Linear Equations. 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber


 Brittney Bonnie Pope
 5 years ago
 Views:
Transcription
1 Linear Equations 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI 83 adapter Math Book Graph Paper TI83 plus Calculators Computers CalculatorBased Ranger (CBR 2) Green Globs Software Pencils Paper Journals
2 2 Unit Objectives Given a five day instruction on linear equations, the following are unit objectives: Given instruction on how to create a table of values on the calculator from a linear equation, students will demonstrate how to make a table of values. Given technology instruction on how to use Geometers Sketchpad, students will be able to graph linear equations in Geometers Sketchpad. Given a technical briefing on the TI83 calculator, the students will be able to graph linear equations with their calculators. Students will calculate the x and y intercepts on the graph given linear equations. Students will create graphs and describe their slopes given instruction on the CBR. Students will be able to find the slope of a line. Students will be able to describe slopes with appropriate mathematical vocabulary. Given the TI83 calculators, students will be able to find the slope. Given the slopeintercept formula, the students will be able to rewrite linear equations into the slopeintercept form. Using the Green Globs software the students will be able to write linear equations. Given the slope and a point on the line, students will be able to write linear equations. Given a technical briefing of the TI83 calculator, students will be able to enter system of equations into the calculator. Given instruction on the matrix program of the TI83 calculator, students will be able to solve systems of equations. Students will be able to explore equations on the calculator by graphing the linear equations. New York State Standards
3 3 Standard 3: Mathematics A.PS.4 Use multiple representations to represent and explain problem situations. A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, function, equations, charts, graphs, Venn diagrams, and other diagrams. A.R.3 Use representation as a tool for exploring and understanding mathematical ideas. A.G.9 Solve system of linear equations graphically. A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equation, or objects created using technology as representation of mathematical concepts. A.G.4 Identify and graph linear functions Given a technical briefing on the TI83 calculator, the students will be able to graph linear equations. A.PS.4 Use multiple representations to represent and explain problem situations. A.A.33 Determine the slope of a line, given the coordinates of two points on the line. A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line. NCTM Standards Create and use representations to organize, record, and communicate mathematical ideas. Use Mathematical models to represent and understand quantitative relationships. Understand patterns, relations, and functions. Organize and consolidate their mathematical thinking through communication. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Analyze and evaluate the mathematical thinking and strategies of others. Represent and analyze mathematical situations and structures using algebraic symbols. Apply and adapt a variety of appropriate strategies to solve problems. Resources
4 4 McDougal Littell, Math Course 3, by Boswell, Laurie, Kanold, Timothy, Larson, Ron, Stiff, Lee, Houghton Mifflin, Chapter 11, pages , copyright Getting Started with the CBR 2 Sonic Motion Detector, Texas Instruments, Holden Custom Products, pages 1013, copyright Graphing Linear Equations, Elizabeth Stapel. Texas Instruments TI84 Plus Silver Edition Guidebook, Texas Instruments, Banta Book Group, pages chapter 12, 193, copyright 2004 Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, chapter 7, pages , copyright Mathematics Core Curriculum MST Standard 3, State Education Department, pages , copyright 2005 Materials Used Daily
5 5 Day 1: Geometer s Sketchpad Class work worksheet Paper Pencil Journals Day 2: TI83 plus Calculator Overhead with TI adapter Instructional worksheet Paper Pencil Journals Day 3: CalculatorBased Ranger TI 83 plus Calculator Overheard with TI84 adapter Graph Paper Worksheet on CBR Paper Pencil Journals Day 4: Green Globs program Worksheet on writing equations Paper Pencil Journals Day 5: TI83 plus Calculator Overhead with TI adaptor Class worksheet Find solutions worksheet Paper Pencil Journals 5Day Overview
6 6 Day 1: Graphs of Linear Equations Class discussion on what makes up a line Creating a table of values of a linear equation Plotting points on Geometers Sketchpad to create a line Assessment: Hand in their class work from Geometer s Sketchpad and there journals. Students will need to complete a worksheet on graphing linear equations. Day 2: Using Intercepts Class discussion on: What is an intercept? Exploring the TI83 Plus calculator Finding intercepts using the TI 83 Plus calculator (looking at graph and table) Group work on finding intercepts Full class discussion on class work Assessment: Turn in journals and class work Day 3: Introduction to Slope Class discussion on positive, negative and zero slope Instruction on CBR Group work with CBR Instruction using slope formula Assessment: Worksheet on finding slopes of different lines and turn in journals Day 4: Writing an equation for a line Class Discussion of equations for a line Instructions on Green Globs program Individually work in Green Globs with prizes Assessment: Worksheet on writing equations and turn in journals Day 5: Introduction to Solving Systems of Equations Class discussion on solving systems of equations Instruction on solving systems of equations with TI 83 Plus calculator Class worksheet on solving systems of equations Group work on solving systems of equations Assessment: Finding solutions to systems of equations worksheet and turn in journals Day One Lesson Plan Lesson Topic: Graphs of Linear Equations
7 7 Grade Level: 9 Materials: Geometer s Sketchpad, Worksheets, Computers, Journals Lesson Overview: Students will work with Geometer Sketchpad to develop an understanding of graphing linear equations.. Lesson Objectives: Students will demonstrate how to make a table of values. Students will be able to graph linear equations in Geometers Sketchpad. New York Standards: A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equation, or objects created using technology as representation of mathematical concepts. A.R.3 Use representation as a tool for exploring and understanding mathematical ideas. A.G.4 Identify and graph linear functions A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable. NCTM Standards: Create and use representations to organize, record, and communicate mathematical ideas. Use Mathematical models to represent and understand quantitative relationships. Anticipatory Set: The teacher will open the class by asking a variety of different questions that pertain to graphing linear equations: 1. What makes up a line? 2. How many points make up a line? 3. If you are given a linear equation, what information would you need from the equation in order to graph it? Possible Responses: 1. A line consists of points 2. 2 points make a line 3. Points Developmental Activity: 1. The teacher will discuss with the students how to find the values of points on a linear equation by creating a table and solving for different values. The teacher will show the students an example of a linear equation and set up a table on the overhead. Then the teacher will show the students how to find the values, by algebraically solving for y when placing different numbers in for x, while using the overhead. (Worksheet)
