School in a Book: Mathematics Skills

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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.


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


  • 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
  • Solving quadratic equations
  • Working with radicals
  • Comparing functions


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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