Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...

Don't stop with two-dimensional learning, go to the next dimension! Learners verify that 3x3 matrices represent linear transformations in the third dimension. Additionally, they verify the algebraic properties that extend to vector...

Can they put it all together? Ninth graders apply what they know about proofs and triangle congruence to complete these proofs. These proofs go beyond the basic triangle congruence proofs and use various properties, theorems, and...

Discover how combinations are different from permutations. In the third installment of a 21-part module, scholars learn how to determine combinations of objects. They learn to distinguish between situations where order is important and...

How can you compare linear functions? The seventh installment of a 12-part module teaches learners how to compare linear functions whose representations are given in different ways. They use real-world functions and interpret features in...

Add more points on the graph ... and it still remains a line! The 13th installment in a series of 33 leads the class to the understanding that the graph of linear equation is a line. Pupils find several solutions to a two-variable linear...

Is there one, none, or more? Through discussion or activity, scholars find the properties of an equation that will determine the number of solutions. They then use the properties discovered to figure out the number of solutions...

Use proportions to determine the travel distance in a given amount of time. The 10th installment in a series of 33 uses tables and descriptions to determine a person's constant speed. Using the constant speed, pupils write a linear...

Don't get out of order! Examine the effect of order on a sequence of transformations. Learners perform reflections and translation transformations in sequence. They see that changing the order of the transformations does not always have...

Develop a better understanding of the value of pi. Learners explore the area of a circle using estimation and graph paper. While continuing to estimate the area of the circle using smaller and smaller grids, the number pi emerges. 

The fifth portion of the 25-part series introduces probabilities calculated from outcomes that are not equally likely. Class members use tables to calculate probabilities of events, add outcome's probabilities, and find...

Solving these percent problems is a matter of counting. Pupils find percents by counting the number of events that meet the criteria and the total number of possibilities. Participants create the ratio and convert it to a percent to...

Display data over a larger interval. The fourth segment in a 22-part unit introduces histograms and plotting data within intervals to the class. Pupils create frequency tables with predefined intervals to build histograms. They describe...

Just how far off is the least squares line? Using a graphing calculator, individuals or pairs create residual plots in order to determine how well a best fit line models data. Three examples walk through the calculator procedure of...

How do you create a residual plot? Work as a class and in small groups through the activity in order to learn how to build a residual plot. The activity builds upon previous learning on calculating residuals and serves as a...

Provide your emerging mathematicians with the tools to learn as they incorporate auxiliary lines to solve unknown angle proofs in this continuing segment. They decipher information from a diagram to uncover the missing pieces and...

Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...

Can segments be considered perpendicular if they don't intersect? Learners look at nonintersecting segments on the coordinate plane and make conclusions about the lines that contain those segments. They determine if they are...

Prove theorems through an analysis. Learners find the midpoint of each side of a triangle, draw the medians, and find the centroid. They then examine the location of the centroid on each median discovering there is a 1:2 relationship....

Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...

A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords...

What do you do when factoring doesn't work? Learners complete the square when faced with quadratic expression that don't factor traditionally. They then use factoring by grouping to solve polynomial equations.