Pre-Algebra: A Complete Middle School/High School Curriculum

Improve place-value skills to add and subtract whole numbers by aligning digits, and applying carry and borrow across ones, tens, hundreds, and thousands in multi-digit problems.

Memorize the 1–12 multiplication tables with flashcards to speed timed tests, then master long multiplication and long division of whole numbers using the four-step process: divide, multiply, subtract, bring down.

Explore the number line to add and subtract, starting at a given number, moving right for positives and left for negatives, and mastering a quick positive-negative subtraction trick.

Explore subtracting on the number line by starting at a number and moving left, producing positive or negative results, with quick tricks for adding when starting negative.

Learn how subtracting negative numbers works using a number line. Recognize that two negatives cancel to a positive and subtraction becomes adding a negative, then solve mixed sign problems.

Learn the same-sign rule for multiplying and dividing negative numbers, where same signs yield positive results and opposite signs yield negative results, illustrated with long division examples.

Explore fractions as parts of a whole; identify numerators and denominators from shaded figures. Learn to find and reduce equivalent fractions with common factors, including 2/4 = 1/2.

Master common denominators to add and subtract fractions using the least common multiple and equivalent fractions. Apply these methods to example problems like 1/2 plus 3/4 and 3/8 plus 1/4.

Learn to solve fraction word problems by finding a common denominator using the least common multiple, converting to equivalent fractions, and performing addition or subtraction.

Multiply fractions by multiplying numerators and denominators; you don't need a common denominator for multiplication, and always reduce when possible; use cross-reducing before multiplying to simplify.

Explains dividing fractions with keep-change-flip, turning division into multiplication, flipping the second fraction, and calculating with examples like 3/5 ÷ 2/3 = 9/10 and 5/11 ÷ 4/10 = 25/22.

Practice multiplying and dividing fraction word problems, including one third and four thirds, adding fractions, and sharing a pizza among four people using keep change flip and cross reduction.

Identify numerator and denominator, multiply numerators and denominators, apply keep-change-flip for division, convert improper fractions to mixed numbers or decimals, and use the least common denominator for addition or subtraction.

Convert mixed numbers to improper fractions by multiplying the whole number by the denominator and adding the numerator, then convert back using long division to obtain the mixed number.

Master decimals through place value, aligning decimal points in addition and subtraction, and learn multiplication, division, and converting between fractions and decimals with real-world examples.

Convert percents to fractions or decimals by placing over 100 and moving the decimal two places; apply these concepts to the simple interest formula.

Explore exponents and powers by identifying the base and exponent, using examples like three squared equals nine and four to the third power equals 64.

Learn scientific notation by moving the decimal to place a single digit in front, then multiply by ten to an exponent, using earth-sun distance and tiny bacteria examples.

Learn the order of operations from parentheses to exponents, then multiplication and division left to right, and finally addition and subtraction left to right.

Define variable as a symbol representing an unknown number. Identify coefficients as the numbers multiplying variables, and teach combining like terms with the same variable by adding coefficients.

Distinguish algebraic expressions from equations by checking for an equal sign and identify which are expressions. Evaluate expressions by substituting values for variables and applying the order of operations.

Absolute value measures distance from zero and is always nonnegative. Use the order of operations inside the absolute value, then evaluate, with practice problems involving integers, fractions, and exponents.

Learn the basics of matrices, including rows, columns, and dimensions, and practice adding and subtracting same-dimension matrices with step-by-step examples.

Explore scalar multiplication of matrices by any scalar, distributing across all elements, with examples using 5A, 3B, 1/2C, and 1/5D, and combine with matrix addition and subtraction.

Explore real-world matrices by analyzing shirt orders, hours worked, pay calculations, class popularity, and product sales to extract totals, intersections, and 30 percent projections.

Discover the associative property for addition and multiplication, where changing parentheses keeps the result unchanged. Identify valid examples and note that mixing operations breaks the property.

Explains the commutative property for addition and multiplication, showing that changing the order of numbers or variables leaves the result unchanged, with examples such as 4+6+g and 12×4×3.

Explore the distributive property, showing how multiplication distributes over addition or subtraction with numerical and variable examples, and identify valid versus invalid applications.

Explore the identity and inverse properties in algebra, including additive identity (a+0=a) and multiplicative identity (a×1=a). Learn additive inverses (a+(-a)=0) and multiplicative inverses (a×(1/a)=1) with examples.

Explore the multiplicative property of zero, where any number times zero is zero, and distinguish it from the zero exponent property, where any number raised to zero power equals one.

Solve equations by using the additive inverse to isolate the variable, balance both sides, and solve for variables such as x and a smiley face.

Apply multiplication and division to solve equations by using the multiplicative inverse (reciprocal) to isolate variables such as m, x, y, k, and z.

Master solving two-step equations by undoing addition and multiplication, applying additive and multiplicative inverses, and practicing with y, x, and k under the order of operations.

Distribute the outside number across parentheses to solve for the variable, then check your solution. Apply this to x, h, n, and g with examples 4(x+2)=-12, 3(h-7)+2=-1, -6n+25=-29, and -5(g+8)+3g=-60.

Solve equations with variables on both sides using additive inverses, distributive property, and combining like terms. Practice verifying solutions by checking both sides for accuracy.

Clear fractions by multiplying through with the least common denominator, scale decimals to whole numbers, and isolate the variable to solve fraction and decimal equations.

Explore how ratios compare quantities using to, colon, and fractions, noting that order matters; practice reducing and finding equivalent ratios with grouping problems and real-world examples.

Explore rates as a ratio of two different units described with fractions. Convert to unit rates by using a denominator of one, with examples like 50 miles per hour and 7 grams per cup.

Learn how proportions link two equivalent ratios, apply cross-multiplication to solve for missing values, and tackle proportion word problems with careful unit alignment.

Use the percent proportion to relate percent, part, and whole, then apply cross-multiplication to find unknown values. Practice includes 20% of 17 and 9% of 30.

Learn direct and inverse variation and how variables relate as they change, including directly proportional relationships like distance equals rate times time. Explore area and width relationships in proportional terms.

Explore how to find the perimeter of squares, rectangles, and triangles by adding sides or using formulas, with units like inches, feet, and meters.

Explore area calculations for squares, rectangles, and triangles, using side squared, length times width, and one-half base times height, with real-life unit examples in square millimeters, square meters, and more.

Learn the simple interest formula i = p r t, with principal, decimal rate, time in years, see borrowing and investing examples of 1000 at 6% for 5 years.

Explore Celsius and Fahrenheit as distinct temperature scales, learn how to convert between them using the proper formulas, and apply reference values like freezing at 0/32 and boiling at 100/212.

Apply the distance–rate–time formula d = r t to solve problems, using a car’s 225 miles at 45 mph and a paper airplane’s 10.4 meters in 8 seconds.

Rearrange the perimeter and area equations to isolate a target variable, solving for side two in a triangle and for length, width, or height in rectangle problems.

apply the percent equation, where percent times the whole equals the part. convert percent to decimal, and solve for the part or whole by multiplication or division.