Lesson Plan
Illustrative Mathematics

Do Two Points Always Determine a Linear Function?

For Teachers 9th - 12th Standards
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...
Lesson Plan
Curated OER

Do Two Points Always Determine a Linear Function II?

For Teachers 9th - 12th Standards
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.
Lesson Plan
Illustrative Mathematics

Chocolate Bar Sales

For Teachers 5th - 7th Standards
In this real-world example, algebra learners start to get a sense of how to represent the relationship between two variables in different ways. They start by looking at a partial table of values that define a linear relationship. They...
Lesson Plan
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Curated OER

Find A System

For Teachers 9th - 12th Standards
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.
Lesson Plan
Illustrative Mathematics

Introduction to Linear Functions

For Teachers 7th - 9th Standards
Introduce your algebra learners to linear and quadratic functions. Learners compare the differences and relate them back to the equations and graphs. Lead your class to discussions on the properties of a function or a constant slope...
Lesson Plan
Illustrative Mathematics

Find the Change

For Teachers 7th - 9th Standards
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...
Activity
Ms. Amber Nakamura's Mathematics Website

Algebra Project

For Teachers 9th - 12th Standards
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.
Activity
5280 Math

More or Less the Same

For Teachers 8th - 10th Standards
Tell the story of the math. Given a graph of a linear system, learners write a story that models the graph before crafting the corresponding functions. Graphs intersect at an estimated point, allowing for different variations in the...
Activity
West Contra Costa Unified School District

Slope-Intercept Sort

For Teachers 8th - 10th
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.
Lesson Plan
Annenberg Foundation

Skeeters Are Overrunning the World

For Teachers 8th - 10th Standards
Skeeters are used to model linear and exponential population growth in a wonderfully organized lesson plan including teachers' and students' notes, an assignment, graphs, tables, and equations. Filled with constant deep-reaching...
Lesson Plan
Illustrative Mathematics

Fixing the Furnace

For Teachers 7th - 9th Standards
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...
Activity
Curated OER

Algebra 2 Desmos Graphing Project

For Teachers 9th - 12th Standards
Encourage class members to get creative with functions. Pairs write their names and draw pictures using a graphing application with a collaborative graphic project. The resource provides the requirements for the project, as well as a...
Activity
5280 Math

Aquarium Equations

For Teachers 8th - 12th
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...
Lesson Plan
Illustrative Mathematics

Two Lines

For Teachers 7th - 9th Standards
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...
Lesson Plan
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Curated OER

Linear and Quadratic System

For Teachers 9th - 12th Standards
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.
Lesson Plan
Curated OER

US Airports, Assessment Variation

For Teachers 7th - 9th Standards
Determining relationships is all part of algebra and functions. Your mathematicians will decide the type of relationship between airports and population and translate what the slope and y-intercept represent. The problem is multiple...
Activity
5280 Math

Go with the Flow

For Teachers 8th - 12th Standards
Round and round they go ... where they stop, only scholars will know. By writing systems of equations, classes determine the number of cars a roundabout can handle given specific constraints. Systems use up to six variables and become...
Lesson Plan
Illustrative Mathematics

Paying the Rent

For Teachers 8th - 12th Standards
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...
Lesson Plan
Curated OER

What Functions do Two Graph Points Determine?

For Teachers 9th - 12th Standards
Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.
Lesson Plan
Curated OER

Heart Rate Monitoring

For Teachers 7th - 9th Standards
Algebra learners like this resource because it is easy to understand and it relates to their lives. Whether you are starting a new workout routine, or just climbing the stairs, your heart rate increases and decreases throughout the day....
Lesson Plan
Illustrative Mathematics

How Many Solutions?

For Teachers 7th - 9th Standards
Determining the number of solutions is an important stepping stone to higher math. In this case, the resource asks algebra pupils to find a second linear equation for a certain solution of a system. When one is asked for a linear...
Lesson Plan
Illustrative Mathematics

Distance across the channel

For Teachers 7th - 9th Standards
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...
Lesson Plan
Illustrative Mathematics

Summer Swimming

For Teachers 7th - 9th Standards
Here is a real-world application for systems of equations. When is it better to pay an enrollment fee and lower daily rate, and when is it better to pay the regular price? The local swim center is having a special offer, reductions in...
Lesson Plan
Curated OER

Solution Sets

For Teachers 9th - 12th Standards
Here is a task that gives the graph of the solutions of a system of linear inequalities and asks learners to analyze and write the algebraic form of the systems. By turning the problem around, learners make the connections between...