Algebra 1 (Semester 1): A High School Curriculum

Master adding and subtracting whole numbers by lining up place values, using carry and borrow steps, and solving varied examples from simple to larger numbers.

Algebra 1 lesson teaches multiplying and dividing whole numbers, urges memorizing the 1–12 multiplication tables for timed tests, and demonstrates long multiplication and division with carrying and remainders.

The number line lesson places zero at the center, with positives to the right and negatives to the left, teaching addition and subtraction through a quick absolute-value trick.

Learn to subtract on the number line by moving left from a starting number, recognizing positive or negative results, and using a trick: add absolute values and keep the sign.

Learn how to subtract negative numbers using a number line, turning subtraction into adding negatives, canceling negatives, and determining whether you move left or right to reach the final value.

apply the same sign rule to multiplication and division: same signs yield positive, opposite signs yield negative; illustrated with negative times negative, and positive divided by negative.

Explore how fractions use numerators and denominators, multiply and divide with keep change flip, and add or subtract with least common denominator, converting improper fractions to mixed numbers or decimals.

Learn to convert mixed numbers to improper fractions and back by applying a simple method: multiply the whole number by the denominator, add the numerator, and keep the denominator.

Learn how decimals express parts of a whole, line up decimal points for addition and subtraction, and multiply, divide, and convert between fractions and decimals across common place values.

Explore how to convert percents to fractions and decimals, reduce fractions, and move the decimal two places, with examples such as 14 percent, 50 percent, and 95 percent.

Describe absolute value as the distance from zero and its positive value, then apply PEMDAS to simplify inside before taking the absolute value in practice problems.

Move the decimal to place a single nonzero digit in front, rewrite as a number in scientific notation with ten to an exponent, and drop trailing zeros.

Master the order of operations using the paradise rule: solve parentheses, exponents, then multiplication and division left to right, followed by addition and subtraction left to right.

Identify variables as symbols representing unknown numbers. Distinguish constants, coefficients, and like terms, and combine like terms by adding their coefficients to simplify expressions.

Differentiate algebraic expressions from equations by identifying the absence of an equals sign. Evaluate expressions by substituting the given values and applying the order of operations to compute results.

Explains what a matrix is as an array of rows and columns, defines dimensions and elements, and demonstrates adding and subtracting matrices with identical dimensions.

Explore scalar multiplication of matrices by distributing a scalar to every element, including fractions, and use it with addition and subtraction across two-by-three and three-by-two matrices.

Explore real-world applications of matrices by analyzing order data, hours worked, pay, class popularity, and furniture sales, using row–column intersections and totals.

Explore the associative property in addition and multiplication, showing that changing parentheses does not change the result. See correct examples, identify non-examples, and distinguish from mixed operations.

Explore the commutative property, which lets you reorder numbers in addition and multiplication without changing the result, as shown by examples like 7+3+9 = 7+9+3 and 12×4×3 = 12×3×4.

Explore additive and multiplicative identities and inverses, showing how adding zero or multiplying by one leaves numbers unchanged, and how additive and multiplicative inverses reach zero or one.

Explore zero properties, including the multiplicative property of zero where any number times zero equals zero, and the zero exponent property where anything to the zero power equals one.

Learn to solve equations with addition and subtraction by applying the additive inverse to both sides, enabling solving for variables like x and smiley face in balanced steps.

Learn to solve equations with multiplication and division using the multiplicative inverse, including fractions and coefficients, to isolate variables like x, y, k, z, and age.

Learn to solve two-step equations by undoing addition and multiplication using additive and multiplicative inverses. Work through order of operations with examples like 3y+8=17 and y/8−3=7.

Apply the distributive property to distribute the outside factor to each term in parentheses. Then solve for the variable and verify the solution.

Multiply by the least common denominator to clear fractions and decimals, solving for variables such as z, k, m, x, and h in fraction and decimal equations.

Learn to express ratios in words, with colons, or as fractions, and recognize that order matters when comparing groups, applying ratio reasoning to totals, reductions, and equivalent ratios.

Study proportions as two equivalent ratios expressed as fractions and learn to cross-multiply to solve for missing values. Apply this to word problems with units, converting between fractions and decimals as needed.

Learn to solve percent proportion problems by using the equation percent over 100 equals part over whole and cross multiplication, with examples like 20% of 17 and 9% of 30.

Explore direct and inverse variation, showing how variables increase together or oppose each other using distance, rate, time, area, and reciprocal relationships.

Learn how to find the perimeter of squares, rectangles, and triangles using addition or formulas, with distance units like inches, feet, meters, and miles.

Explore area calculations for squares, rectangles, and triangles, using side squared, length times width, and base times height, with square unit measurements.

Apply the simple interest formula I = PRT to calculate interest from principal, rate (as decimal), and time (in years), with borrowing and investing examples.

Convert Celsius and Fahrenheit using F = 9/5 C + 32 and C = 5/9 (F - 32). Use 0 C = 32 F and 100 C = 212 F.

Apply the distance rate time formula d = r × t to compute distance from speed and time, with examples of 225 miles and 10.4 meters.

Learn to rearrange formulas by solving for a target variable using the additive inverse and the multiplicative inverse, including triangle perimeter, rectangle area, and height, length, and width calculations.

Discover how the percent equation compares to the percent proportion, using decimals to solve for the part, whole, or percent with 'of' to separate terms.

Explore the four measures of central tendency: mean, median, mode, and range, and learn how to calculate them from data sets, including even-sized samples and negative values.

Learn how to construct and interpret box-and-whisker plots by sorting data, finding the median, determining lower and upper halves, and identifying quartiles and the interquartile range.

Analyze box-and-whisker plots to infer medians, Q1 and Q3, and interquartile range; compute percentages above 63, and compare two plots for grades and wages data.

Explore theoretical probability, sample spaces, and calculating likelihoods using coins, dice, and spinners with fractions, decimals, and percent representations.

Compare theoretical probability with experimental probability using coins, dice, and spinners; calculate sample space and event probabilities like tails, 5 or 6, and red, and observe real outcomes.

Explain how odds form a ratio of the event occurring to the event not occurring, distinguishing them from probability with coin, die, and sample space examples.