Lesson 3: Linear Equations in x Understand that a linear equation is a statement of equality between 2 expressions. Solutions are those numbers x that satisfy a given equation. Equality Examples: All Exercises:1-6, and 7 as a discussion Problem Set 1-4 Yes 1 Lesson 4: Solving a linear equation Using properties of equality to solve linear equations with rational coefficients. Solving Linear Equations with Rational Coefficients Examples 1-3 Exercises 1-5 Problem Set 1-5 1-3 Modify to solve and check only 2
Lesson Big Idea Emphasize Suggested Examples and Exercises Suggested Problems Exit Ticket Suggested Days Lesson 5: SKIP UNTIL LATER Using geometry to write and solve linear equations Writing Linear Equations Good review lesson prior to exam. Examples Exercises Lesson 6: Solutions of a Linear equation Using distributive property of simplify equation. Not every linear equation has a solution. Solving Linear Equations Examples 1-4 Exercises 1-2 Plus 4,5,6 if time permits Problem Set 1-3, 5,7 1-2 2-3 Lesson 7: Classification of solutions What represents a linear equation with one solution, no solution, or infinite solutions? Classification of Solutions * Can be correlated with OnRamp Examples none Exercises 1-3, (only transform until equation can be classified) and 8-10 Problem Set 1-3 1-3 1-2 Lesson 8: Linear equation in disguise Using properties of equality to solve non-linear equations Solving Complex Proportions using Cross Multiplication Examples 3-4 Exercises 1,3 Problem Set 1-4 Yes 1 Lesson 9: SKIP- Rewriting an exponential expression that represents a series as a linear equation Application Examples Exercises
TOPIC B Lesson Big Idea Emphasize Suggested Examples and exercises Examples Suggested Problems Exit Ticket Suggested Days Lesson 10: A critical look at proportional relationships Using average and constant speed to write a linear equation in 2 variables, then answer questions about distance and time. Constant Rate & Writing Proportions * Lesson 10 should be combined with lesson 11. Examples 1,2 Exercises 1,2 Problem Set 1-5 all 1.5 Lesson 11: constant rate Seeing constant rate in context: Graphing points on a coordinate plane, defining constant rate using 2 variables (where one is time) Constant Rate used with: Table of Variable Graph Examples 1-2 Exercises 1 Problem Set 1-4 All 1.5 Lesson 12: linear equations in two variables Using a table to find solutions to linear equations and then plot on coordinate plane. ax + by = c (2 variables) in relationship to tables and graphs Examples none Exercises: opening exercise as whole group 1-5 exploratory in pairs Problem Set 1,2 all 2
Lesson Big Idea Emphasize Suggested Examples and exercises Suggested Problems Exit Ticket Suggested Days Lesson 13: The graph of a linear equation in two variables Find and plot solutions to linear equations on a coordinate plane to predict shape of a graph. Explaining shape of graph in terms of a given linear equation. Graph of a Linear Equation * This Lesson 13 should be combined with Lesson 14. Exercise 1 as Problem Set 1 1 Lesson 14: The graph of a linear equation – horizontal and vertical lines Graphing linear equations in standard form that produce a horizontal or vertical line. Vertical and Horizontal Lines (a=0, b=0) Exercises 1-3 Problem Set 1,2 1 TOPIC C Lesson 15: the slope of a line Lesson 16: the computation of the slope of a line Understanding that slope is the slant of a line, and that it represents a unit rate. Using slope formula to compute slope, and similar triangles to explain why slope is the same between 2 distinct points. Determining slope based on a graph, and using the formula to calculate slope. Use similar triangles to emphasize that you can pick any two points on a line, to find slope and the ratio is always the same. (Look at discussion so that when looking at examples you can reference this.) Day 1/2: Lesson 15, Examples 1-4. Lesson 16 examples 1-3, but allow for gradual release with independent practice. Day 3: Lesson 15, Example 5: An Application. More Practice on Slope. Lesson 15/16, all problems sets are helpful. Choose based on student need. Day 1: Lesson 15 - 1 & 2 Day 2: Lesson 16 - 1 2-3 Lesson Big Idea Emphasize Suggested Examples and exercises Suggested Problems Exit Ticket Suggested Days
Lesson 17 : the line joining two distinct points of the graph y = mx + b has slope m The line joining two distinct points of the graph of the linear equation 𝒚=𝒎𝒙+𝒃 has slope 𝒎. The 𝒎 of 𝒚=𝒎𝒙+𝒃 is the number that describes the slope. Exercises: 1-5 *Use exercises 6, 7, and 8 at teacher discretion. These problems are expectations for level 4 only according to the performance level descriptions document. 1-4 1 - 3 1 Lesson 18 : there is only one line passing through a given point with a given slope Understand that straight lines with the same slope and one common point are the same line, using equations in the form y=mx +b Students need to recognize that the y-intercept is named as a point (x, y) and a solution to the linear equation. Examples 1 - 3 Exercises 1 – 4 *Use exercises 5 and 6 at teacher discretion. These problems are expectations for level 4 according to the performance level descriptions document. Do even or odd sets. Make sure students do question 8 or 9. 1 - 2 1 Lesson Big Idea Emphasize Suggested Examples and exercises Suggested Problems Exit Ticket Suggested Days
Lesson 19 : the graph of a linear equation in two variables is a line Skip Proofs Using y=mx+b to show that a line is made up of a series of points. Using intercepts is an easier way to graph a line than making a table of solutions. Graphing using intercepts. Skip Exercises 1 – 8, but use exercise 5’s equation as example 1 so you can find other integer coordinates points that are solution. 1-3 1 Lesson 20: every line is a graph of a linear equation Y=mx+b represents any non-vertical line, with b as a constant. Write the equation that represents the graph of a line. Opening, Examples 1-3, Exercises 1,2, 4, 6 1-4 1 Lesson Big Idea Emphasize Suggested Examples and exercises Suggested Problems Exit Ticket Suggested Days Lesson 21: some facts about graphs of a linear equation in two variables Writing an equation when given 2 points and a slope. Know the forms of a slope formula and equation. Example 1, 2 Exercises 1-4 1, 2 2 Days
Lesson 22: Constant rates revisited SKIP Students know that any constant rate problem can be described by a linear equation in two variables where the slope of the graph is the constant rate. TOPIC D Lesson 24: Introduction to Simultaneous Equations Understanding of systems of equations and notation. Comparing graphs for systems in the context of rate Opening Exercises Exercise 4 1 1 day Lesson 25: Geometric interpretation of the solutions of a linear system Graphing equations to find point of intersection, identified as solution. Solution also determined by computation. Exercises 1,2, 5, 6 Problem Set 1, 3, 4 1 2 days Lesson 26: Characterization of parallel lines A System of equations with no solution will be parallel lines Exercise 1-3 Problem Set 1-4 1-3 1 day Lesson Big Idea Emphasize Suggested Examples and exercises Suggested Problems Exit Tickets Suggested Days
Lesson 27: Nature of solutions of a system of linear equations Students must know if a system of equations has one unique solution, no solution, or infinitely many solutions. Exercises 1-3, 4 Example 1, 2 Exercise 5, 6 1-3 (Hint: use substitution, not elimination) 2 Days Lesson 28: Another Computational Method of Solving a Linear System Elimination method, rational number properties using substitution to solve a system of linear equations. Examples 1, 2 Exercise 1 Problem set 2, 4, 9, 10 1, 2 2 Days Lesson 29: Word Problems SKIP Writing and solving linear equation system word problems using substitution and elimination methods Lesson 30: Conversion between Celsius and Fahrenheit SKIP A real world application of linear equations.