Using a similar process from the first lesson in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference...

What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...

The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...

A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords...

There's a fine line between a numerator and a denominator! Learners find common denominators in order to add and subtract rational expressions. Examples include addition, subtraction, and complex fractions.

Show learners how to apply rational equations to the real world. Learners solve problems such as those involving averages and dilution. They write equations to model the situation and then solve them to answer the question —...

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.

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...

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.

Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...

More constructions! In this third installment of a 36-part series, learners watch a YouTube video on creating door trim to see how to bisect an angle. They then investigate how to copy an angle by ordering a given list of steps.

It's scary how fast bacteria can grow — exponentially. Class members solve exponential equations, including those modeling bacteria and population growth. Lesson emphasizes numerical approaches rather than graphical or algebraic.

Factoring doesn't have to be intimidating. Build on prior knowledge of multiplying binomials and factoring simple trinomials to teach advanced factoring of quadratic expressions with a lesson that uses various methods of exploring the...

Zero in on your pupils' understanding of solving quadratic equations. Spend time developing the purpose of the zero product property so that young mathematicians understand why the equations should be set equal to zero and how that...

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,...

Need a less abstract approach to introducing extraneous solutions? This is it! Young mathematicians explore properties used to solve equations and determine which operations maintain the same solutions. They...

English and math have more in common than you think. Make a connection between a compound sentence and a compound inequality with an activity that teaches learners the difference between an "and" and "or" inequality through solutions...

How are systems related? Build on your pupils' previous knowledge of solving systems of equations by introducing systems of inequalities. Learners explore similarities between systems of equations and inequalities to make a strong...

Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...

There's a function for that! Scholars examine real-world situations to determine which type of function would best model the data in the 23rd installment of a 35-part module. It involves considering the nature of the data in addition to...

Complex solutions are not always simple to find. In the fourth lesson 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 lesson....

Conjugating in the math classroom — and we're not talking verbs! The seventh lesson plan in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...

The 14th lesson in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for the...