of linear equations will be perfectly straight lines. Why would we say that A and B are not both zero? College algebra Linear Functions : Definition, Horizontal and Vertical Lines, Slope, Rate of Change, Slopeintercept Form, Point-slope Form, Parallel and Perpendicular Lines, Linear Regression (sections.3

More information

Discovery Activity: Slope

Discovery Activity: Slope Page 1 of 14 1. Lesson Title: Discovering Slope-Intercept Form 2. Lesson Summary: This lesson is a review of slope and guides the students through discovering slope-intercept form using paper/pencil and

More information

Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form.

Algebra Success. LESSON 16: Graphing Lines in Standard Form. [OBJECTIVE] The student will graph lines described by equations in standard form. T328 [OBJECTIVE] The student will graph lines described by equations in standard form. [MATERIALS] Student pages S125 S133 Transparencies T336, T338, T340, T342, T344 Wall-size four-quadrant grid [ESSENTIAL

More information

E. Slope-Intercept Form and Direct Variation (pp )

E. Slope-Intercept Form and Direct Variation (pp ) and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the

More information

Lesson 1b Linear Equations

Lesson 1b Linear Equations In the first lesson we looked at the concepts and rules of a Function. The first Function that we are going to investigate is the Linear Function. This is a good place to start because with Linear Functions,

More information

Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004

Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined

More information

6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line.

6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. 6.1 Slope of a Line Name: Date: Goal: Determine the slope of a line segment and a line. Toolkit: - Rate of change - Simplifying fractions Main Ideas: Definitions Rise: the vertical distance between two

More information

Exploring the Pythagorean Theorem

Exploring the Pythagorean Theorem Exploring the Pythagorean Theorem Lesson 11 Mathematics Objectives Students will analyze relationships to develop the Pythagorean Theorem. Students will find missing sides in right triangles using the

More information

Use Linear Regression to Find the Best Line on a Graphing Calculator

Use Linear Regression to Find the Best Line on a Graphing Calculator In an earlier technology assignment, you created a scatter plot of the US Student to Teacher Ratio for public schools from the table below. The scatter plot is shown to the right of the table and includes

More information

VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University Visual Algebra for College Students Copyright 010 All rights reserved Laurie J. Burton Western Oregon University Many of the

More information

Math 165 Section 3.1 Linear Functions

Math 165 Section 3.1 Linear Functions Math 165 Section 3.1 Linear Functions - complete this page Read the book or the power point presentations for this section. Complete all questions on this page Also complete all questions on page 6 1)

More information

Algebra/Geometry. Slope/Triangle Area Exploration

Algebra/Geometry. Slope/Triangle Area Exploration Slope/Triangle Area Exploration ID: 9863 Time required 60 90 minutes Topics: Linear Functions, Triangle Area, Rational Functions Graph lines in slope-intercept form Find the coordinate of the x- and y-intercepts

More information

Looking for Pythagoras An Investigation of the Pythagorean Theorem

Looking for Pythagoras An Investigation of the Pythagorean Theorem Looking for Pythagoras An Investigation of the Pythagorean Theorem I2t2 2006 Stephen Walczyk Grade 8 7-Day Unit Plan Tools Used: Overhead Projector Overhead markers TI-83 Graphing Calculator (& class set)

More information

Excel Tool: Plots of Data Sets

Excel Tool: Plots of Data Sets Excel Tool: Plots of Data Sets Excel makes it very easy for the scientist to visualize a data set. In this assignment, we learn how to produce various plots of data sets. Open a new Excel workbook, and

More information

Aim #35.1: How do we graph using a table?

