Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...

Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...

Discover the extension of parametric equations to model linear transformations. Scholars first write parametric equations to model lines through two points. They then find the parametric equations that represent a linear transformation.

Learn about life in the Arctic while practicing how to graph and interpret data with this interdisciplinary lesson. Starting with a whole group data-gathering exercise, students are then given a worksheet on which they analyze and create...

Ten bales of hay divided into equal parts. Which two bales of hay are equivalent to each other? Here, young mathematicians match equivalent bale of hay fractions to one another.

Student statisticians calculate ratios to determine how many shades of green were mixed by Ms. Baca's art class. They graph the number of blue parts against the number of yellow parts for each combination and discover that some produce...

Cut it up into parts and make fractions. The short video provides a definition of fractions as being a representation of parts of a whole. Using drawings, the presentation shows how to determine the bottom and top numbers for a fraction...

Factoring polynomials is an important skill through high school math and beyond. It provides instructions for the basic types of factoring and a practice set with an answer key.

The object of this activity is to compute how far Rosa ran to school. Given in the exercise is the fractional number of miles between home and school and the fractional distance Rosa ran. The commentary shows several ways to have your...

Why are only four colors needed to color webs from regular pentagons, not five? An assessment task requires young mathematicians to first construct regular pentagons using a compass and straightedge, then has them consider a shape...

A great hands-on activity involving adding and subtracting, beginner mathematicians determine how many games can be played with 20 tickets. Instead of tickets, youngsters use 20 counters or linking cubes to represent the amount of...

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. 

That's the ticket! Pupils write and investigate two linear functions representing the cost of printing tickets. Individuals then determine which of two printing companies would be a better buy.

Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students...

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...

From derivatives to antiderivatives and back again. Building on the second instructional activity of the three-part series covering functions, learners explore the concept of an antiderivative. They connect the concept to the graph of...

What came first, pedestrian one or pedestrian two? Scholars consider a problem scenario in which two people walk at different rates at different times. They must decide who reaches a checkpoint first. Their answers are likely to surprise...

It all adds up to one. Pupils solve several items that involve finding sums of fractions in relationship to a whole. The assessment task uses fractions with unlike denominators to determine the amount of a tank of gas and the amount of...

High school classes can use manipulatives too! Offer hands-on, interactive lessons that venture away from the typical day in your algebra class. Young mathematicians will be involved in collaborative learning, visual...

Discover relationships between linear and nonlinear functions. Initially, a set of data seems linear, but upon further exploration, pupils realize the data can model an infinite number of functions. Scholars use multiple representations...

What information can your class determine if they know the number of people attending movie showings? Using the information about the number of people at each screening, learners develop a frequency table. The pupils analyze the type of...

Maximize a profit with an understanding of geometric dimension. A real-world task challenges learners to design a pattern using three different brick shapes. The bricks are dedicated with a different donation for each shape, so part of...

Raise the bar for hockey fans. Using data about favorite hockey teams, pupils build a bar graph. They use the information from the graph to make comparisons and solve one- and two-step problems.

Scholars see cross sections come to life using an app to investigate cross sections of three-dimensional solids. They look at prisms, pyramids, cylinders, cones, and double cones.