Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...

Linear or not linear — that is the question. The lesson plan has class members translate descriptions into algebraic expressions. They take the written expressions and determine whether they are linear or nonlinear based upon the...

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...

When complicated algebraic expressions are involved, it is sometimes easier to use a table or graph to model a context. The exercises in this lesson are designed for business applications and require complex algebraic...

Ready to share the beauty of the inverse function with your classes? This algebra II lesson guides the discovery of an inverse function through a numerical, graphical, and an algebraic approach. Connections are made between the three,...

Your class will be very interested in the results of this activity. How long does it take a MP3 and video game player to charge?  Sam only has an hour and the MP3 player only has 40% of its battery life left. Plus, his video player...

Use 2x2 matrices to move along a line. The second day of a two-day lesson is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given...

Mathematicians can embark on a math challenge. Fourteen pages of exercises for young algebra learners on fractions, decimals, and percentages let your students put their skills to the test.  

Can your mathematicians come up with an easy way to convert miles to kilometers? Start by asking learners to write an algebraic expression for each of the descriptions given. Once they determine that they are both the same, ask...

Use this resource to present your number crunchers with how to write a constraint equation and to determine viable solutions. The price of an object limits the amount that can be purchased. The speed at which you walk limits the number...

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...

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...

Bring algebra to life with scientific applications. Math minded individuals calculate and graph the time it takes a bacterium to double. They discuss geometric sequences and use a chart to graph their findings. There are 38...

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and  cf(x) for...

Kimi and Jordan have taken summer jobs to supplement their weekly allowances. Kimi earns more per hour than Jordan, but Jordan's weekly allowance is greater. This activity asks students to determine how the incomes of the two workers...

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...

Here is a coin problem where the algebra learner determines the pair of linear equations needed to solve the system. Whether the equations are taken from a table, or your scholars recognize the format of a coin problem, it is an...

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 class is asked to use inverse operations to solve eleven equations for unknown variables or to rearrange formulas to highlight a quantity of interest. By using the same reasoning as solving one- and two-step equations, algebra...

According to the resource graph, which costs more: peaches or plums? Algebra learners compare two proportional relationships and then throw in a banana. Leaving out the scale helps students become intuitive about graphing. 

Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...

A graph not only tells us who won the bike race, but also what happened during the race. Use this resource to help learners understand graphs. The commentary suggests waiting until the end of the year to introduce this topic, but why...

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...