Progress from proportional relationships to linear functions. Pupils first review concepts of proportionality covered in earlier grades. They then extend these concepts to linear functions, such as determining the slope of a...

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...

Many organizations put on barbecues in order to make money. In a real-world math problem, the money allotted to purchase steak and chicken at this barbecue is only one hundred dollars. It is up to your potential chefs to figure out how...

An inquiry-based algebra lesson explores real-world applications of linear functions. Scholars investigate four different situations that can be modeled by linear functions, identifying the rate of change, as well as the...

Your movie fans will be interested in this resource. They will compare video streaming plans. One plan charges a set rate per month and a reduced viewing fee, and the other has a flat rate per each video viewed. Unfortunately, learners...

A mail truck travels the same amount of miles per day. It will be up to your algebra learners to find an equation for this mailman’s truck. One needs a good understanding of rate of change and the initial value for this model. The...

Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the...

Teaching linear function relationships using contextual information is beneficial to pupils' understanding. The lesson uses problem solving to build linear functions given different information for each problem. This is the second...

How can you tell if number relationships are proportional? Mathematicians investigate proportional relationships. They compare and contrast functions and graphs to determine the characteristics of proportional relationships, as well as...

How does your garden grow? Use proportions to help Tim answer that question. By using their understanding of proportional relationships, pupils determine the number of seeds that will sprout. They create their own linear...

Graphs, functions, symbols, and more! Use these strategies to model everything from the flow of a river to the number of cars passing a toll booth. Presented differently but solved similarly, learners consider five different scenarios...

Can your class write linear equations three different ways? Here is a study guide that includes slope-intercept, standard, and point-slope forms. Learners are given the slope and a point on the line, or two points and are asked to write...

Enhance pupil understanding of proportions and variable relationships by studying direct and inverse variation. Use the idea of a proportional relationship to teach direct variation. Then use a similar pattern to help individuals...

Here is a resource that demonstrates growth and the initial state of an equation. In this case, your class will be looking at baseball collections. How many baseball cards did the collector start out with, and how many were added or...

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...

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...

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...

Playing with values in this fruit salad problem allows learners to find out how many cherries were mixed in. Your middle schoolers can organize their thoughts in a chart before going into the equation. Eigth graders can skip the chart...

Determine the better deal. Pupils write the equation for the cost of printing tickets from different printers. They compare the costs graphically and algebraicaly to determine which printer has the best deal based upon the quantity of...

Adjust this lesson to fit either beginning or more advanced learners. Build a scatter plot, determine appropriate model (linear, quadratic, exponential), and then extend to evaluate the model with residuals. This problem uses real-world...

Time to show what you know about functions! The review concludes a series of nine lessons on the basics of functions. The problems included are modeled from the previous lessons. Pupils determine if a table represents a function,...

Use this instructional activity to write equations in both point-slope form and slope-intercept form. Start by writing equations given one point and the slope and finish by writing equations given two points and a few real-world...

It's all about lines when going around. Pupils graph the relationship between the length of a side of a square and its perimeter. Class members explain the origin in context of the side length and perimeter. They compare the graph to the...

Pupils analyze a pattern of conference tables to determine the number of tables needed and the number of people that can be seated for a given size. Individuals develop general formulas for the two growing number patterns and...