Aim #35.1: How do we graph using a table? A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)

More information

Mathematics Success Grade 6

Mathematics Success Grade 6 T428 Mathematics Success Grade 6 [OBJECTIVE] The students will plot ordered pairs containing rational values to identify vertical and horizontal lengths between two points in order to solve real-world

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]

More information

Geometer s Sketchpad Version 4

Geometer s Sketchpad Version 4 Geometer s Sketchpad Version 4 For PC Name: Date: INVESTIGATION: The Pythagorean Theorem Directions: Use the steps below to lead you through the investigation. After each step, be sure to click in the

More information

Review Journal 6 Assigned Work: Page 146, All questions

Review Journal 6 Assigned Work: Page 146, All questions MFM2P Linear Relations Checklist 1 Goals for this unit: I can explain the properties of slope and calculate its value as a rate of change. I can determine y-intercepts and slopes of given relations. I

More information

Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane

Chapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant

More information

8.EE. Development from y = mx to y = mx + b DRAFT EduTron Corporation. Draft for NYSED NTI Use Only

8.EE. Development from y = mx to y = mx + b DRAFT EduTron Corporation. Draft for NYSED NTI Use Only 8.EE EduTron Corporation Draft for NYSED NTI Use Only TEACHER S GUIDE 8.EE.6 DERIVING EQUATIONS FOR LINES WITH NON-ZERO Y-INTERCEPTS Development from y = mx to y = mx + b DRAFT 2012.11.29 Teacher s Guide:

More information

MATH 150 Pre-Calculus

MATH 150 Pre-Calculus MATH 150 Pre-Calculus Fall, 2014, WEEK 5 JoungDong Kim Week 5: 3B, 3C Chapter 3B. Graphs of Equations Draw the graph x+y = 6. Then every point on the graph satisfies the equation x+y = 6. Note. The graph

More information

Slope-Intercept Form of a Line

Slope-Intercept Form of a Line Lesson Plan Lecture Edition Slope-Intercept Form of a Line Objectives Students will: discover how slope effects the graph of a line. relate b to the y-intercept of a line. determine the equation of a line

More information

Section 3.5. Equations of Lines

Section 3.5. Equations of Lines Section 3.5 Equations of Lines Learning objectives Use slope-intercept form to write an equation of a line Use slope-intercept form to graph a linear equation Use the point-slope form to find an equation

More information

Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis

Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis Pre-AP Algebra 2 Unit 8 - Lesson 2 Graphing rational functions by plugging in numbers; feature analysis Objectives: Students will be able to: Analyze the features of a rational function: determine domain,

More information

In Lesson 2.5 you were introduced to linear functions. Slope-intercept form is the most common equation

In Lesson 2.5 you were introduced to linear functions. Slope-intercept form is the most common equation GRAPHING USING SLOPE-INTERCEPT FORM LESSON 3.1 In Lesson 2.5 you were introduced to linear functions. Slope-intercept form is the most common equation used to represent a linear function. It is called

More information

Manchester College Education Department. Lesson Plan by Daniel Haffner

Manchester College Education Department. Lesson Plan by Daniel Haffner Manchester College Education Department Lesson Plan by Daniel Haffner Lesson: Quiz on Slope, Slope-Intercept Form, and Standard Form Length: 70 min Age or Grade Level Intended: Algebra 1 Academic Standard(s):

More information

Appendix 3 - Using A Spreadsheet for Data Analysis

Appendix 3 - Using A Spreadsheet for Data Analysis 105 Linear Regression - an Overview Appendix 3 - Using A Spreadsheet for Data Analysis Scientists often choose to seek linear relationships, because they are easiest to understand and to analyze. But,

More information

Chapter 2: Functions and Graphs Lesson Index & Summary

Chapter 2: Functions and Graphs Lesson Index & Summary Section 1: Relations and Graphs Cartesian coordinates Screen 2 Coordinate plane Screen 2 Domain of relation Screen 3 Graph of a relation Screen 3 Linear equation Screen 6 Ordered pairs Screen 1 Origin

More information

Getting Started with Algebra 2. Perimeter and Area Models ID: 9837

Getting Started with Algebra 2. Perimeter and Area Models ID: 9837 Perimeter and Area Models ID: 9837 By Holly Thompson Time required 30 minutes Activity Overview Students will look at data for the perimeter and area changes of a rectangle and triangle as their dimensions

More information

Linear, Quadratic and Cubic Function Explorer Teacher Notes

Linear, Quadratic and Cubic Function Explorer Teacher Notes Introduction LinQuadCubic Explorer Linear, Quadratic and Cubic Function Explorer Teacher Notes The aim of this.tns file is to provide an environment in which students can explore all aspects of linear,

More information

LINEAR EQUATIONS IN TWO VARIABLES

LINEAR EQUATIONS IN TWO VARIABLES LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.