8 8 2. The teacher will give the students a worksheet, with an example on how to find different values for y. Also on the worksheet will be many different linear equations for which the students will need to create a table and find a few points on that linear equation. 3. The teacher will walk the students through the procedure of graphing lines from the tables they have created using Geometers Sketchpad. Then show the students how to plot points, and then find the linear equation from those points within Geometers Sketchpad. 4. With the worksheet on linear equations the students will find a few points for each equation. Then each student will plot the points in Geometers Sketchpad and find the linear equation in the program. By finding the linear equation within Geometers Sketchpad, will be a way to check to see if they graphed the equation correctly. 5. Once the students find the linear equations in Geometers Sketchpad they will print there results. Closure: The students will write into their journals how to draw a linear equation on graph paper without using geometers sketchpad. The students will write down how they felt about Geometers Sketchpad and if they were confused about anything. Assessment: The teacher will collect the worksheet and printed results of the graphs they created in Geometers Sketchpad. The students will be given a handout which will include linear equations, which they will need to create a table of values and graph for homework. Worksheet Name: Date:
9 9 Given equation the equation y = 3x + 2 find at least 4 values for y by creating a table X Y Just by plugging 4, 2, 0, and 2 into the equation y = 3x + 2 for x, we were able to solve for y! Directions: Create a table of points for each linear equation. Then in Geometers Sketchpad plot the points on the graph and create the linear equation. 1. y = ½ x y = x 2 3. y = 6 4. y = x y = x y = 8x Homework Name: Date:
10 10 Directions: Similar to class, create a table of values for each linear equation. With your table of values, DRAW the linear equation on graph paper. 1. y = x y = 2x y = 7x y = 6 5. x = x + 3y = You are taking a photography class and need a digital camera. The payment plan for the camera can be modeled by the equation C = 10m +50, where C is the total amount paid and m is the number of months. Graph the equation and then estimate how much you pay in 12 months. Answer Key:
11
12 In 12 months you pay: $170. Because when x = 12 the yvalue is 170.
13 13 Day Two Lesson Plan Lesson Topic: Using Intercepts Grade Level: 9 Materials: TI83 plus calculator, Overhead with calculator adaptor, Instruction Worksheet (graphing), Instruction Worksheet (finding intercepts), XY Intercepts Worksheet. Lesson Overview: Students will work with their calculators to develop an understanding of intercepts. Lesson Objectives: Students will be able to graph linear equations. Given linear equations, students will calculate the x and y intercepts on the graph. Given linear equations, students will be able to draw conclusions about linear equations and their intercepts. A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable. New York Standard: A.CM.1 Communicate verbally and in writing a correct, complete, coherent, and clear design and explanation for the steps used in solving a problem. A.CM.5 Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid. A.R.3 Use representation as a tool for exploring and understanding mathematical ideas. NCTM Standards: Understand patterns, relations, and functions. Organize and consolidate their mathematical thinking through communication. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Analyze and evaluate the mathematical thinking and strategies of others. Create and use representations to organize, record, and communicate mathematical ideas. Anticipatory Set: The teacher will begin class with a few questions: 1. What does intercept mean? 2. How many intercepts do you think there are in graphing a line? 3. What do you think intercepts represent in graphing a line? Possible Responses: 1. When something crosses something, where they cross is the intercept 2. 1 or 2 3. Where a line crosses the axis
14 14 Developmental Activity: Lecture/Activities: 1. We are going to look at the yintercept of different linear equations. First we need know how to enter an equation into our calculator. Go through instruction page with students. (Instruction Worksheet) 2. The students will now follow along with the teacher on how to find the intercepts using the graph and table with their calculator. They will also have an instruction worksheet to follow. (Instruction Worksheet) 3. The students will now get a worksheet of a variety of linear equations, where they will need to work independently to find the x and y intercepts. (X/Y intercepts worksheet) 4. When the students finish their worksheet they will need to get into groups of 3 and compare answers. They will also need to answer the questions on the bottom of the worksheet within their groups. 5. When all the groups have completed their handout, the class will come together and each group will present an assigned problem from the worksheet using the overhead adaptor with their calculators. 6. The teacher will monitor each group while they work together and correct the students as they present their problems, if there is a mistake. 7. Once the groups present their assigned problem, the whole class will have a discussion on the written questions, on the worksheet. Closure: The students will write a paragraph into their journals about what they learned from the lesson. They will also write down at least one question that they have about the calculator or anything that they were confused about. Assessment: The teacher will collect the worksheet on finding the intercepts that the students completed in class. The teacher will collect and read the student s journals to see how they feel about find intercepts with the calculators. The students will be graded on the group work they did in class. Instruction
15 15 (Graphing an equation) Graph the equation y = x First press the [Y=] button: 2. Now type your equation into the y1 slot: 3. Press the [Zoom] button: 4. Select Zoom Fit (It will graph your equation): You can play with the zoom features and the window button, to find an appropriate view Instruction
16 16 (Finding intercepts with a graph and table) Find the xintercept and y intercept of the equation y = x First graph the line: 2. To find xintercept press [2 nd ] then [CALC] then select Zero. Make sure your curser is to the left of the xaxis and on the line and press [enter]. 3. Then move your curser so it passes the xaxis and still on the line, and select [enter]. 3. Now make a guess where you believe the line crosses the xaxis by moving your curser.
