Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...

Who knew the sum of a number's digits gives such interesting information? The 18th installment of a 21-part module has scholars investigate division by three and nine. After looking at several examples, they develop divisibility tests...

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...

How many ways can you create a dilation? Many! Individuals strengthen their understanding of dilations by using various methods to create them. The new technique builds on pupils' understanding of the ratio method. Using the ratio,...

You can explain it, but can you do it? After learners view a sequence of transformations, the next logical step is creating the transformation. Challenge your classes to construct a composition of transformations and verify the...

Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...

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. 

What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...

If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...

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...

What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...

Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.

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.

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.

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...

Without data, all you are is another person with an opinion. Show learners the power of statistics and probability in making conclusions and predictions. Using two-way frequency tables, learners determine independence by analyzing...

Show scholars the importance of recognizing a normal curve within a set of data. Learners analyze normal curves and calculate mean and standard deviation.

Increase your sample and increase your accuracy! Scholars complete an activity that compares sample size to variability in results. Learners realize that the greater the sample size, the smaller the range in the distribution of sample...

(vegetable)^(1/2) = root vegetable? The fourth installment of a 35-part module has scholars extend properties of exponents to rational exponents to solve problems. Individuals use these properties to rewrite radical expressions in...

If mathematicians know the secret to compound interest, why aren't more of them rich? Young mathematicians explore compound interest with exponential functions in the twenty-seventh installment of a 35-part module. They calculate future...

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...

Count the benefits of using the resource. The second installment of a 21-part module focuses on the fundamental counting principle to determine the number of outcomes in a sample space. It formalizes concepts of permutations and...

Avoid the trap of memorizing steps when completing the square with a resources that provides a conceptual approach to completing the square. Learners that are able to recognize a perfect square trinomial are ready to complete the...

In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.