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 is the fastest way to get from point A to line l? A straight perpendicular line! Learners use what they have learned in the previous lessons in this series and develop a formula for finding the shortest distance from...

Isn't paper pushing supposed to be boring? Learners attempt a paper-pushing puzzle to develop ideas about angles inscribed on a diameter of a circle. Learners then formalize Thales' theorem and use geometric properties to develop a proof...

What is an annulus? Pupils first learn about how to create an annulus, then consider how to find the area of such shapes. They then complete a problem set on arc length and areas of sectors.

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.

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

Ensure your pupils are rule followers! Learners add the addition rule to the set of probability rules examined in the previous lesson. Problems require both the multiplication and addition rule.

The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are...

If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...

Let's paint the town equal parts yellow and violet, or simply brown. Pupils calculate the amount of blue and red paint needed to make six quarts of brown paint. Individuals then explain how they determined the percentage of the brown...

Scaling needs to be picture perfect. Pupils use proportional reasoning to find the missing dimension of a photo. Class members determine the sizes of paper needed for two configurations of pictures in the short assessment task.

Prompt scholars to complete a magic square using only variables. Then they can attempt to solve a numerical magic square using algebra. 

Number towers use addition or multiplication to ensure each level is equal. While this is common in factoring, it is often not used with algebraic equations. Solving these six questions relies on problem solving skills and being able to...

It is positive that how one performs on the first test relates to their performance on the second test. The three-question assessment has class members read and analyze a scatter plot of test scores. They must determine whether...

What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...

Population density, it is not all that it is plotted to be. Pupils analyze a scatter plot of population versus area for some of the states in the US. The class members respond to eight questions about the graph, specific points and...

Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...

What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

You've investigated relationships between chords, radii, and diameters—now it's time for arcs. Learners investigate relationships between arcs and chords. Learners then prove that congruent chords have congruent arcs, congruent arcs have...

Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...

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...

Learners solve complex radical equations. Solutions vary from one, two, and none, allowing pupils to gain experience solving a variety of problems.

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.