17 17 4. Finally the calculator gives us the point at which the line crosses the xaxis. The exact values that cross the xaxis. This line crosses the xaxis at point (5, 0). 1. First graph the equation: Find the yintercept of y = x Press [2 nd ] then press [CALC] and select Value: 3. Enter into 0 into the X= (because where the line crosses the y axis the value for x is zero. Then press [enter]. This point is where the line crosses the yaxis, which is (0, 5). This is the yintercept point.
18 18 Find the x and y intercept point according to the table. 1. Press [2 nd ] then press [Tblset], In this situation, enter 10 for Tblstart and 1 for Tbl = 2. Press [2 nd ] then press [TABLE] 3. Now look for when x = 0 and where y = 0. These are your intercepts on the x and y axis. In this situation you can find that xintercept = 5 and yintercept = 5. X/Y Intercepts
19 19 Directions: With your calculator, graph each equation and find the x and y intercepts. Once you find the x and y intercepts by the graph, check it by looking at your table. Once you have finished the problems, get together with your group and discuss your answers. Then with your groups answer the questions at the bottom. Make sure that your equations are solved for y in terms of x before graphing. 1. y = 5x y = 2.5x x + 10y = y = 1/2x y = 1.95x Group work: 1. What kind of line has no yintercept? 2. If the xintercept of a line is positive and the yintercept is negative, does the line slat up or down from left to right? Explain your reasoning. 3. What did you notice about the intercepts and slope in relation to the equation? Answer Key:
20 20 1. yintercept = 15 xintercept = 3 2. yintercept = 6.5 xintercept = yintercept = 3 xintercept = yintercept = 1 xintercept = yintercept = xintercept = What kind of line has no yintercept? A line that does not cross the yaxis, for example the equation x = 5 2. If the xintercept of a line is positive and the yintercept is negative, does the line slat up or down from left to right? Explain your reasoning. Slants up from left to right as the line would cross the y axis through the negative portion of the axis and it would cross the xaxis through the positive portion of the xaxis. 3. What did you notice about the yintercept and the equation? That the yintercept matches the b in the linear equation y = mx + b. The slope is the coefficient of the xvalue. Day Three Lesson Plan Lesson Topic: Introduction to Slope
21 21 Grade Level: 9 Materials: CalculatorBased Ranger (CBR 2), Overhead with TIadapter, TI83 plus Calculator, Graph paper, CBR Worksheet 1, Homework Worksheet, Journals, Pencil. Lesson Overview: Students will work the CBR to develop an understanding of slope. The students will also be introduced to the slope formula to compute slope. Lesson Objectives: Given instruction on the CBR, the students will create graphs and describe their slopes Given the slope formula, students will be able to find the slope of a line. Students will be able to describe slopes with appropriate mathematical vocabulary. Given the TI83 calculators, students will be able to graph a linear equation and find the slope. New York State Standards: A.PS.4 Use multiple representations to represent and explain problem situations. A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagrams. A.R.3 Use representation as a tool for exploring and understanding mathematical ideas. A.A.33 Determine the slope of a line, given the coordinates of two points on the line. A.A.32 Explain slope as a rate of change between dependant and independent variables. NCTM Standards: Understand patterns, relations, and functions. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Use the language of mathematics to express mathematical ideas precisely. Create and use representations to organize, record, and communicate mathematical ideas. Anticipatory Set: The teacher asks the students to answer the following question: Determine whether each statement is positive slope, negative slope or no slope 1. John walks up a hill 2. Marie walks down a hill 3. Bill walks across flat ground. Possible Response:
22 22 1. Positive slope 2. Negative slope 3. No slope Developmental Activity: Lecture/Activities: 1. Teacher introduces the CalculatorBased Ranger (CBR 2) by direct instruction as it is connected to the overhead. The teacher does a few examples of walking close to the CBR and walking away from the CBR. Then shows the students the different graphs created by the CBR of him walking. The teacher will ask the students what do the graphs look like when I walk close to the CBR and what do the graphs look like when I walk away from the CBR? 2. The teacher discusses why the graphs look the way they do. For example, as the teacher walks close to the CBR the slope is negative. 3. To find slope the teacher traces the graphs that were created from the CBR and finds two random points. Then uses the slope formula to calculate the slope of the graphs. This will be done by direct instruction from the teacher on the board. 4. The students break up into groups of 3 and with their TI83 plus calculators and CBR they need to complete a handout. (Worksheet 1) 5. The teacher will demonstrate to the students how to find the slope of a linear equation by finding the coefficient of the x term on the overhead, from a linear equation when the students have finished their CBR activity. Closure: 1. The students will write in there journals what they learned in class about different slopes. 2. The students will turn in there journals and their handout they completed with the CBR, before they leave class. Assessment: Give the student s homework on finding slopes of given points and there will also be a writing question for the students to do. (Worksheet 2) Worksheet 1 Name: Date:
