Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.

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.

Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...

Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...

Help pupils see the world through the eyes of a mathematician. As they examine tide patterns, sound waves, and stock market patterns using trigonometric functions, learners create scatter plots and write best-fit functions. 

Have class members going in circles as they model the path of a Ferris Wheel using trigonometric functions. Building on the previous lesson in this series on transformations, learners use trigonometric functions to model wheels of...

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...

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. 

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...

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...

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...

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...

Use the power of mathematics to find the number of red chips in a bag — it's a little like magic! The activity asks learners to collect data to determine the percentage of red chips in a bag. They calculate the margin of error and...

Error does not mean something went wrong! Learners complete a problem from beginning to end using concepts developed throughout the last five lessons. They begin with a set of data, determine a population proportion, analyze their result...

How accurate is data collected from a sample? Learners answer this question using a simulation to model data collected from a sample population. They analyze the data to understand the variability in the results.

Don't leave your classes vulnerable in their calculations! Help them understand the importance of calculating a margin of error to represent the variability in their sample mean. 

Statistics can be manipulated to say what you want them to say. Teach your classes to be wise consumers and sort through the bias in those reports. Young statisticians study different statistical reports and analyze them for...

We know that sample data varies — it's time to quantify that variability! After calculating a sample mean, pupils calculate the margin of error. They repeat the process with a greater number of sample means and compare the results.

Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison. 

(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...

Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...