Variables can vary in meaning. A reference material for AP® Statistics explains the difference between random and algebraic variables. It provides a hypothetical situation involving dice—great for use in a classroom situation.

Interpreting algebraic expressions is a fundamental skill in beginning algebra. This lesson approaches the task in numerous ways. First, learners assess their understanding with a short worksheet on converting between words and...

Don't rush into algebra, let learners visualize, guess, and predict their way to a successful math career. The introductory unit incorporates beginner algebraic concepts with shapes instead of variables. Young mathematicians use a...

Don't just go through the steps to solve an algebraic equation, show learners how to balance an equation with visual models. The packet introduces the idea of mobile balances to reinforce the idea that both sides must match to make the...

Watch video clips titled, "Frog Hops Part I" and "Frog Hops Part II," then discuss patterns demonstrated in the videos. Learners will complete an algebraic expressions and equations handout and discuss the answers. They will be able to...

Practice basic operations for young mathematicians in fun ways! Using two decks of cards (Ace through 10 plus the joker), learners play "memory" by matching numbers that can be added to make 10 and writing number sentences. In another...

Banks are responsible for keeping our financial information safe. Mathematics is what allows them to do just that! Pupils learn the math behind the cryptography that banks rely on. Using polynomial identities, learners reproduce the...

Do your classes truly understand the distributive property? Use a demonstrative lesson to represent the distributive property in various ways. Learners solidify understanding by creating a geometric pattern for distributive...

Math really is just one big puzzle waiting to be solved. Show learners that math can be intriguing and provide them with visually engaging problems and puzzles. The focus is on solving simple equations and looking at expressions. 

Help learners translate word problems into algebraic equations. They will rewrite words using symbols and evaluate algebraic expressions using real life scenarios, animation sequences, video presentations, and activities to help students...

The Pythagorean Theorem makes an appearance yet again in this lesson on polynomial identities. Learners prove a method for finding Pythagorean triples by applying the difference of squares identity. 

Just because one integer is larger than another doesn't mean it will make sense right away. Go beyond note taking and show learners, through the use of algebra tiles and a Four-Pan Algebra Balance, how the numbers relate to one...

Patterns in math emerge from seemingly random places. Learners explore the patterns for factoring the sum and differences of perfect roots. Analyzing these patterns helps young mathematicians develop the polynomial identities.

Don't give your classes the third degree when working with polynomials! Teach them to recognize the successive differences and identify the degree of the polynomial. The lesson leads learners through a process to develop an understanding...

Examine the power of technology while modeling with polynomial functions. Using the website wolfram alpha, learners develop a polynomial function to model the shape of a riverbed. Ultimately, they determine the flow rate through the river.

What do you get when you cross a circle and a line? One, two, or maybe no solutions! Teach learners to find solutions of quadratic and linear systems. Connect the visual representation of the graph to the abstract algebraic methods. 

Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson, pupils learn algebraic methods of solving the systems. 

Have young mathematicians create new identities! They explore the even/odd, cofunction, and periodicity identities through an analysis of tables and graph. Next, learners discover the relationships while strengthening their...

Tables are useful for more than just eating. Learners use tables to organize data and calculate probabilities and conditional 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...

Help your classes find the significance in this lesson! Learners analyze the probability of Diff values. They then determine if the difference is significant based on their probability of occurrence. 

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...

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. 

Tackle a common misconception using a performance task. Dividing by a variable to eliminate a variable may seem like a good idea, but simplifying the variable eliminates solutions as well. Learners develop algebraic and graphical support...