23 23 Directions: Connect your CBR to the calculator and place the CBR onto your desk. First stand 1meter away from CBR, facing away from CBR and walk away from the CBR. Then answer questions 14. Now stand 3 meters away from the CBR and walk towards the CBR. Then answer questions 58. Lastly stand 3 meters away and stand still and answer questions What kind of slope did you come up with? Why? 2. Sketch your graph on graph paper. 3. Find two points from the graph on your calculator and find the slope of the graph using the slope formula. 4. What does the slope of the graph tell you? 5. What kind of slope did you come up with? Why? 6. Sketch your graph on graph paper 7. Find two points from the graph on your calculator and find the slope of the graph using the slope formula. 8. What does the slope of the graph tell you? 9. What kind of slope did you come up with? Why? 10. Sketch your graph on graph paper 11. Find two points from the graph on your calculator and find the slope of the graph using the slope formula. 12. What does the slope of the graph tell you? Answer Key:
24 24 1. Positive Slope. As I walked away the slope of the graph increased steadily, this is a positive slope graph: 3. Point 1: (0.0, 1.13) slope = =.50 Point 2: (2.7, 2.47) That the slope of the graph is.50. That I was walking away from the CBR at a rate of.5meters per second 5. Negative Slope. As I walked toward the CBR, the slope of the graph decreased steadily, this is a negative slope. 6. graph: Point 1: (0.0, 2.46) slope = = .56 Point 2: (2.7,.96) The slope of the graph is That I was walking toward the CBR at a rate of.56 meters per second 9. Zero Slope. As I stood still the slope of the graph stayed the same. There is a zero slope.
25 slope Point 1: (.35,.85) Slope = = 0.0 Point 2: (.40,.85) There is no slope. The horizontal line gives you no slope. 8
26 26 Homework Name: Date: Directions: Find the slope of the line passing through the points. Also write down the type of slope of the points: (positive, negative, Zero or Undefined). HINT: If there is a zero in the numerator than the line is undefined. If there is a zero in the denominator the slope does not exist or undefined. Write a paragraph on the last question. Use your calculator, if needed. 1. (4, 8), (6, 6) 2. (1, 4), (1, 7) 3. (2, 4), (4, 2) 4. (5, 4), (3,4) 5. (5, 8), (0, 5) 6. (3, 1), (3, 2) 7. (6, 2), (6, 7) 8. (9, 8), (15, 8) 9. (12, 22), (20, 19) 10. One line passes through eh points M (1, 1) and N (3, 4) and another line passes through points P (2, 5) and Q (5, 8). Which line has a greater slope? Explain why?
27 27 Answer Key: Undefined undefined The line that passes through points M and N has a slope of 1.5, which is a greater slope than the line that passes through points P and Q which has a slope of 1. The first line with point M and N has a greater number as a slope compared to the line with points P and Q.
28 28 Day Four Lesson Plan Lesson Topic: Writing an equation for a line Grade Level: 9 Materials: Computers, Green Globs Software, Homework handout, Pencil, Paper. Lesson Overview: Students will work with Green Globs software to develop an understanding of writing equations. Lesson Objectives: Given the slopeintercept formula, the students will be able to rewrite linear equations. Using the Green Globs software the students will be able to write linear equations. Given the slope and a point on the line, students will be able to write an equation of a line. New York State Standards: A.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts. A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line. A.G.4 Identify and graph linear functions. NCTM Standards: Represent and analyze mathematical situations and structures using algebraic symbols. Understand patterns, relations, and functions. Create and use representations to organize, record, and communicate mathematical ideas. Anticipatory Set: The teacher will ask the students to find the slope and yintercept of a linear equation. 1. x y = y = 6 x 3. 1 = 2x y Possible Response: 1. Slope = 1, yintercept = Slope = 1, yintercept = 6 3. Slope = 2, yintercept = 1 Main Activity:
29 29 Lecture/Activities 1. The teacher will have a direct instruction on the overhead on the slopeintercept form of an equation: y = mx + b. 2. The direct instruction will have an example of rewriting an equation into the slopeintercept form, on the overhead. The example will be: 1 = 2x y which can be written as y = 2x The teacher will then review with the students by discussion, where the slope and yintercept can be found in an equation. For example in the equation y = 2x 1, the slope is 2 and the yintercept is The teacher will also show the students that if you are given a point and the slope you can write a linear equation. For example if you are given the point (1, 2) and slope = 2 then the equation is y = 2x + 2. This example will be done on the overhead. 5. The teacher will introduce the Green Globs program to the class. The teacher will show the students how to type equations into the program, by doing an example. 6. The students will work in the Linear and Quadratics Program. Within this program the students will work with lines. 7. Green Globs will give the students a line on a graph. The students are to write the equation of the line. If they are right they can advance to the next level. If they are wrong, the program will graph the line you typed and the student s can change your response so it is correct. 8. With this activity the students are learning by discovering. They are exploring linear equations through the Green Globs program. Closure: At the end of the class the students can play the Green Globs game. In this game the students try to hit all the green dots on the graph paper by writing equations and graphing them. If the line crosses through a green dot, the dot gets hit and you receive points. The more dots you hit with a line the more points you get. The top five students who get the most points will receive a cool mechanical pencil. Assessment: The students will first rewrite equations into the slopeintercept form in the homework assignment. Then students will also have to write down the equation of a line for each problem which will consist of a point on the line and the slope. (Homework Worksheet) Homework
30 30 Name: Date: Part I Directions: Write the equations into slopeintercept form 1. 4x + 2y = x 2y = y + 2 = 1/2x Part II Directions: Given a point on the line and the slope of the line write down the equation of the line. 1. (0, 2) Slope: 2 2. (1, 2) Slope: 1 3. (4, 5) Slope: ½ 4. (3, 2) Slope: 5 5. (0, 10) Slope: (0, 0) Slope: 1 7. (7, 8) Slope: (9, 10) Slope: (15, 18) Slope: 2/3 10. (5, 3) Slope: 1/5 Answer Key:
