School in a Book: Mathematics Skills

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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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