Creating Equations. Set 3: Writing Linear Equations Instruction. Student Activities Overview and Answer Key


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1 Creating Equations Instruction Goal: To provide opportunities for students to develop concepts and skills related to writing linear equations in slopeintercept and standard form given two points and a point and slope Common Core Standards Algebra: Creating Equations Create equations that describe numbers or relationships. ACED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Algebra: Reasoning with Equations and Inequalities Represent and solve equations and inequalities graphically. AREI.0. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Student Activities Overview and Answer Key Station Students will be given spaghetti noodles, graph paper, and the general pointslope form of an equation. Students will use the spaghetti noodles to model different equations. Then they will write the slopeintercept form of an equation given the slope and yintercept. They will also write the slopeintercept form of an equation given the yintercept and a parallel or perpendicular equation. Answers. y = 5x y = 4x 8 3. y = x y = 4x Walch Education Algebra I Station Activities for Common Core Standards
2 Creating Equations Station 2 Instruction Students will be given spaghetti noodles, graph paper, and the general slopeintercept and pointslope forms of a linear equation. They will determine which form of the equation to use first in order to write a linear equation when given the slope and a point on the line. They will use spaghetti noodles to model the equations. Then they will write the slopeintercept form of a line given the slope and a point on the line. Answers. Use pointslope form first because you can plug in the given point for x and y. 2. y = 2x y = x y = 3x y = 2 x Station 3 Students will be given a number cube. They will use it to populate two ordered pairs. From the ordered pairs, they will find the slope and write the equation in slopeintercept form. Then they will explain how they found the slope and the equation in slopeintercept form. Answers. Answers will vary. 2. Answers will vary. 3. Answers will vary. 4. Slope = rise run = y2 y x2 x 5. Find the slope from the two points. Plug one of the points and the slope into y = mx + b to find b. Then write the equation in slopeintercept form. 00 Algebra I Station Activities for Common Core Standards 20 Walch Education
3 Creating Equations Station 4 Students will be given 0 index cards with the following equations written on them: Instruction y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = They will work as a group to match the equations written in standard form with the equations written in slopeintercept form. Then they convert an equation written in standard form to slopeintercept form and vice versa. Answers. y = x + 6and x + 2y = y = 2 x 20and2x + 3y = y = 0x 24 and 5x + y = x 2y = 24 and y = 2x x y = 4 andy = 5x y = x x 5y = 50 Materials List/Setup Station Station 2 Station 3 Station 4 spaghetti noodles; graph paper spaghetti noodles; graph paper number cube 0 index cards with the following equations written on them: y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = Walch Education Algebra I Station Activities for Common Core Standards
4 Creating Equations Discussion Guide Instruction To support students in reflecting on the activities and to gather some formative information about student learning, use the following prompts to facilitate a class discussion to debrief the station activities. Prompts/Questions. How do you write the standard form of a linear equation? 2. How do you write the slopeintercept form of a linear equation? 3. How do you write the slopeintercept form of a linear equation given a point and the slope? 4. How do you write the slopeintercept form of a linear equation given two points on the line? 5. How do you convert the standard form of a linear equation into slopeintercept form? 6. How do you convert the slopeintercept form of a linear equation into standard form? Think, Pair, Share Have students jot down their own responses to questions, then discuss with a partner (who was not in their station group), and then discuss as a whole class. Suggested Appropriate Responses. ax + by = c 2. y = mx + b 3. Use the pointslope form of the equation to plug in the given point and slope. Then write the equation in slopeintercept form. 4. Find the slope from the two points. Plug one of the points and the slope into y = mx + b to find b. Then write the equation in slopeintercept form. 5. Solve for y. 6. Move the xvalue to the lefthand side of the equation by using either the addition or subtraction property of equality and make sure that the coefficients are whole numbers with the coefficient of x being positive. Possible Misunderstandings/Mistakes Mixing up the x and yvalues when plugging them into the pointslope or slopeintercept forms Not keeping track of positive and negative signs when converting from standard form to slopeintercept form and vice versa Incorrectly finding the slope as run rise 02 Algebra I Station Activities for Common Core Standards instead of rise run 20 Walch Education
5 NAME: Creating Equations Station You will find spaghetti noodles and graph paper at this station. Draw a coordinate plane on your graph paper by creating and labeling the xaxis and the yaxis. For each problem, use the given information and the spaghetti to find the slopeintercept form of the equation. Slopeintercept form is written as y = mx + b.. The equation has a yintercept of (0, 0) and a slope of 5. Model this equation using the spaghetti. Then write the equation in slopeintercept form. 2. The equation has a yintercept of (0, 8) and is parallel to the line y = 4x 6. Model this equation using the spaghetti. Then write the equation in slopeintercept form. 3. The equation has a yintercept of 8 and is perpendicular to the line y = 3x + 9. Model this equation using the spaghetti. Then write the equation in slopeintercept form. 4. The graph of the equation passes through the origin and is perpendicular to y x 4. Model this equation using the spaghetti. Then write the equation in slopeintercept form Walch Education Algebra I Station Activities for Common Core Standards
6 NAME: Creating Equations Station 2 You will find spaghetti noodles and graph paper at this station. Draw a coordinate plane on your graph paper by creating and labeling the xaxis and the yaxis. Use the spaghetti and what you know about the slopeintercept and pointslope forms of a linear equation to answer the questions. Slopeintercept form is written as y = mx + b. Pointslope form is written as y y = m(x x ).. You want to find a linear equation. Which form should you use first if you are given the slope and a point on the line? 2. Use spaghetti to model a line that has a slope of 2 and passes through ( 3, 8). Then write the equation for this line in slopeintercept form. 3. Use spaghetti to model a line that has a slope of equation for this line in slopeintercept form. 8 and passes through (, 2). Then write the 4. Use spaghetti to model a line that has a slope of 3 and passes through ( 4, 0). Then write the equation for this line in slopeintercept form. 5. Use spaghetti to model a line that has a slope of 2 the equation for this line in slopeintercept form. 5 and passes through ( 5, 20). Then write 04 Algebra I Station Activities for Common Core Standards 20 Walch Education
7 NAME: Creating Equations Station 3 You will be given a number cube. For each problem, roll the number cube four times to create two ordered pairs. Then use these ordered pairs to find the slope and write the equation in slopeintercept form. Slopeintercept form is written as y = mx + b.. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slopeintercept form: 2. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slopeintercept form: 3. First ordered pair: (, ) Second ordered pair: (, ) Slope = Equation written in slopeintercept form: 4. How did you find the slope from the two ordered pairs? 5. How did you find b in the slopeintercept form of the equation? Walch Education Algebra I Station Activities for Common Core Standards
8 NAME: Creating Equations Station 4 At this station, you will find 0 index cards with the following equations written on them: y = 2x + 2 y = 5x 8 y = x + 6 y = 2 x 20 y = 0x x + 2y = 32 2x + 3y = 60 4x 2y = 24 5x + y = 36 x y = As a group, shuffle the cards. Work as a group to match the linear equation written in standard form with the same equation written in slopeintercept form. Write your matches on the lines below Rewrite the equation 3x + 9y = 2 so that it s in slopeintercept form. Show your work. 7. Rewrite the equation y = x 0 so that it s in standard form. Show your work Algebra I Station Activities for Common Core Standards 20 Walch Education
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