# Mathematical modeling done right

## 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.

**Directions:**

**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)

## LEARN MATH THROUGH KNOWING, DOING, AND MAKING.

# KNOW

KNOW activities help learners know the definitions of math concepts. They expose learners to examples of a concept as well as non-examples, focusing on tangible examples.

# DO

DO activities help learners translate between the three representations of a concept: symbolic, concrete, and simulation.

# MAKE

MAKE activities help learners be creative with the math they learn. They ask learners to use mathematical simulations to imagine and create new possibilities in their world.

# Manifest Micro-Courses

Manifest is a new service that will eventually feature a wide range of instructional micro-courses. Here’s our first micro-course on linear functions, which is still in the process of being built. Click the link to start progressing through the course for free.

## Linear Functions

This is not your typical linear functions instruction! In this micro-course, students learn to know, do, and make things with linear functions. Focusing on three different representations (concrete, simulation, and symbolic) the course develops a deep, intuitive understanding of what linear functions describe. Students will become fluent with linear functions and learn to use them to describe and understand the world around them.