Compass Resources

### Compass Essential Skills: Pre-Algebra

#### Integers

Properties of Real Numbers

What properties do real numbers share?

Real Number Types [CC]

Pick a number ... any number. Do you know its type?

Number Types

What are all of the different types of numbers?

Properties of Addition

What do all addition problems have in common?

Add Integers

How can you add single-digit, double-digit, and triple-digit numbers?

Subtract Integers

How can you find the difference between 2 integers?

Absolute Value and Signed Integers

What do -4 and +4 have in common?

Absolute Value [CC]

What do -5 and +5 have in common?

Add Signed Integers

How can you add negative and positive numbers?

Signed Number Addition and Subtraction [CC]

How can you add and subtract signed numbers?

Signed Number Arithmetic

How can you add, subtract, multiply, and divide with signed numbers?

Subtraction Application Problems

How do you know when a word problem is asking you to subtract?

Subtraction Application Problems [CC]

When do you actually use subtraction?

#### Fractions

Understanding Fractions

Can you explain what a fraction is?

Simplify Fractions

How can you reduce a fraction to its simplest form?

Simplify Fractions

How do you know when a fraction can be simplified?

Equivalent Fractions

How can 2/3 and 8/12 be equivalent?

Equivalent Fractions

How can you identify equivalent fractions?

Compare Fractions [CC]

5/7 vs 6/7. Which value is greater?

Improper Fractions and Mixed Numbers

How can you convert improper fractions to mixed numbers and vice versa?

Convert Mixed Numbers to Improper Fractions

How can you convert a mixed number into an improper fraction?

Convert Improper Fractions to Mixed Numbers

How can you convert an improper fraction into a mixed number?

Add Fractions

Why do you need a common denominator to add fractions?

Subtract Fractions

Why do you need a common denominator to subtract fractions?

Multiply Fractions (Video)

How can you multiply fractions?

Divide Fractions [CC]

Why do we use reciprocals to divide fractions?

Add Fractions and Mixed Numbers

How can you add a fraction to another fraction, a whole number, or a mixed number?

Subtract Fractions and Mixed Numbers

What are 2 strategies that you can use to subtract fractions and mixed numbers?

Subtract Fractions and Mixed Numbers

Review how to subtract a fraction from another fraction, a whole number, or a mixed number.

Multiply Fractions and Mixed Numbers

How can you multiply fractions by other fractions, whole numbers, and mixed numbers?

Divide Fractions and Mixed Numbers

Why do reciprocals help you divide fractions?

#### Decimals

Round Decimals

How does rounding decimals differ from rounding whole numbers?

Rounding Decimals

How can you round decimals to a given place value?

Write Decimals

How can you write decimals out in word form?

Writing Decimals

How can you use your knowledge of place value to write decimals?

Compare Decimals

How can you compare decimals?

Comparing Decimals

How can you use place value to compare decimals?

Addition with Decimals

Does the decimal point change the process?

Subtraction with Decimals [CC]

Does the decimal point change the process?

Addition and Subtraction with Decimals

How can you add and subtract decimals?

Multiply Decimals [CC]

Why are zeroes are so important in these problems?

Division with Decimals [CC]

How can you use a decimal point to help you divide decimals?

Multiplication and Division with Decimals

How can you multiply and divide decimals?

Decimals and Fractions

How can you change decimals into fractions and fractions into decimals?

Convert Fractions, Decimals, and Percentages

How can you convert decimals to fractions and percentages.

#### Exponents

Rules of Exponents

How can you work with exponents?

Scientific Notation

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (CCSS: 8.EE.A.4)

Scientific Notation [CC]

How can you work with unimaginably large and small numbers?

Powers and Exponents

How can you use a power's base and exponent to rewrite the value as a product of factors?

Rule of Zero [CC]

What is the value of a number with a zero as an exponent?

Power Rule of Exponents

How can you raise one power to another power?

Negative and Rational Exponents

Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CCSS: HS.N-RN.A.2)

Quotient of Powers Property

How can you divide and simplify exponential expressions?

#### Square Roots

Simplify Square Roots

How can you simplify expressions that contain square roots?

Simplify Square Roots

How can you search for perfect squares, the factors that allow us to simplify square roots?

Add and Subtract Square Roots

How can you add and subtract square roots?

Add and Subtract Square Roots

How can you add and subtract square roots?

Multiply Square Roots

How can you multiply expressions with square roots?

Multiply Square Roots [CC]

How can you multiply expressions with square roots?

Working with Roots and Radicals

What is a root, and how can you work with it?

The Imaginary Unit i

Define complex number i such that i2=–1, and show that every complex number has the form a+bi where a and b are real numbers. (CCSS: HS.N-CN.A.1)

#### Percentages

Understanding Percent

What is a percentage?

Percent as a Proportion

How can you solve problems by writing a percentage as a proportion?

Percent as Proportion [CC]

How can you solve problems by writing a percentage as a proportion?

Percent Equations

How can you find the percent of a number and understand the different parts of the basic percent equation?

Percent Equations [CC]

How can you find the percent of a number and understand the different parts of the basic percent equation?

Percent Change

How can you use percent to understand how much a quantity has increased or decreased?

Percent Change [CC]

How can you use percent to understand how much a quantity has increased or decreased?

Convert Fractions, Decimals, and Percents

How can you convert percentages to decimals or fractions?

#### Ratios, Rates, and Proportions

True Proportion

How can you identify true proportions?

Ratios

What is a ratio?

Ratios

How can you work with ratios?

Rates

How can you use rates to set up expressions?

Rates [CC]

How can you use rates to set up expressions?

