Young mathematicians extend their knowledge of rational numbers on a number line to graph inequalities by first using number cards to compare rational numbers. They finish by using similar reasoning to graph inequalities on a number line.

Which comes first in an adjective phrase: a word denoting a noun's quality, or a word describing a noun's function? If your elementary grammarians don't know the answer, have them review ten pairs of adjective phrases and circle the one...

Helmets not included! Scholars brainstorm adjustments and sensors to football helmets in an engineering design project to help prevent injuries, such as concussions and spinal injuries.

Explain the importance of radioactive half-life as your high school biologists demonstrate the concept by performing a series of steps designed to simulate radioactive decay. Pupils use pennies to perform an experiment and gather data....

Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.

Relations, and functions, and line tests, oh my! An instructional slideshow demonstrates the definitions of a relation, a function, and the domain and range of a relation. Viewers then learn how to use mappings and vertical...

Step up to learn about step functions. The lesson, designed for high schoolers, first covers piecewise functions and how to draw their graphs. It then introduces step functions, including the greatest integer (floor) and...

Two for one—create an invertible and non-invertible function from the same data. The task presents a function table with missing outputs for the class to use to create two functions. One of the functions should have an inverse while the...

Learners tackle a wide range of intimidating topics in this comprehensive unit that spans piecewise functions, absolute value of functions, and inverse functions (among other topics). Investigative group work alternates with more...

Ready to apply the concepts related to the natural exponential equations and logarithmic equations? A math lesson reviews concepts from inverse properties to solving to derivatives and integrals. 

Solve a real-life problem using function-building skills. Presented with an open-ended question, scholars complete a checklist to create and justify a solution in an interesting algebra project. The checklist asks for justifications of...

Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...

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...

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...

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...

Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function. 

Machines can be so helpful sometimes. A simple interactive has learners enter input values for a function machine and observe output values. These values help determine a function that represents the input-output relationship in the...

Use a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...

Analyze functions by their shape and equation and identify decay and growth based on the equation given. Learners graph their exponential functions and differentiate it using the logarithmic versus the exponential function.

How high is too high for a belly flop? Learners analyze data to model the world record belly flop using a quadratic equation. They create a graph and analyze the key features and apply them to the context of the video.

You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase...

Looking for higher-level thinking questions? This assessment provides questions that challenge young mathematicians to think and analyze rather than simply memorize. Topics include piecewise functions, linear modeling, exponential...

Introducing inverse functions! The 20th installment of a 35-part lesson encourages scholars to learn the definition of inverse functions and how to find them. The lesson considers all types of functions, not just exponential and...

To the point and deeper thinking are both types of questions included in the worksheet. Begin the practice of solving quadratics and then finish with five questions asking quadratic and exponential application problems.