# School in a Book: Mathematics Skills

Obviously, math knowledge is more than just knowledge. The trick to this subject is in the application. Since this isn’t a how-to book, but a terminology-based review, further math study will be important. Use this list like a checklist, noting what you’ve already learned in school and elsewhere. Any areas that were skipped can be learned on your own, either by using a user-friendly book like Everything You Need to Ace Math in One Big Fat Notebook by Workman Publishing or by taking advantage of the wonders of YouTube.

## ESSENTIAL SKILLS: ARITHMETIC AND MEASUREMENT

How to add and subtract large numbers without using a calculator or writing instruments: Break the numbers into ones, tens and hundreds. For example, 72 + 83 becomes 70 + 80, then 2 + 3, then 150 + 5.

How to round numbers up or down: The two main rules that apply when rounding numbers to the nearest ones, fives, tens, hundreds, etc. are: 1. Round the number up if it is past the halfway point and down if it is less than the halfway point; and 2. Round numbers that are at the halfway point up, not down. For example, 56 rounded to the nearest multiple of 10 is 60, and 55 is also 60.

• Adding, subtracting, multiplying and dividing
• Memorizing the times tables up to 12
• Recognizing common shapes
• Solving basic story problems
• Using a calculator
• Using a ruler and drawing compass
• Calculating map distances
• Deciphering information on line graphs, bar graphs, circle graphs, tables and Venn diagrams
• Adding, subtracting, multiplying and dividing fractions, decimals and positive and negative numbers

## ESSENTIAL SKILLS: ALGEBRA

• Using algebraic symbols
• Solving for variables
• Solving and graphing inequalities
• Calculating ratios, rates, percentages and proportions (as when finding taxes, discounts, markups, gratuities, commissions, simple interest, the percent rate of change, exponential growth and more)
• Finding prime numbers and square roots
• Comparing functions

## ESSENTIAL SKILLS: GEOMETRY

Formula for calculating the area of squares and rectangles: Multiply height by width: hxw. Note that some areas can be divided into multiple squares and rectangles and the results can be added together to find the total area.

Formula for calculating square footage: Use the same formula as for finding the area of a square, using feet as the measurement: hxw

Formula for calculating the area of a triangle: Multiple the height by the width, then divide by two: (h x w)/2

Formula for calculating diameter: Multiply the radius by two: d = 2r

Formula for calculating perimeter: Add length and width, then multiply this by two: 2(l + w)

Formula for calculating the volume of a cube or rectangle-based shape: Multiply width, length and height: l x w x h

Formula for calculating the volume of a sphere: Cube the radius, then use this formula: 4/3 × π × R3

Formula for calculating the volume of a prism or cylinder: Find the area of the end shape, then multiply by its depth

Formula for calculating the volume of a cone or pyramid: Calculate the volume of the base as if the base were a square, then divide by 3.

• Calculating scale
• Measuring angles
• Calculating arc length
• Graphing lines and slopes
• Working with coordinate planes
• Proving simple geometric theorems
• Making geometric constructions based on a given set of numbers
• Working with the Pythagorean theorem
• Solving linear equations
• Working with functions ***

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