More information

MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change

MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points Mr. Deyo Find Slope and Rate of Change Title: 5.5a Find Slope Given Two Points Date: Learning Target By the end of the period, I will find the slope

More information

Visualizing Integers TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Visualizing Integers TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System Math Objectives Students will identify expressions that balance an equation. Students will find values that satisfy integer equalities. Students will recognize and use the additive inverse property. Students

More information

TImiddlegrades.com. Science. Watt s The Deal

TImiddlegrades.com. Science. Watt s The Deal Watt s The Deal ID: 13435 Time required: 1 class period Suggested Grade Levels: 7 8 Activity Overview In this activity, students will use the CBL to collect data on the brightness of different light bulbs

More information

Algebra 2. Slope of waste pipes

Algebra 2. Slope of waste pipes Algebra 2 Slope of waste pipes Subject Area: Math Grade Levels: 9-12 Date: Aug 25 th -26 th Lesson Overview: Students will first complete a worksheet reviewing slope, rate of change,, and plotting points.

More information

2.3 Quick Graphs of Linear Equations

2.3 Quick Graphs of Linear Equations 2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear

More information

Points, Lines, & Slopes (Oh My!)

Points, Lines, & Slopes (Oh My!) About the Lesson In this activity students will explore the relationship among coordinates of points and locations on the coordinate plane, the relationships of lines with their equations, slopes and y-intercepts,

More information

Algebra. Teacher s Guide

Algebra. Teacher s Guide Algebra Teacher s Guide WALCH PUBLISHING Table of Contents To the Teacher.......................................................... vi Classroom Management..................................................

More information

Assignment 5 due Monday, May 7

Assignment 5 due Monday, May 7 due Monday, May 7 Simulations and the Law of Large Numbers Overview In both parts of the assignment, you will be calculating a theoretical probability for a certain procedure. In other words, this uses

More information

Economics 101 Spring 2015 Answers to Homework #1 Due Thursday, February 5, 2015

Economics 101 Spring 2015 Answers to Homework #1 Due Thursday, February 5, 2015 Economics 101 Spring 2015 Answers to Homework #1 Due Thursday, February 5, 2015 Directions: The homework will be collected in a box before the lecture. Please place your name on top of the homework (legibly).

More information

TIalgebra.com Algebra 1

TIalgebra.com Algebra 1 Perpendicular Slopes ID: 8973 Time required 45 minutes Topic: Linear Functions Graph lines whose slopes are negative reciprocals and measure the angles to verify they are perpendicular. Activity Overview

More information

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two

More information

Section 1.3. Slope formula: If the coordinates of two points on the line are known then we can use the slope formula to find the slope of the line.

Section 1.3. Slope formula: If the coordinates of two points on the line are known then we can use the slope formula to find the slope of the line. MATH 11009: Linear Functions Section 1.3 Linear Function: A linear function is a function that can be written in the form f(x) = ax + b or y = ax + b where a and b are constants. The graph of a linear

More information

Actual testimonials from people that have used the survival guide:

Actual testimonials from people that have used the survival guide: Algebra 1A Unit: Coordinate Plane Assignment Sheet Name: Period: # 1.) Page 206 #1 6 2.) Page 206 #10 26 all 3.) Worksheet (SIF/Standard) 4.) Worksheet (SIF/Standard) 5.) Worksheet (SIF/Standard) 6.) Worksheet

More information

Algebra I Notes Unit Seven: Writing Linear Equations

Algebra I Notes Unit Seven: Writing Linear Equations Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of

More information

The Picture Tells the Linear Story

The Picture Tells the Linear Story The Picture Tells the Linear Story Students investigate the relationship between constants and coefficients in a linear equation and the resulting slopes and y-intercepts on the graphs. This activity also

More information

Excel Lab 2: Plots of Data Sets

Excel Lab 2: Plots of Data Sets Excel Lab 2: Plots of Data Sets Excel makes it very easy for the scientist to visualize a data set. In this assignment, we learn how to produce various plots of data sets. Open a new Excel workbook, and