31 31 Part I 1. y = 2x y = 3x 5 3. y = 1/2x 2 Part II 1. y = 2x y = x y = 1/2x y = 5x y = 10x y = x 7. y = y = 11x y = 2/3x y = 1/5x 3 Day Five Lesson Plan
32 32 Lesson Topic: Introduction to system of equations Materials: TI83 plus Calculator, Overhead with TI adaptor, Paper, Pencil Grade Level: 9 Lesson Overview: Students work with their TI83 calculators to develop an understanding of solving a system of equations. Lesson Objectives: Given a technical briefing of the TI83 calculator, students will be able to enter system of equations into the calculator. Given instruction on the matrix program of the TI83 calculator, students will be able to solve systems of equation. Students will be able to explore equations on the calculator by graphing the linear equations. New York State Standards: A.PS.4 Use multiple representations to represent and explain problem situations. A.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, function, equations, charts, graphs, Venn diagrams, and other diagrams. A.R.3 Use representation as a tool for exploring and understanding mathematical ideas. A.G.9 Solve system of linear equations graphically. NCTM Standards Represent and analyze mathematical situations and structures using algebraic symbols. Apply and adapt a variety of appropriate strategies to solve problems. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Create and use representations to organize, record, and communicate mathematical ideas. Anticipatory Set: The teacher will present the problem: Solve the linear system: x + 4y = 4 x y = 6 The class will have a discussion with the teacher on what it means to solve a system of equation. Possible ideas: When the two linear lines cross. The two linear equations have the same x and y value. Developmental Activity:
33 33 Lecture/Activities: 1. The teacher will go through on the overhead how to use the matrix program in the TI83 plus calculator. (Instructional Worksheet) 2. The students will follow with the teacher on how to solve a system equation in the matrix program as the teacher demonstrates with the calculator on the overhead. Each student will have a copy of the Instructional worksheet for a reference. 3. The teacher will also go through graphing the two linear equations on the calculator as a way to check their answers by finding the intersection. 4. The students will be given a worksheet of different system of equations, where they will need to work independently to solve the equations. (Worksheet) 5. When the students are finished with their worksheet they will get into groups of 3 and compare answers. 6. In their groups they will answer a few thinking questions that are on the handout. 7. When all the groups are finished discussing their answers and group questions, the class will come together and the teacher will have a class discussion on the problems they have been working on. Closure: The students will write into their journals about the lesson. They will write down something they learned and something they are still confused about in regards to the lesson. Assessment: The students will be given a homework assignment of many systems of equations. (Homework) Instructional Worksheet (System of Equations)
34 34 Solve the linear system: x + 4y = 4 x y = 6 First make sure that the two equations are lined up by their variables. (Which they are) 1. Press [2 nd ] then press [MATRIX] 2. Move over from NAMES to EDIT using the arrow keys 3. Now press [ENTER] 4. Make sure that size of the matrix is the size that you want. (In this case it is 2 x 3, because there are two columns and 3 rows). If the system is larger or smaller change the numbers next to where it says MATRIX[A]. 5. Now move your curser into the matrix using the arrow keys and input the numbers of your system into the matrix.
35 35 6. Press [2 nd ], then press [Quit] once you have the matrix you want on the screen, this will take you back to the home screen. 7. Now Press [2 nd ], then press [CATALOG] 8. Now Press [r] and look for rref( and press [ENTER], rref( should appear on your home screen 9. Press [2 nd ], then press [MATRIX] 10. Make sure that that the number of the matrix that you imputed into your calculator is highlighted, in this case 1: [A] 2x 3, and press [ENTER]
36 Now press ) to close your equation and then press [ENTER] Your answer is located in the last column, in this problem the answer is (4, 2) Class Work (Solving System of Equations)
37 37 Name: Date: Directions: Using the matrix program in your calculator, solve the systems of equations. Then in your groups discuss your answers and answer the questions at the bottom of this worksheet. You have to make sure that your variables match up before putting the system into your calculator. 1. y = x +3 y = x x y = 1 5x 4y = 0 3. y = 2x 15 x = 2y Group Work Questions 1. What does the answer to the system of equations tell you? 2. Can you find the answers to the system of equations algebraically? If so How? 3. Can you find the answer to the system of equations using your graph in your calculator? If so How? Answer Key to Class Work: 1. (1, 2)
38 38 2. (4, 5) 3. (6, 3) Group Work Questions 1. This is the two lines cross. This is where the two linear equations have the same x and y values. 2. Yes, Solve for Y and substitute that equation into the other equation for Y. Now solve for x. This is your answer for x. Then put the xvalue into an equation and solve for y. This is your yvalue. 3. Yes, solve each equation for Y, and then graph both equations into your calculator. Go into CALC and find there intersection. Homework Name: Date: Directions: Solve the system of equations
39 39 1. x = 4 y = x a + b = 4 4a + b = w z = 2 4w + z = x + 4y = 14 3x 5y = You have 100 trading cards and your friend has 20, every day you give your friend one card. Use the equations c = 100 d and c = 20 + d to model this situation. Use the matrix or graph to find out when both of you have the same number of cards. Answer Key: 1. (4, 5)
40 40 2. (1, 5) 3. (11/3, 16/3) or (3.67, 5.33) 3. (3, 2) 5. In 40 days they will have the same number of cards. They will both have 60 cards.
Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationGraphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
More informationPlot the following two points on a graph and draw the line that passes through those two points. Find the rise, run and slope of that line.
Objective # 6 Finding the slope of a line Material: page 117 to 121 Homework: worksheet NOTE: When we say line... we mean straight line! Slope of a line: It is a number that represents the slant of a line
More informationActivity 6 Graphing Linear Equations
Activity 6 Graphing Linear Equations TEACHER NOTES Topic Area: Algebra NCTM Standard: Represent and analyze mathematical situations and structures using algebraic symbols Objective: The student will be
More informationLines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan
Lines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan I. Topic: SlopeIntercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
More informationSlopeIntercept Form of a Linear Equation Examples
SlopeIntercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the yintercept of AB. Suppose you want to find an equation
More informationAcademic Support Center. Using the TI83/84+ Graphing Calculator PART II
Academic Support Center Using the TI83/84+ Graphing Calculator PART II Designed and Prepared by The Academic Support Center Revised June 2012 1 Using the Graphing Calculator (TI83+ or TI84+) Table of
More informationOverview. Observations. Activities. Chapter 3: Linear Functions Linear Functions: SlopeIntercept Form
Name Date Linear Functions: SlopeIntercept Form Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review,
More informationLesson 4: Solving and Graphing Linear Equations
Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A2M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,
More informationSection 1.1 Linear Equations: Slope and Equations of Lines
Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of
More informationSolving Systems of Linear Equations Graphing
Solving Systems of Linear Equations Graphing Outcome (learning objective) Students will accurately solve a system of equations by graphing. Student/Class Goal Students thinking about continuing their academic
More informationTI83/84 Plus Graphing Calculator Worksheet #2
TI83/8 Plus Graphing Calculator Worksheet #2 The graphing calculator is set in the following, MODE, and Y, settings. Resetting your calculator brings it back to these original settings. MODE Y Note that
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationBrunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year.
Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year. Goal The goal of the summer math program is to help students
More informationBasic Graphing Functions for the TI83 and TI84
Basic Graphing Functions for the TI83 and TI84 The primary benefits of the TI83 and TI84 are the abilities to graph functions and to identify properties those functions possess. The purpose of this
More informationMSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions
MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial
More informationName of Lesson: Properties of Equality A Review. Mathematical Topic: The Four Properties of Equality. Course: Algebra I
Name of Lesson: Properties of Equality A Review Mathematical Topic: The Four Properties of Equality Course: Algebra I Time Allocation: One (1) 56 minute period Prerequisite Knowledge: The students will
More informationGraphing Linear Equations in Two Variables
Math 123 Section 3.2  Graphing Linear Equations Using Intercepts  Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the
More informationWrite the Equation of the Line Review
Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Objective: Students will be assessed on their ability to write the equation of a line in multiple methods. Connections
More informationEquations, Lenses and Fractions
46 Equations, Lenses and Fractions The study of lenses offers a good real world example of a relation with fractions we just can t avoid! Different uses of a simple lens that you may be familiar with are
More informationSlope & yintercept Discovery Activity
TI83 Graphing Calculator Activity Slope & yintercept Discovery Activity Justin Vallone 11/2/05 In this activity, you will use your TI83 graphing calculator to graph equations of lines. Follow the steps
More informationGraphing Quadratic Functions
Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x value and L be the yvalues for a graph. 1. How are the x and yvalues related? What pattern do you see? To enter the
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationx x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =
Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the
More informationAccommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego
Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 67 Grade: 8th Number of Students: 25 Date: May 1213, 2011 Goal: Students will
More informationA synonym is a word that has the same or almost the same definition of
SlopeIntercept Form Determining the Rate of Change and yintercept Learning Goals In this lesson, you will: Graph lines using the slope and yintercept. Calculate the yintercept of a line when given
More informationThe fairy tale Hansel and Gretel tells the story of a brother and sister who
Piecewise Functions Developing the Graph of a Piecewise Function Learning Goals In this lesson, you will: Develop the graph of a piecewise function from a contet with or without a table of values. Represent
More informationF.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions
F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed
More informationIntroduction to Quadratic Functions
Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions...617.2
More informationSolving Equations Involving Parallel and Perpendicular Lines Examples
Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationIn this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form).
CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,
More informationTechnology: CBR2, Graphing Calculator & Cords, Overhead Projector, & Overhead Unit for Calculator
Analyzing Graphs Lisa Manhard Grade Level: 7 Technology: CBR2, Graphing Calculator & Cords, Overhead Projector, & Overhead Unit for Calculator Materials: Student Worksheets (3) Objectives Evaluate what
More informationhttps://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...
of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach BellRinger Activity Students
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1100 Overview: This unit models realworld situations by using one and twovariable linear equations. This unit will further expand upon pervious
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationSolving Systems of Linear Equations Substitutions
Solving Systems of Linear Equations Substitutions Outcome (lesson objective) Students will accurately solve a system of equations algebraically using substitution. Student/Class Goal Students thinking
More informationProcedure for Graphing Polynomial Functions
Procedure for Graphing Polynomial Functions P(x) = a n x n + a n1 x n1 + + a 1 x + a 0 To graph P(x): As an example, we will examine the following polynomial function: P(x) = 2x 3 3x 2 23x + 12 1. Determine
More informationGraphing  SlopeIntercept Form
2.3 Graphing  SlopeIntercept Form Objective: Give the equation of a line with a known slope and yintercept. When graphing a line we found one method we could use is to make a table of values. However,
More informationHow Many Drivers? Investigating the SlopeIntercept Form of a Line
. Activity 1 How Many Drivers? Investigating the SlopeIntercept Form of a Line Any line can be expressed in the form y = mx + b. This form is named the slopeintercept form. In this activity, you will
More informationAnswer Key Building Polynomial Functions
Answer Key Building Polynomial Functions 1. What is the equation of the linear function shown to the right? 2. How did you find it? y = ( 2/3)x + 2 or an equivalent form. Answers will vary. For example,
More informationGeometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
More informationGuide for Texas Instruments TI83, TI83 Plus, or TI84 Plus Graphing Calculator
Guide for Texas Instruments TI83, TI83 Plus, or TI84 Plus Graphing Calculator This Guide is designed to offer stepbystep instruction for using your TI83, TI83 Plus, or TI84 Plus graphing calculator
More informationAlgebra Cheat Sheets
Sheets Algebra Cheat Sheets provide you with a tool for teaching your students notetaking, problemsolving, and organizational skills in the context of algebra lessons. These sheets teach the concepts
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationCoordinate Plane, Slope, and Lines LongTerm Memory Review Review 1
Review. What does slope of a line mean?. How do you find the slope of a line? 4. Plot and label the points A (3, ) and B (, ). a. From point B to point A, by how much does the yvalue change? b. From point
More informationPoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey)
PoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey) 1. The Problem: A Phoney Deal? [Problem #3280] With cell phones being so common these days, the phone companies are all competing to earn
More informationGRADE 8 MATH: TALK AND TEXT PLANS
GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculumembedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems
More informationis the degree of the polynomial and is the leading coefficient.
Property: T. HrubikVulanovic email: thrubik@kent.edu Content (in order sections were covered from the book): Chapter 6 HigherDegree Polynomial Functions... 1 Section 6.1 HigherDegree Polynomial Functions...
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More information7 th Grade Integer Arithmetic 7Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School
7 th Grade Integer Arithmetic 7Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School Page 1 of 20 Table of Contents Unit Objectives........ 3 NCTM Standards.... 3 NYS Standards....3 Resources
More informationTitle: Line of Best Fit. Brief Overview:
Title: Line of Best Fit Brief Overview: This Concept Development Lesson is based on the skills needed to determine the line best fit for a set of data. The focus is based on grade levels 712. Students
More informationHOW MUCH WILL I SPEND ON GAS?
HOW MUCH WILL I SPEND ON GAS? Outcome (lesson objective) The students will use the current and future price of gasoline to construct Tcharts, write algebraic equations, and plot the equations on a graph.
More informationMath Tools Cell Phone Plans
NATIONAL PARTNERSHIP FOR QUALITY AFTERSCHOOL LEARNING www.sedl.org/afterschool/toolkits Math Tools Cell Phone Plans..............................................................................................
More informationGrade Level Year Total Points Core Points % At Standard 9 2003 10 5 7 %
Performance Assessment Task Number Towers Grade 9 The task challenges a student to demonstrate understanding of the concepts of algebraic properties and representations. A student must make sense of the
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationWriting the Equation of a Line in SlopeIntercept Form
Writing the Equation of a Line in SlopeIntercept Form SlopeIntercept Form y = mx + b Example 1: Give the equation of the line in slopeintercept form a. With yintercept (0, 2) and slope 9 b. Passing
More informationStudents will use various media (computer, graphing calculator, paper and pencil) to graph/sketch linear equations.
Title: Lines, Lines, Everywhere!! A discovery/exploration lesson investigating equations of the form y = mx + b to see how the values of b and m affects the graph. Link to Outcomes: Communication/ Cooperation
More informationIn the Herb Business, Part III Factoring and Quadratic Equations
74 In the Herb Business, Part III Factoring and Quadratic Equations In the herbal medicine business, you and your partner sold 120 bottles of your best herbal medicine each week when you sold at your original
More informationFunctional Math II. Information CourseTitle. Types of Instruction
Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade
More informationMath 113 Review for Exam I
Math 113 Review for Exam I Section 1.1 Cartesian Coordinate System, Slope, & Equation of a Line (1.) Rectangular or Cartesian Coordinate System You should be able to label the quadrants in the rectangular
More informationExamples of Tasks from CCSS Edition Course 3, Unit 5
Examples of Tasks from CCSS Edition Course 3, Unit 5 Getting Started The tasks below are selected with the intent of presenting key ideas and skills. Not every answer is complete, so that teachers can
More informationTemperature Scales. The metric system that we are now using includes a unit that is specific for the representation of measured temperatures.
