Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...

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...

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...

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...

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...

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...

Twenty-one pieces of tagboard can lead your class to a greater understanding of integers when you use them to form a human number line. After creating this math tool, two strategies for adding and subtracting will have your...

Objects may be more linear than they appear. Scholars investigate the relationship between the number of bone mineral density scanners in the US and time. Once they take the natural logarithm of the number of scanners, a linear...

Learning how a bank account works is a useful tool. The exercise in the resource is to deduct rent from a checking account and create an equation from a description. Participants then graph the balance of the bank account versus months...

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 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...

Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.

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...

Learners must think critically about the graphical and algebraic forms of a system of linear equations in order to come up with their own system when given a point that is the solution to the system.

This comprehensive resource applies simultaneous equations to a real-life problem. Though the commentary starts with a graph, some home consumers may choose to begin with a table. A graph does aid learners to visualize the shift of one...

It is not always easy to walk the straight and narrow. In the sixth portion of a nine-part unit, groups actively recreate a graph depicting motion. Individuals walk toward or away from a motion detector while trying to match a given...

How many nurses does it take to support one doctor? A project-based activity asks learners to analyze state data to answer this question. Classes create polynomial functions from the data of doctors and nurses over a seven-year...

Who knew quilting would be so mathematical? Introduce linear equations and graphing while working with the lines of pre-designed quilts. Use the parts of the design to calculate the slope of the linear segments. The project...

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.

A different-than-normal problem that allows learners to practice their reasoning to find an answer. The problem bases itself off a graph drawing of a store that needs to install security cameras. The challenge is to find which placement...

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 does math have to do with a sore throat? When you mix water and salt you have a great review of how to represent proportional relationships by an equation or graph. Here the proportions of the mixtures may be different, but the...

The idea in the resource is to understand the connections between proportional relationships, lines, and linear equations. To stay within the context of the standard, skip the part of the resource that solves with unit rates. Instead,...

Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...