Scale

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)

Scale Factor

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)

Solve Proportions

How can you read proportions and simplify the expressions?

Proportion

How can you read proportions and simplify expressions?

#### Averages

Mean, Median, Mode, Range

Why would you need to find the mean, median, mode, and range of a group of values?

Mean, Median, and Mode [CC]

How can you analyze a data set in 3 different ways?

Weighted Average

How can you find the average of quantities that have different values?

Weighted Average [CC]

What happens when each quantity in a set has a different value?

### Compass Essential Skills: Algebra

#### Expressions

Write Expressions and Equations [CC]

Do you want to learn how to read word problems and convert them to algebraic expressions?

Combine Like Terms

Interpret complicated expressions by viewing one or more of their parts as a single entity. (CCSS: HS.A-SSE.A.1.b)

Distributive Property

Interpret complicated expressions by viewing one or more of their parts as a single entity. (CCSS: HS.A-SSE.A.1.b)

Monomials

What are the fundamental characteristics of monomials?

Multiply Monomials

How do you go about multiplying terms that contain both constants and variables?

Multiply Monomials [CC]

How do you go about multiplying terms that contain both constants and variables?

Algebraic Expressions

What is an algebraic expression and how can it be simplified?

Evaluate Algebraic Expressions

How do you evaluate algebraic expressions?

Evaluate Algebraic Expressions [CC]

How do you evaluate algebraic expressions?

Simplify Algebraic Expressions

What steps must be taken when simplifying algebraic expressions?

Simplify Algebraic Expressions [CC]

What steps must be taken when simplifying algebraic expressions?

Simplify Complex Fractions

How do you simplify complex fractions?

Least Common Denominator

Working with rational expressions. How can you find the lowest common denominator?

Simplify Rational Expressions with Polynomials

Interested in revisiting the basic steps for simplifying rational expressions?

Absolute Value [CC]

What do -5 and +5 have in common?

Translating Phrases to Mathematical Expressions

Math is a language! How can you translate phrases into mathematical expressions?

#### Equations

Simplify Rational Expressions [CC]

How are rational expressions simplified?

Graphing Relations, Domain, and Range

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. (CCSS: HS.F-IF.B.5)

Domain and Range, Part 1 [CC]

What are the important concepts of domain and range?

Domain and Range, Part 2 [CC]

What are the important concepts of domain and range?

Direct and Inverse Variation

Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CCSS: HS.A-CED.A.2)

Direct and Inverse Variation [CC]

Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CCSS: HS.A-CED.A.2)

Exponential Equations

Can you identify the fundamentals of exponential equations?

Exponential Equations

Can you identify the fundamentals of exponential equations?

Solve Equations by Using Proportion

How do you solve equations using proportions?

Solve Systems of Linear Equations by Graphing

How are graphs used to solve systems of linear equations?

Coordinate System [CC]

What is the coordinate system and how are equations represented on graphs?

Solve Radical Equations

How are radical equations solved?

Solve Radical Equations

How are radical equations solved?

Solve Linear Equations with Rational Numbers

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS: HS.A-CED.A.1)

Linear Equations

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS: HS.A-CED.A.1)

Linear Equations

What are the basic principles of linear equations?

Divide Polynomials

What are the steps involved in polynomial division?

Divide Rational Expressions

How is division of rational expressions carried out?

Solve Linear Equations with Variables on Both Sides of the Equation

How can you find the value of variables when they appear on both sides of an equation?

Solve Equations with a Variable on One Side of the Equation

How can you find the value of a variable when it appears on one side of an equation?

Absolute Value

What do -5 and +5 have in common?

Linear Inequalities

How are linear inequalities interpreted?

Literal Equations

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V=IR to highlight resistance R. (CCSS: HS.A-CED.A.4)

Slope-Intercept Form

How are equations written in slope-intercept form?

Equations with Radicals

What role do radicals play within equations?

Solve Linear Systems

What are the most common methods used when solving linear systems?

#### Polynomials

Simplify Rational Expressions

How are rational expressions simplified?

Expand Polynomials

Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CCSS: HS.A-APR.A.1)

Factoring a Monomial from a Polynomial

Is it possible to factor a polynomial to get a monomial?

Factor Polynomials

Factor a quadratic expression to reveal the zeros of the function it defines. (CCSS: HS.A-SSE.B.3.a)

Factor Polynomials (2 Strategies)

What methods can be used to factor polynomials?

Factor and Solve Polynomial Equations

How can polynomials be factored and solved?

Add, Subtract, and Multiply Polynomials

What are the fundamental aspects of polynomial manipulation?

Add and Subtract Polynomials

What are the fundamental aspects of polynomial manipulation?

Polynomial Division

How are polynomials divided?

Multiply Binomials

What are the steps in binomial multiplication?

### Compass Essential Skills: Reading

Vocabulary in Context

A dictionary is not your only source of definitions -- How can you use reasoning to figure out what unfamiliar words mean as you read?

Finding the Main Idea

What strategies can you use to figure out the main idea of a passage?

Drawing Conclusions

Are you sure of that? Draw conclusions and be able to support them.

Author's Purpose

How can you figure out the main purpose of a passage?

Literal Questions

How can you identify these types of questions and make sure that you're responding correctly?

Making Inferences

What makes an inference different from a wild guess?

### Compass Essential Skills: Writing

The Brainfuse Writing Lab Essential Grammar Guide

A Quick Reference for Grammar, Usage, and Mechanics

Writing for the Academic Audience

Why should an audience affect your style of writing?

Audience

Who will read your writing?

Purpose

Why are you writing about that topic?

Formal vs. Informal Style

How can you decide which style to use?

Use Specific Words

How can a word transform the way you see a topic?