More information

Algebra/Geometry. Slope/Triangle Area Exploration

Algebra/Geometry. Slope/Triangle Area Exploration Slope/Triangle Area Exploration ID: Time required 60 minutes Topics: Linear Functions, Triangle Area, Rational Functions Graph lines in slope-intercept form Find the coordinate of the x- and y-intercepts

More information

Optimization Exploration: The Inscribed Rectangle. Learning Objectives: Materials:

Optimization Exploration: The Inscribed Rectangle. Learning Objectives: Materials: Optimization Exploration: The Inscribed Rectangle Lesson Information Written by Jonathan Schweig and Shira Sand Subject: Pre-Calculus Calculus Algebra Topic: Functions Overview: Students will explore some

More information

CLEMSON MIDDLE SCHOOL MATHEMATICS PROJECT UNIT 5: GEOMETRIC RELATIONSHIPS

CLEMSON MIDDLE SCHOOL MATHEMATICS PROJECT UNIT 5: GEOMETRIC RELATIONSHIPS CLEMSON MIDDLE SCHOOL MATHEMATICS PROJECT UNIT 5: GEOMETRIC RELATIONSHIPS PROBLEM 1: PERIMETER AND AREA TRAINS Let s define a train as the shape formed by congruent, regular polygons that share a side.

More information

MS Algebra A-F-IF-7 Ch. 5.6a Graph Using Slope-Intercept Form. Mr. Deyo Graph Using Slope-Intercept Form

MS Algebra A-F-IF-7 Ch. 5.6a Graph Using Slope-Intercept Form. Mr. Deyo Graph Using Slope-Intercept Form MS Algebra A-F-IF-7 Ch. 5.6a Graph Using Slope-Intercept Form Mr. Deyo Graph Using Slope-Intercept Form Title: 5.6a Slope-Intercept Form Date: Learning Target By the end of the period, I will apply the

More information

Introduction to the Graphing Calculator for the TI-86

Introduction to the Graphing Calculator for the TI-86 Algebra 090 ~ Lecture Introduction to the Graphing Calculator for the TI-86 Copyright 1996 Sally J. Glover All Rights Reserved Grab your calculator and follow along. Note: BOLD FACE are used for calculator

More information

Title: Quadrilaterals Aren t Just Squares

Title: Quadrilaterals Aren t Just Squares Title: Quadrilaterals ren t Just Squares Brief Overview: This is a collection of the first three lessons in a series of seven lessons studying characteristics of quadrilaterals, including trapezoids, parallelograms,

More information

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below:

PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below: Math (L-3a) Learning Targets: I can find the vertex from intercept solutions calculated by quadratic formula. PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to

More information

Objective: Plot points, using them to draw lines in the plane, and describe

Objective: Plot points, using them to draw lines in the plane, and describe NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 7 5 6 Lesson 7 Objective: Plot points, using them to draw lines in the plane, and describe patterns within the coordinate pairs. Suggested Lesson Structure

More information

Outcome 7 Review. *Recall that -1 (-5) means

Outcome 7 Review. *Recall that -1 (-5) means Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into

More information

Year 11 Graphing Notes

Year 11 Graphing Notes Year 11 Graphing Notes Terminology It is very important that students understand, and always use, the correct terms. Indeed, not understanding or using the correct terms is one of the main reasons students

More information

Excel 2003: Discos. 1. Open Excel. 2. Create Choose a new worksheet and save the file to your area calling it: Disco.xls

Excel 2003: Discos. 1. Open Excel. 2. Create Choose a new worksheet and save the file to your area calling it: Disco.xls Excel 2003: Discos 1. Open Excel 2. Create Choose a new worksheet and save the file to your area calling it: Disco.xls 3. Enter the following data into your spreadsheet: 4. Make the headings bold. Centre

More information

Objective: Investigate patterns in vertical and horizontal lines, and. interpret points on the plane as distances from the axes.

Objective: Investigate patterns in vertical and horizontal lines, and. interpret points on the plane as distances from the axes. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 5 6 Lesson 6 Objective: Investigate patterns in vertical and horizontal lines, and Suggested Lesson Structure Fluency Practice Application Problem Concept

More information

Optimization: Constructing a Box

Optimization: Constructing a Box Optimization: Constructing a Box Lesson Information Written by Jonathan Schweig and Shira Sand Subject: Pre-Calculus Calculus Algebra Topic: Functions Overview: This lesson walks students through a classic

More information

Today We will: Create linear equations from a context and model with tables and graphs.

