Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...

Here is a resource that helps your algebra learners understand the connection between the graph of two lines, the equations of lines, and the solutions and intersecting points of lines. It would make a great assessment question, but can...

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.

This exercise is an opportunity for algebra learners to understand the connection between the slope of a line and points found on the line. Use similar triangles to explain why slope m is the same between any two points. Discuss with the...

Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.

Compare two different proportional relationships on a graph. It is up to your mathematicians to determine which of two moving objects have greater speed. A good example of a Common Core multiple choice question. 

Turn your algebra learners into meteorologists. Students are given three graphs that contain information about the weather in Santa Rosa, California during the month of February, 2012. Graph one shows temperatures, graph two displays the...

What is the financial benefit for attending a community college for the first two years before transferring to a four-year college? The second part of the educational lesson asks young scholars to explore this question through data...

The resource is a good introduction to what makes a proportional relationship between two lines. Discuss the similarities of both lines and the possibility of intersection. Use this opportunity to list other acceptable forms of each...

What's so special about slope? Pupils first match cards with slope and y-intercept to graphs of linear equations. They continue the lesson by matching equations in slope-intercept form to the same graphs.

Predict the year that college costs will double in your state using linear modeling. The first part of this two-part project based learning activity asks young mathematicians to use data from the College Board. They graph the data,...

This is a great exercise in graphing proportional quantities to interpret the unit rate as the slope of a graph. It is not easy for learners to understand what a unit rate is. When it is presented as the slope of a linear line graph,...

What would your dream house look like? A cottage? A medieval castle? High schoolers enrolled in Algebra design the perfect house while using slopes to write equations for various aspects of the project.

An upper-level treatment of what is often presented as a basic concept (the right angle of an inscribed circle on the diameter), this activity really elevates the mathematical thought of the learner! Expected to develop formulas...

Making money is important to teenagers. It is up to your apprentices to determine how much two wage earners make with their after school jobs. Participants work with a table, an equation, and a graph and compare the two workers to see...

Combine algebraic and geometric strategies to find solutions. The task asks learners to find the coordinates of a third vertex of a triangle to create a triangle with a specific area. The project is a set of seven problems that...

Take a look at linear functions in a new environment. A three-stage algebra project first asks learners to model the salt concentration of an aquarium using linear functions. Then, using iterations, pupils create a set of input-output...

Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...

Take the mystery out of linear functions. Provided an image with no scale, learners guess where the line that connects them might cross the y-axis. After providing the coordinates of the points, they realize scale is an important...

Learners first determine the slope-intercept and standard forms of inequalities given graphs, and then determine key features of the graphs.

The last segment of the nine-part unit makes a connection between springs and linear equations. Groups hang weights from the spring and measure its length. Then, using the data collected, they calculate the slope to find the k-value...

Here's a resource that models rising water levels with a linear function. The task contains three parts about the level of water in a cylinder in relationship to the number of golf balls placed in it. Class members analyze the data and...

The intent of this resource is to show algebra learners that there is a proportional relationship between two lines that have an intersecting point. As the coordinate x increases by a constant, the y coordinate also increases.  It...

Your learners will explore linear functions by analyzing a graph of the linear equations.Then learners analyze through calculating f(x+P) and g(x+p)