Mirror, mirror on the wall, which is the fairest resource of them all? Individuals write and solve one-step equations for problems about angle measurement, including those involving mirrors. Both mathematical and real-world problems are...

How do you balance a set of data? Using a ruler and some coins, learners determine whether the balance point is always in the middle. Through class and small group discussions, they find that the mean is the the best estimate of the...

Does standard deviation work for non-symmetrical distributions, and what does it mean? Through the use of examples, high schoolers determine the standard deviation of a variety of distributions and interpret its...

Through a series of problems, learners determine the variability of a data set by looking at the deviations from the mean. Estimating means of larger data sets presented in histograms and providing a way to calculate an...

Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both...

What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...

Not all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems. 

How do 2-D properties relate in 3-D? Lead the class in a discussion on how to draw and see relationships of lines and planes in three dimensions. The ability to see these relationships is critical to the further study of volume and...

Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder. 

Rational expressions are just fancy fractions! Pupils apply fractions concepts to rational expressions. They find equivalent expressions by simplifying rational expressions using factoring. They include limits to the domain of the...

Learners solve complex radical equations. Solutions vary from one, two, and none, allowing pupils to gain experience solving a variety of problems.

Put together the pieces and model a parabola. Learners work through several examples to develop an understanding of a parabola graphically and algebraically. 

Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

What function will describe the insect population growth? Pairs or small groups work together to determine which type of function and specific function will model given scenarios. The scenarios differentiate between linear,...

Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of...

Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.

Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...

Protect yourself from identity theft! Establishing a strong understanding of the Pythagorean identity allows learners to prove that sine^2x + cos^2x = 1. They then use the identity to find sine or cosine ratios given the other.

Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.

Proving a trig identity might just be easier than proving your own identity at the airport. Learners first investigate a table of values to determine and prove the addition formulas for sine and cosine. They then use this result to...

Want a leg up on the competition? Show classes how to use mathematics to their advantage when playing games. Learners calculate probabilities to determine a reasonable scoring strategy for a game. 

Time for statistics and learning to overlap! Learners examine Venn Diagrams as a means to organize data. They then use the diagrams to calculate simple and compound probabilities.

In statistics, probability rules—literally! Learners use their previous knowledge and explore a set of rules for conditional probability, independent probability, and complements. Given different scenarios, they must determine what type...