## ESSENTIAL ARITHMETIC AND MEASUREMENT SKILLS

**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 ALGEBRA SKILLS

- 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

## ESSENTIAL GEOMETRY SKILLS

**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 × R^{3}

**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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