Temperature Scales INTRODUCTION The metric system that we are now using includes a unit that is specific for the representation of measured temperatures. The unit of temperature in the metric system is
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationALGEBRA I (Created 2014) Amherst County Public Schools
ALGEBRA I (Created 2014) Amherst County Public Schools The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies
More informationPerformance Based Learning and Assessment Task
Performance Based Learning and Assessment Task Activity/Task Title I. ASSESSSMENT TASK OVERVIEW & PURPOSE: Students will be asked to find various characteristics of a polynomial function, modeled by a
More informationAdding and Subtracting Integers Unit. Grade 7 Math. 5 Days. Tools: Algebra Tiles. FourPan Algebra Balance. Playing Cards
Adding and Subtracting Integers Unit Grade 7 Math 5 Days Tools: Algebra Tiles FourPan Algebra Balance Playing Cards By Dawn Meginley 1 Objectives and Standards Objectives: Students will be able to add
More informationElements of a graph. Click on the links below to jump directly to the relevant section
Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and yintercept in the equation of a line Comparing lines on
More informationBecause the slope is, a slope of 5 would mean that for every 1cm increase in diameter, the circumference would increase by 5cm.
Measurement Lab You will be graphing circumference (cm) vs. diameter (cm) for several different circular objects, and finding the slope of the line of best fit using the CapStone program. Write out or
More information1.6. Solve Linear Inequalities E XAMPLE 1 E XAMPLE 2. Graph simple inequalities. Graph compound inequalities
.6 Solve Linear Inequalities Before You solved linear equations. Now You will solve linear inequalities. Why? So you can describe temperature ranges, as in Ex. 54. Key Vocabulary linear inequality compound
More informationAlgebra 2 YearataGlance Leander ISD 200708. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks
Algebra 2 YearataGlance Leander ISD 200708 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks
More informationRevenge of the Angry Birds. Accommodation Assignment. Chosen Student: Elaine
Revenge of the Angry Birds Accommodation Assignment Chosen Student: Elaine Tracy Harrison 12/5/2013 Title: Revenge of the Angry Birds Date: 12/5/2013 Grade Level: 910 Course: Algebra I Time Allotted:
More informationReview of Fundamental Mathematics
Review of Fundamental Mathematics As explained in the Preface and in Chapter 1 of your textbook, managerial economics applies microeconomic theory to business decision making. The decisionmaking tools
More informationSolving Systems of Linear Equations Putting it All Together
Solving Systems of Linear Equations Putting it All Together Outcome (lesson objective) Students will determine the best method to use when solving systems of equation as they solve problems using graphing,
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table covariation least squares
More informationPolynomial and Rational Functions
Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving
More informationGraphing calculators Transparencies (optional)
What if it is in pieces? Piecewise Functions and an Intuitive Idea of Continuity Teacher Version Lesson Objective: Length of Activity: Students will: Recognize piecewise functions and the notation used
More informationEXCEL Tutorial: How to use EXCEL for Graphs and Calculations.
EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your
More informationSubject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1
Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1 I. (A) Goal(s): For student to gain conceptual understanding of the metric system and how to convert
More informationTeacher: Maple So School: Herron High School. Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles
Teacher: Maple So School: Herron High School Name of Lesson: Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles Subject/ Course: Mathematics, Algebra I Grade Level: 9 th
More information10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED
CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours Essential Question: LESSON 2 Absolute Value Equations and Inequalities How do you
More informationMATH 10034 Fundamental Mathematics IV
MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.
More information1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.
1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points
More informationUnit 4: Analyze and Graph Linear Equations, Functions, and Relations
Unit 4 Table of Contents Unit 4: Analyze and Graph Linear Equations, Functions and Relations Video Overview Learning Objectives 4.2 Media Run Times 4.3 Instructor Notes 4.4 The Mathematics of Analyzing
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationComparing Simple and Compound Interest
Comparing Simple and Compound Interest GRADE 11 In this lesson, students compare various savings and investment vehicles by calculating simple and compound interest. Prerequisite knowledge: Students should
More informationUnit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:
Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning
More informationActivity 5. Two Hot, Two Cold. Introduction. Equipment Required. Collecting the Data
. Activity 5 Two Hot, Two Cold How do we measure temperatures? In almost all countries of the world, the Celsius scale (formerly called the centigrade scale) is used in everyday life and in science and
More informationGraphs of Proportional Relationships
Graphs of Proportional Relationships Student Probe Susan runs three laps at the track in 12 minutes. A graph of this proportional relationship is shown below. Explain the meaning of points A (0,0), B (1,),
More informationGetting to know your TI83
Calculator Activity Intro Getting to know your TI83 Press ON to begin using calculator.to stop, press 2 nd ON. To darken the screen, press 2 nd alternately. To lighten the screen, press nd 2 alternately.
More informationEL9650/9600c/9450/9400 Handbook Vol. 1
Graphing Calculator EL9650/9600c/9450/9400 Handbook Vol. Algebra EL9650 EL9450 Contents. Linear Equations  Slope and Intercept of Linear Equations 2 Parallel and Perpendicular Lines 2. Quadratic Equations
More informationBasic Understandings
Activity: TEKS: Exploring Transformations Basic understandings. (5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential to understanding underlying
More information3. Evaluate the objective function at each vertex. Put the vertices into a table: Vertex P=3x+2y (0, 0) 0 min (0, 5) 10 (15, 0) 45 (12, 2) 40 Max
SOLUTION OF LINEAR PROGRAMMING PROBLEMS THEOREM 1 If a linear programming problem has a solution, then it must occur at a vertex, or corner point, of the feasible set, S, associated with the problem. Furthermore,
More informationYears after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540
To complete this technology assignment, you should already have created a scatter plot for your data on your calculator and/or in Excel. You could do this with any two columns of data, but for demonstration
More information