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 is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions,...

Do properties of equations hold true for inequalities? Teach solving inequalities through the theme of properties. Your class discovers that the multiplication property of equality doesn't hold true for inequalities when multiplying by a...

Complex solutions are not always simple to find. In the fourth activity of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first...

Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the...

Doubling a network or combining two networks is quick and easy when utilizing matrices. Learners continue the network example in the second lesson of this series. They practice adding, subtracting, and multiplying matrices by a scalar...

Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...

Data encryption is an important security measure for sensitive data stored on computers. Pupils learn how to utilize matrices for creating code. They also get a great review of matrix multiplication, inverse matrices, and the identity...

Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson in the series, pupils now test the associative and distributive properties. The...

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...

There's a strong chance that class members enjoy learning math through engaging games. Scholars analyze games of chance to determine long-term behavior. They learn to calculate expected value to help with this assessment.

Learn how to increase the probability of success. The 19th installment of a 21-part module teaches future mathematicians how to use probability to analyze decisions. They determine strategies to maximize the chances of a desired outcome.

Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...

Develop an understanding of the properties of exponents through this series of activities. This third instructional activity of 15 explores the patterns associated with the power property. Scholars expand the powers before applying the...

Build an understanding of the powers of 10. Pupils investigate the results of raising 10 to positive and negative powers. They relate this understanding to the magnitude these powers represent in this seventh lesson of 15.

Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...

Explore how to graph lines from different pieces of information. Scholars learn to graph linear functions when given an equation, given two points that satisfy the function, and when given the initial value and rate of change. They solve...

Is it possible to add infinitely long decimals? As pupils complete the examples in the ninth lesson of this 25-part series, they determine that adding these decimals cannot be done without error. Their task is then to determine the size...

Sometimes dealing with decimals is so much easier than dealing with fractions. The ninth lesson in a 21-part module has the class consider situations when it might be easier to add or subtract fractions by first converting to...

Make multiplication of decimals easier by applying the distributive property. Pupils investigate how they can use the distributive property to multiply decimals. After learning the strategy, they work on some practice problems at...

Scholars learn how to find the distance of vertical and horizontal line segments on the coordinate plane in the 19th installment of a 21-part module. The use of absolute value comes in handy.

Use a unit approach in developing a fraction division strategy. The teacher leads a discussion on division containing units, resulting in a connection between the units and like denominators. Pupils develop a rule in dividing fractions...

Future mathematicians learn how to evaluate numerical expressions by applying the order of operations. They evaluate similar-looking expressions to see how the location of parentheses and exponents affects the value.