Today We will: Create linear equations from a context and model with tables and graphs. U2D11 Math 8C U2D11 Today We will: Create linear equations from a context and model with tables and graphs. U2D11 A quick review: Plotting Points Plot the points A(2, 3) B(-1, -4) C(-3, 3) C A D(4, -2)

More information

ACTIVITY 6. Intersection. You ll Need. Name. Date. 2 CBR units 2 TI-83 or TI-82 Graphing Calculators Yard stick Masking tape

ACTIVITY 6. Intersection. You ll Need. Name. Date. 2 CBR units 2 TI-83 or TI-82 Graphing Calculators Yard stick Masking tape . Name Date ACTIVITY 6 Intersection Suppose two people walking meet on the street and pass each other. These motions can be modeled graphically. The motion graphs are linear if each person is walking at

More information

Investigation and Exploration Dynamic Geometry Software

Investigation and Exploration Dynamic Geometry Software Investigation and Exploration Dynamic Geometry Software What is Mathematics Investigation? A complete mathematical investigation requires at least three steps: finding a pattern or other conjecture; seeking

More information

Rate of Change and Slope by Paul Alves

Rate of Change and Slope by Paul Alves Rate of Change and Slope by Paul Alves Activity overview This lesson was designed for the Grade 10 Applied curriculum in Ontario. In that course, students are expected to connect the rate of change of

More information

Lesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions.

Lesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions. Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable

More information

One of the classes that I have taught over the past few years is a technology course for

One of the classes that I have taught over the past few years is a technology course for Trigonometric Functions through Right Triangle Similarities Todd O. Moyer, Towson University Abstract: This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and

More information

Patterns and Graphing Year 10

Patterns and Graphing Year 10 Patterns and Graphing Year 10 While students may be shown various different types of patterns in the classroom, they will be tested on simple ones, with each term of the pattern an equal difference from

More information

Honors Chemistry Summer Assignment

Honors Chemistry Summer Assignment Honors Chemistry Summer Assignment Page 1 Honors Chemistry Summer Assignment 2014-2015 Materials needed for class: Scientific or Graphing Calculator Mrs. Dorman ldorman@ringgold.org Notebook with folder

More information

CHM 109 Excel Refresher Exercise adapted from Dr. C. Bender s exercise

CHM 109 Excel Refresher Exercise adapted from Dr. C. Bender s exercise CHM 109 Excel Refresher Exercise adapted from Dr. C. Bender s exercise (1 point) (Also see appendix II: Summary for making spreadsheets and graphs with Excel.) You will use spreadsheets to analyze data

More information

1 Write a Function in

1 Write a Function in www.ck12.org Chapter 1. Write a Function in Slope-Intercept Form CHAPTER 1 Write a Function in Slope-Intercept Form Here you ll learn how to write the slope-intercept form of linear functions and how to

More information

G.2 Slope of a Line and Its Interpretation

G.2 Slope of a Line and Its Interpretation G.2 Slope of a Line and Its Interpretation Slope Slope (steepness) is a very important concept that appears in many branches of mathematics as well as statistics, physics, business, and other areas. In

More information

Products of Linear Functions

Products of Linear Functions Math Objectives Students will understand relationships between the horizontal intercepts of two linear functions and the horizontal intercepts of the quadratic function resulting from their product. Students

More information

Angles formed by Transversals

Angles formed by Transversals Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel

More information

Objective: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

Objective: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes. Lesson 5 Objective: Investigate patterns in vertical and horizontal lines, and interpret Suggested Lesson Structure Application Problem Fluency Practice Concept Development Student Debrief Total Time (7

More information

Student Exploration: Standard Form of a Line

Student Exploration: Standard Form of a Line Name: Date: Student Exploration: Standard Form of a Line Vocabulary: slope, slope-intercept form, standard form, x-intercept, y-intercept Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1.

