EngageNY
The Graph of a Linear Equation in Two Variables
Add more points on the graph ... and it still remains a line! The 13th installment in a series of 33 leads the class to the understanding that the graph of linear equation is a line. Pupils find several solutions to a two-variable linear...
Radford University
Finding a Location for Your Kitchen Island
Where is the best place to work? Small groups map out a kitchen on a coordinate plane and find the centers of the work triangle to find the best place to install an island. The teams use algebraic methods to locate the center by finding...
EngageNY
The Slope of a Non-Vertical Line
This lesson introduces the idea of slope and defines it as a numerical measurement of the steepness of a line. Pupils then use the definition to compare lines, find positive and negative slopes, and notice their definition holds for...
EngageNY
The Graph of a Linear Equation in Two Variables Is a Line
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
Curated OER
Do Two Points Always Determine a Linear Function II?
Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.
BW Walch
Solving Systems of Linear Equations
Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what...
Illustrative Mathematics
Do Two Points Always Determine a Linear Function?
Your learners can approach this task algebraically, geometrically, or both. They analyze the building of a linear function given two points and expand the concrete approach to the abstract when they are asked to find the general form of...
Radford University
Linear Equations in Real Word Problems
Make up a story about a linear graph. Scholars identify key features of a linear graph, such as intercepts, domain and range, and slope. They then create a word problem that could be represented by the graphed line.
Radford University
Triangular Irrigation
Try to keep the pipe short. Learners investigate where to place a water pump to use the least amount of pipe. Scholars use their knowledge of reflections and congruent triangles to find the best location for the water pump. Finally, they...
Virginia Department of Education
Linear Curve of Best Fit
Is foot length to forearm length a linear association? The class collects data of fellow scholars' foot length and the length of their forearms. They plot the data and find a line of best fit. Using that line, they make predictions of...
EngageNY
Understanding Addition of Integers
Count up or down to find sums. The third lesson in a 25-part series uses number lines to build an understanding of the sums of integers. Pupils make the connection between the distance and direction of a sum from the first addend, then...
EngageNY
Geometric Interpretations of the Solutions of a Linear System
An intersection is more than just the point where lines intersect; explain this and the meaning of the intersection to your class. The 26th segment in a 33-part series uses graphing to solve systems of equations. Pupils graph linear...
Radford University
Ramp It Up
Pupils gather measurements of real-world objects that have slopes. They then plot the measurements and find an equation of a line that fits the measurements. Finally, groups investigate the ADA and determine whether different ramps meet...
EngageNY
Finding One Hundred Percent Given Another Percent
Class members solve problems to find the whole when given a percent. They use double line numbers and factors of hundred to help break the 100 percent into equal segments.
EngageNY
From Ratio Tables, Equations and Double Number Line Diagrams to Plots on the Coordinate Plane
Represent ratios using a variety of methods. Classmates combine the representations of ratios previously learned with the coordinate plane. Using ratio tables, equations, double number lines, and ordered pairs to represent...
American Statistical Association
What Fits?
The bounce of a golf ball changes the result in golf, mini golf—and a great math activity. Scholars graph the height of golf ball bounces before finding a line of best fit. They analyze their own data and the results of others to better...
BW Walch
Solving Linear Inequalities in Two Variables
Although graphing a linear inequality on the plane is but a few steps added onto the graphing of a linear equation, for many learners the logical leap is quite intimidating. This approachable PowerPoint presentation breaks graphing...
Mathematics Vision Project
Module 3: Arithmetic and Geometric Sequences
Natural human interest in patterns and algebraic study of function notation are linked in this introductory unit on the properties of sequences. Once presented with a pattern or situation, the class works through how to justify...
West Contra Costa Unified School District
Conics Introduction and Parabolas
Where did conic sections get their name? The equation and graph of a parabola are developed from the definition of the conic section. Teacher examples on graphing the equation and writing an equation from the graph round out the plan.
02 x 02 Worksheets
Slope
What does slope have to do with lines? Pupils work with lines and determine the slope of the lines informally and with the slope formula. Groups use their knowledge to calculate the slopes of parallel and perpendicular lines. They also...
EngageNY
Addition and Subtraction of Rational Numbers
Apply addition and subtraction of integers to solve problems with rational numbers. Pupils apply the rules for adding and subtracting integers to add and subtract rational numbers. Class members represent the problem with equations and...
West Contra Costa Unified School District
Connecting Graphing and Solving Absolute Value Equations and Functions
Can you solve an equation graphically? Absolutely! This Algebra II lesson makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through the process of...
Mathematics Vision Project
Module 7: Connecting Algebra and Geometry
The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...
West Contra Costa Unified School District
Solving a System by Substitution
Solving systems by substitution can be a challenging topic in algebra I. Here is a lesson that builds on students' understanding of intercepts to begin the process of substitution, and all work is reinforced graphically to build...