# Appendix M for Math

If you need some more help with your basic math skills, there is a wealth of resources our there to help you. You can do it. Math is the language of physics, so it is worth your time to play and practise it before or during your physics and astronomy courses.

**The Khan Academy**

“Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization.” Many good videos on a variety of subjects, but it started off with math help.

https://www.khanacademy.org/math

https://www.khanacademy.org/science

**Crash Course **

Many subjects are covered here. Started by Hank Green. A youtube channel with more than 9 million subscribers. Here is YouTube done well.

https://www.youtube.com/channel/UCX6b17PVsYBQ0ip5gyeme-Q

**Sci-Show**

Hank Green does science well.

https://www.youtube.com/user/scishow

**PheT simulations for Math**

PhET started off as physic simulations, but they realized that they needed to do some basic math ones as well. These are well researched. Start here first.

https://phet.colorado.edu/en/simulations/category/new

https://phet.colorado.edu/en/simulations/category/math

Addition or “Make A Ten”

Powers of ten

https://phet.colorado.edu/en/simulation/make-a-ten

**Topics**

Place Value

Addition

Subtraction

Arithmetic

**Description**

Add numbers by making tens. Break apart and combine numbers while focusing on place value. Use the adding screen to add any two numbers. Use the game screen to apply your make-a-ten strategies!

**Arithmetic**

https://phet.colorado.edu/en/simulation/arithmetic

**Topics**

Multiplication

Division

Factoring

**Description**

Remember your multiplication tables? Practice your multiplication, division, and factoring skills with this exciting game. No calculators allowed!

**Sample Learning Goals**

Explain how multiplication tables help understand multiplication, factoring, and division.

Use an array model to understand multiplication, factoring, and division.

Increase accuracy in multiplying, factoring and dividing.

Develop multiple strategies for arithmetic problems.

**Fractions**

https://phet.colorado.edu/en/simulation/fraction-matcher

**Topics**

Fractions

Equivalent Fractions

Mixed Numbers

**Description**

Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars!

**Sample Learning Goals**

Find matching fractions using numbers and pictures

Make the same fractions using different numbers

Match fractions in different picture patterns

Compare fractions using numbers and patterns

**Equalities**

https://phet.colorado.edu/en/simulation/equality-explorer-basics

Equations

Inequalities

Proportional Reasoning

### Description

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Find all the ways to balance cats and dogs or apples and oranges.

### Sample Learning Goals

Use a balance model to solve an equation for an unknown, and justify your strategies for solving

Use proportional reasoning to determine the value of a single object

**Proportion Playground – Ratios**

https://phet.colorado.edu/en/simulation/proportion-playground

**Topics**

Ratios

Proportional Reasoning

Unit Rate

**Description**

Play with ratios and proportions by designing a necklace, throwing paint balloons, playing billiards, or shopping for apples! Make predictions about proportions before they are revealed.

**Unit Rates**

https://phet.colorado.edu/en/simulation/unit-rates

**Topics**

Ratios

Proportional Reasoning

Double Number Line

Unit Rate

**Description**

Discover the unit rate while shopping for fruits, vegetables, and candy. Construct a double number line and look for patterns. Challenge yourself on the race track as you compare cars with different rates!

*Sample Learning Goals*

*Sample Learning Goals*

Interpret ratios of mixed units (e.g. $/lb)

Define the unit rate and determine a method to calculate it

Predict how changing the numerator or denominator of a rate will affect the unit rate

Use the double number line to reason about rates and solve real-world problems

Develop strategies to use the unit rate to solve problems

Compare unit rates between two simultaneous situations

**Graphing Lines – Introduction – Slope and Intercept**

https://phet.colorado.edu/en/simulation/graphing-slope-intercept

**Graphing Lines**

https://phet.colorado.edu/en/simulation/graphing-lines

**Trigonometry**

https://phet.colorado.edu/en/simulation/trig-tour