Math that Means Something
WHAT IS MANIFEST?
Manifest is a new and exciting vision for math education. This website houses resources that bring the vision to life.
Learners struggle to find meaning in mathematics because they don’t have experience linking math to concrete experiences. Manifest solves that problem. Using a new, systematic approach to visualizing quantities in terms of the way we experience the world, Manifest makes math concrete. Watch the video to find out more.
MANIFEST VISUAL CALCULATORS
Manifest Visual Calculators are calculators for the 21st century. They don’t just evaluate expressions, they visualize them as well. And they don’t graph functions, they simulate the relationship that the function describes.
MANIFEST FUNCTION VISUALIZERS
If you want to visualize a function, launch one of the calculators below.
MANIFEST EXPRESSION VISUALIZERS
If you want to visualize expressions, launch one of the calculators below.
EMERGE LESSONS
Uncover Hidden Mathematical Relationships
Emerge lessons combine hands-on math, game-based learning, and the Manifest framework to deliver mathematically rich, meaningful, rigorous, fun, and flexible learning experiences.
Scoring and Leaderboard App
Click the button below to be taken to the official scoring app for Emerge lessons. The app lets up to 7 teams play. You can input each team’s guess for each round. Then input the correct answer for each round and let the app do the scoring and the leaderboard updates. The app can’t be edited at first. To get an editable version, you need to make a copy of it. To do this, select “Make a copy” from the File menu.
Emerge Lesson: Toppling Cube Tower
Quadratic – Suitable for Grades 7-12
In this Emerge lesson, students investigate towers of blocks being tipped over, causing the blocks to topple. As the towers get higher, the toppling blocks tumble further and further from the tower’s base. Students compete in teams to uncover the relationship between the number of blocks in the tower and how far the blocks tumble. Click the video to preview the challenge the students will encounter. Game on!
Emerge Lesson: String on a Tape Roll
Linear Function – Suitable for Grades 5-11
In this Emerge lesson, a string is wound around a roll of masking tape, making the string shorter. Students compete in teams to uncover the relationship between the number of times the string is wrapped and the length of the loose string. Click the video to preview the challenge the students will encounter. Game on!
Emerge Lesson: Cubes in a Dixie Cup
Linear Function – Suitable for Grades 5-11
In this Emerge lesson, students compete in teams to uncover the relationship between the number of cubes in a cup and the total mass of the cup and cubes. Click the video to preview the challenge the students will encounter. Game on!
FEATURED LESSON
Paper Airplanes!
In this one-lesson activity, learners create 6 different paper airplanes by varying the angle that the wings are folded. Learners fly these planes and investigate the connection between wing angle and flight distance. This lesson can be accessed without a sign-up, but lesson navigation is a little easier if you are signed in. This is a great lesson to be used as a capstone to the Linear Functions micro-course.
MANIFEST MICRO-COURSES
Manifest is a new service that will eventually feature a wide range of instructional micro-courses. Here’s our first two completed micro-courses, Linear Functions and Polynomial Functions. See below for some of the micro-courses that are currently under construction.
Linear Functions
This is not your typical linear functions instruction! This course immerses learners in a series of hands-on lessons that explore how linear functions describe the world around us. It includes study of Addition and Subtraction Functions, Multiplication and Division Functions, and general Linear Functions.
Polynomial Functions
This course immerses learners in a series of hands-on lessons that explore how polynomial functions describe the world around us. It includes study of Quadratic Functions, Cubic Functions, and Polynomial Functions of higher degrees.
PRE-MICRO-COURSES
These micro-courses are currently under construction. Some only have one lesson created. Others have multiple lessons created but aren’t completed. Feel free to play with them anyway!
Trigonometric Functions
This course immerses learners in a series of hands-on lessons that explore how trigonometric functions describe the world around us. It currently includes study of Sine Functions
Single Variable Equations
This course immerses learners in a series of hands-on lessons that explore how single variable equations describe the world around us.
Addition and Subtraction
This course immerses learners in a series of hands-on lessons that explore how addition and subtraction expressions describe the world around us. It currently has one lesson that begins to explore integer addition.
Multiplication
This course immerses learners in a series of hands-on lessons that explore how multiplication expressions describe the world around us. It currently has three lessons the begin to explore simple integer multiplication equations.
Manifest helps learners make sense of numbers by perceiving them as units of measure.
Number of Objects
Temperature
Length
Time
Amount of Light
Rotation
These quantities can be explored individually or combined to create functions.
Try them! Here’s part of a sample lesson from our Linear Functions micro-course:
SAMPLE LESSON
ACTIVITY #1
Watch this video.
ACTIVITY #2
Brainstorm: In the box below, type more examples from life where a number of objects or actions affects the length of something.
ACTIVITY #3
Watch this video, which introduces a simulation designed to think about these situations mathematically.
ACTIVITY #4
Read about Addition and Subtraction functions below. Then create your own examples.
An addition or subtraction function is a function in the following form:
or 
where 
is any real number.
Here are some examples and non-examples. Add an example of your own as well as a non example.
EXAMPLES
NON-EXAMPLES
ACTIVITY #5
Simulate Addition and Subtraction functions in context.
Directions: Simulate each of the following functions using the Length vs. Number of Objects simulation below. Three of the functions are addition or subtraction functions, and two of them are not. Your job is to find out what all addition and subtraction function simulations have in common by comparing them to each other and to the non-examples. Record your notes in the text area below the simulation.
EXAMPLES
NON-EXAMPLES
END OF SAMPLE LESSON
Manifest is a new website that is just beginning to develop its resources.
What does Manifest have to offer?
CLASSROOM TOOLS
Manifest has resources you can use to enrich your math class. Our math simulations allow learners to visualize and interact with any number or function. Our puzzles are wonderful for enrichment in class or for use in math clubs. Classroom tools can be found in the Resources menu.
MICRO-COURSES
Micro-courses will form the heart and soul of Manifest. Using our revolutionary hands-on approach, our courses immerse learners in the tangible world of mathematics. Micro-courses can me found in the Micro-Courses menu.
ADVICE
Manifest will soon begin publishing articles that focus on helping you teach according to our core principals. Articles will be practical guides to and valuable how-to’s that will make an immediate difference in you instruction. These can be found in the Articles menu.
(coming soon)