#Prealgebra 1 Skill Set (20-Weeks Scope) Grade 6-8 Foundation

1. Properties of Arithmetic

• Commutative, associative, and distributive properties

• Order of operations (PEMDAS)

• Mental math using arithmetic properties

• Simplifying complex arithmetic expressions

2. Exponents

• Understanding powers and base/exponent notation

• Multiplication/division rules for exponents

• Zero exponent rule

• Negative exponents and their meaning

• Simplifying expressions with exponents

3. Number Theory

• Multiples and factors

• Prime and composite numbers

• Prime factorization

• Fundamental Theorem of Arithmetic

• Least Common Multiple (LCM)

• Greatest Common Divisor (GCD)

• Divisibility rules

4. Fractions

• Simplifying fractions

• Comparing and ordering fractions

• Adding, subtracting, multiplying, dividing fractions and mixed numbers

• Converting between improper fractions and mixed numbers

• Real-world and word problems involving fractions

5. Equations and Inequalities

• Understanding expressions, equations, and inequalities

• Solving one-variable linear equations

• Word problems with linear equations

• Solving and graphing linear inequalities

• Understanding solution sets

6. Decimals

• Place value and decimal notation

• Adding, subtracting, multiplying, dividing decimals

• Rounding and estimating

• Comparing and ordering decimals

• Converting between fractions and decimals

• Understanding rational numbers

7. Ratios, Conversions, and Rates

• Understanding and simplifying ratios

• Solving proportion problems

• Unit rates and conversions (e.g., inches to feet, grams to kilograms)

• Using ratios in word problems (e.g., part-to-whole, part-to-part)

• Speed = Distance ÷ Time problems

• Joint work, relative speed, average speed problems

# Prealgebra 2 Skill Set (20-Weeks Scope)

8. Percents

• Definition of percent

• Converting between percents, fractions, and decimals

• Calculating a percent of a number

• Solving percent increase and decrease problems

• Word problems involving percent change, discounts, markups, and tax

9. Square Roots

• Definition of square root

• Estimating and simplifying square roots (including non-integer roots)

• Arithmetic with square roots

• Solving equations involving square roots

• Using square roots in geometry and problem-solving

10. Angles

• Measuring and identifying types of angles

• Angle relationships with parallel lines (alternate interior, corresponding, etc.)

• Triangle angle sum and angle properties

• Angles in polygons (including quadrilaterals and others)

• Solving angle problems using diagrams and equations

11. Perimeter and Area

• Measuring and calculating segment lengths and perimeters

• Triangle inequality theorem

• Area of various triangles

• Circumference and area of a circle

• Solving problems involving composite or “unusual” areas

12. Right Triangles and Quadrilaterals

• Pythagorean Theorem and its applications

• Pythagorean triples

• Properties of 30-60-90 and 45-45-90 triangles

• Identifying types of quadrilaterals

• Calculating area of quadrilaterals (parallelograms, trapezoids, etc.)

13. Data and Statistics

• Calculating average (mean)

• Understanding average as a balancing point

• Finding median, mode, and range

• Identifying limitations and misleading aspects of basic statistics

• Interpreting and comparing various types of graphs and charts

14. Counting (Intro to Discrete Math)

• Counting elements in lists

• Using Venn diagrams for overlapping sets

• Applying the multiplication principle

• Using systematic casework in counting problems

• Counting ordered and unordered pairs

• Basic probability concepts

15. Problem-Solving Strategies

• Identifying and applying patterns

• Making organized lists

• Drawing diagrams or visual models

• Working backwards to solve problems

• Combining strategies for complex problem-solving

🌟 Algebra Skill Set (22-Week Scope)

Week 1: Follow the Rules

• Order of operations (PEMDAS)

• Substitution and simplification

• Evaluating algebraic expressions

• Intro to algebraic properties (commutative, associative, distributive)

Weeks 2–3: Fractional Exponents, Radicals, and Variables

• Simplifying expressions with fractional exponents

• Understanding radical notation (√) and converting between radicals and exponents

• Multiplying, dividing, and simplifying radicals

• Rationalizing denominators

• Variable expressions involving exponents and radicals

Week 4: Linear Equations

• Solving one-variable linear equations

• Applying inverse operations

• Checking solutions

• Word problems with linear equations

Week 5: More Variables

• Expressions with multiple variables

• Substitution and evaluation

• Introduction to combining like terms

• Distributive property with multiple variables

Week 6: Linear Equations with Multiple Variables

• Solving equations in terms of one variable

• Using substitution and elimination

• Solving systems of equations

• Interpreting solutions graphically and algebraically

Week 7: Ratio and Percent

• Simplifying ratios

• Finding part-to-whole and part-to-part relationships

• Calculating percentages, percent change, and percent error

• Solving real-world percent problems

Week 8: More Ratios and Proportion

• Solving proportions and setting up proportions from word problems

• Using cross-multiplication

• Understanding scale and similar figures

• Working with unit rates and conversions

Week 9: Common Errors and Challenging Problems

• Identifying and correcting common algebra mistakes

• Misuse of negative signs, parentheses, and operations

• Logical problem-solving strategies

• Non-routine word problems

Weeks 10–11: Graphing Lines

• Cartesian plane and coordinate pairs

• Slope (rate of change) and y-intercept

• Slope-intercept and standard forms of linear equations

• Graphing using tables, intercepts, and slope

• Intro to inequalities and their graphs on number lines

Week 12: Graphing Inequalities

• Graphing linear inequalities in one and two variables

• Shading regions and understanding boundary lines

• Systems of inequalities and solution sets

Week 13: Quadratic Equations (Part 1)

• Recognizing quadratic forms

• Solving quadratics by factoring

• Graphing simple quadratic functions

• Applications of quadratic equations

Week 14: Special Factorizations

• Perfect square trinomials

• Difference of squares

• Factoring common patterns

• Recognizing and applying factoring shortcuts

Week 15: Simon’s Favorite Factoring Trick & Complex Numbers

• Factoring techniques for symmetric expressions (Simon's Trick)

• Introduction to imaginary numbers: i=−1i = \sqrt{-1}

• Simplifying complex numbers

• Basic arithmetic with complex numbers

Week 16: Quadratic Equations (Part 2)

• Solving quadratics by completing the square

• Using the quadratic formula

• Discriminant analysis

• Complex roots and their interpretation