Alg I: Linear Relationships

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Linear Relationships Unit: A linear relationship is a statistical term that describes a straight-line relationship between two variables. In 8th grade math, a linear relationship is typically represented by the equation y=mx+b. Linear relationships can also be expressed graphically as a straight line in the coordinate plane that crosses the x-axis at a point. The slope of a non-vertical line is the measure of vertical change over the measure of horizontal change between any two points on the line. And linear functions can be used to model quantities that change at a constant rate, such as distances and prices. Throughout the units, students have explore linear equations and used their understanding to calculate, identify and contextualize slope and intercepts to make logical decisions. The second part of the unit focuses on teaching students how to solve problems that involve finding the values of variables that satisfy multiple equations simultaneously. This unit is crucial for developing algebraic reasoning and problem-solving skills, and it lays the groundwork for more advanced studies in mathematics and science. Students begin with an understanding of what a system of equations isβ€”two or more equations working together. They learn that the solution to a system of linear equations is the point(s) where the graphs of the equations intersect, representing the values that satisfy all equations in the system simultaneously. They will also learn the three different ways solve a system of equations. The unit emphasizes real-world applications, showing students how systems of equations are used to solve practical problems in areas such as business, engineering, and science. PDF is hyper linked with over 120 items. The pdf contains links to:

  • 19 Printable Student Handout with QR code for video instruction

  • 19 Printable Daily Assessment: Mid-Lesson Assessment to check for understanding and/or differentiated flexible groupings

  • 19 Instructional Video Link: Includes Teacher Model and Guided Practice.

  • Google Slide Decks for each lesson

  • Teacher Notes and Answer Key for each lesson

  • Formative Link: e-Copy of the Student Materials on GoFormative.

Also provided is a complete unit overview, a PreTest, PostTest, 1 Quiz and Student Reflections for each assessment. Answer Keys also added on GoFormative for instant data and student feedback. 30 Day free trial of GoFormative.

Linear Relationships Unit: A linear relationship is a statistical term that describes a straight-line relationship between two variables. In 8th grade math, a linear relationship is typically represented by the equation y=mx+b. Linear relationships can also be expressed graphically as a straight line in the coordinate plane that crosses the x-axis at a point. The slope of a non-vertical line is the measure of vertical change over the measure of horizontal change between any two points on the line. And linear functions can be used to model quantities that change at a constant rate, such as distances and prices. Throughout the units, students have explore linear equations and used their understanding to calculate, identify and contextualize slope and intercepts to make logical decisions. The second part of the unit focuses on teaching students how to solve problems that involve finding the values of variables that satisfy multiple equations simultaneously. This unit is crucial for developing algebraic reasoning and problem-solving skills, and it lays the groundwork for more advanced studies in mathematics and science. Students begin with an understanding of what a system of equations isβ€”two or more equations working together. They learn that the solution to a system of linear equations is the point(s) where the graphs of the equations intersect, representing the values that satisfy all equations in the system simultaneously. They will also learn the three different ways solve a system of equations. The unit emphasizes real-world applications, showing students how systems of equations are used to solve practical problems in areas such as business, engineering, and science. PDF is hyper linked with over 120 items. The pdf contains links to:

  • 19 Printable Student Handout with QR code for video instruction

  • 19 Printable Daily Assessment: Mid-Lesson Assessment to check for understanding and/or differentiated flexible groupings

  • 19 Instructional Video Link: Includes Teacher Model and Guided Practice.

  • Google Slide Decks for each lesson

  • Teacher Notes and Answer Key for each lesson

  • Formative Link: e-Copy of the Student Materials on GoFormative.

Also provided is a complete unit overview, a PreTest, PostTest, 1 Quiz and Student Reflections for each assessment. Answer Keys also added on GoFormative for instant data and student feedback. 30 Day free trial of GoFormative.

CCSSHSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems.

CCSSHSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

CCSSHSA-REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

CCSSHSA-REI.D.12
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

CCSSHSF-IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

CCSSHSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

CCSSHSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSSHSF-LE.A.4
For exponential models, express as a logarithm the solution to 𝘒𝘣 to the 𝘀𝘡 power = π˜₯ where 𝘒, 𝘀, and π˜₯ are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.

CCSSHSS-ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.