More information

(VIDEO GAME LEARNING TASK)

(VIDEO GAME LEARNING TASK) (VIDEO GAME LEARNING TASK) John and Mary are fond of playing retro style video games on hand held game machines. They are currently playing a game on a device that has a screen that is 2 inches high and

More information

10 GRAPHING LINEAR EQUATIONS

10 GRAPHING LINEAR EQUATIONS 0 GRAPHING LINEAR EQUATIONS We now expand our discussion of the single-variable equation to the linear equation in two variables, x and y. Some examples of linear equations are x+ y = 0, y = 3 x, x= 4,

More information

The learner will understand and use linear relations and functions.

The learner will understand and use linear relations and functions. The learner will understand and use linear relations and functions. Notes 5and textbook 5.01 Develop an understanding of function. a) Translate among verbal, tabular, graphic, and algebraic representations

More information

Section Assignments and Suggested Problems Do more odd numbered problems if you have difficulties with a certain topic

Section Assignments and Suggested Problems Do more odd numbered problems if you have difficulties with a certain topic Homework Math 180 Fall 2007 OLD (4 TH ) EDITION OF THE BOOK In order to succeed in the class you need to read the book and do problems on a daily basis. Spend at least two hours per day in your math homework.

More information

Essential Question How can you describe the graph of the equation y = mx + b?

Essential Question How can you describe the graph of the equation y = mx + b? .5 Graphing Linear Equations in Slope-Intercept Form COMMON CORE Learning Standards HSA-CED.A. HSF-IF.B. HSF-IF.C.7a HSF-LE.B.5 Essential Question How can ou describe the graph of the equation = m + b?

More information

Graphing Lines with a Table

Graphing Lines with a Table Graphing Lines with a Table Select (or use pre-selected) values for x Substitute those x values in the equation and solve for y Graph the x and y values as ordered pairs Connect points with a line Graph

More information

CHM 152 Lab 1: Plotting with Excel updated: May 2011

CHM 152 Lab 1: Plotting with Excel updated: May 2011 CHM 152 Lab 1: Plotting with Excel updated: May 2011 Introduction In this course, many of our labs will involve plotting data. While many students are nerds already quite proficient at using Excel to plot

More information

PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES

PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES Proportional means that if x is changed, then y is changed in the same proportion. This relationship can be expressed by a proportional/linear function

More information

4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz

4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12,

More information

Making Middle School Math Come Alive with Games and Activities

Making Middle School Math Come Alive with Games and Activities Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Sharon Rendon (605) 431-0216 sharonrendon@cpm.org 1 2-51. SPECIAL

More information

ACT Coordinate Geometry Review

ACT Coordinate Geometry Review ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this

More information

Name: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope.

Name: Date: Period: Activity 4.6.2: Point-Slope Form of an Equation. 0, 4 and moving to another point on the line using the slope. Name: Date: Period: Activity.6.2: Point-Slope Form of an Equation 1.) Graph the equation y x = + starting at ( ) 0, and moving to another point on the line using the slope. 2.) Now, draw another graph

More information

Sect Linear Equations in Two Variables

Sect Linear Equations in Two Variables 99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite

More information

Slope as Rate TEACHER NOTES

Slope as Rate TEACHER NOTES Math Objectives Students will be able to interpret the slope of a line as the rate of change of the y-coordinate per unit increase in the x-coordinate as one moves from left to right along the line. Students

More information

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.

Warm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.

More information

CAD Orientation (Mechanical and Architectural CAD)

CAD Orientation (Mechanical and Architectural CAD) Design and Drafting Description This is an introductory computer aided design (CAD) activity designed to give students the foundational skills required to complete future lessons. Students will learn all

More information

Economics 101 Spring 2017 Answers to Homework #1 Due Thursday, Feburary 9, 2017

Economics 101 Spring 2017 Answers to Homework #1 Due Thursday, Feburary 9, 2017 Economics 101 Spring 2017 Answers to Homework #1 Due Thursday, Feburary 9, 2017 Directions: The homework will be collected in a box before the large lecture. Please place your name, TA name and section

More information

Heads Up! A c t i v i t y 5. The Problem. Name Date

Heads Up! A c t i v i t y 5. The Problem. Name Date . Name Date A c t i v i t y 5 Heads Up! In this activity, you will study some important concepts in a branch of mathematics known as probability. You are using probability when you say things like: It

More information