Math Fundamentals Masterclass - Build a Solid Foundation

Discover how multiplication expresses repeated addition, with the multiplier indicating repeats and the product arising from two factors. Note symbols like x, dot, and parentheses and the zero property.

Practice long multiplication of a one-digit number by multi-digit numbers, lining up digits by place value, carrying when necessary, and combining partial products to find the final result.

Line up the two numbers, multiply each bottom digit by the top number to form results, shift for place value, and add the results.

Learn how to multiply numbers ending with zeros by ignoring trailing zeros, multiplying the nonzero parts, and reapplying zeros, with cautions about internal zeros and using long multiplication when needed.

Explore the commutative, associative, and distributive properties of multiplication and the multiplicative identity, with examples like five times eight equals eight times five and two times (three plus four).

Understand division as the opposite of multiplication using repeated subtraction, and learn dividend, divisor, quotient, including zero cases: zero divided by nonzero is zero; nonzero divided by zero is undefined.

Master long division by solving left-to-right, digit-by-digit problems, breaking the process into divide, multiply, subtract, remainder, and bring down steps with examples like 976 by 4.

Explore long division with two-digit divisors through examples like 1620 by 12 and 214 by 91, detailing grouping, multiplication, subtraction, and estimation.

Explore division with a remainder using long division, learn to find the quotient and remainder, and read results as 'quotient with remainder'.

Learn to multiply and divide signed numbers with the rules: same signs yield positive; different signs yield negative; even negatives give positive, odd negatives give negative.

Apply the order of operations: exponent and roots first, then multiplication and division left-to-right, then addition and subtraction left-to-right, using grouping symbols such as parentheses, brackets, and division bars.

Explore divisibility rules for numbers 2 through 10 and learn to determine divisibility using last-digit tests, digit-sum checks, and end-with-zero criteria.

Explore multiples and factors: multiples are the results of multiplying a number, and factors are numbers that divide another number with no remainder, illustrated with 2, 4, 8, and 24.

Distinguish prime and composite numbers by examining their factors in natural numbers, with examples like 7, 8, 39, and 47, and understand why 2 is the only even prime.

Explore prime factorization by breaking numbers into prime factors through division from two, using examples like twelve and fifty to express results with exponents.

Learn how to find the least common multiple for two or more numbers by listing multiples, starting with the greatest number, and by using the prime factorization method.

Discover methods to find the greatest common factor, compare factors of numbers, and use prime factorization to identify the gcf for two or more numbers.

Understand fractions as parts of a whole through visual circle and rectangle examples. See how shaded parts express fractions like one over two, three over four, and five over eight.

Learn how to simplify fractions by dividing numerator and denominator by common factors, using prime factorization, and canceling shared factors to reach the simplest form.

Master how to compare fractions, using same-denominator rules, cross-multiplication for different denominators, and simplifying results to show equality or superiority.

Explore equivalent fractions and learn to create them by multiplying numerator and denominator by the same number, with cross multiplication and simplifying via prime factorization.

Learn to multiply fractions by multiplying numerators and denominators, reduce to lowest terms, and extend to multiple fractions; then divide fractions by using reciprocals and converting division to multiplication.

Learn to add and subtract fractions by using common denominators or the least common multiple, adjust numerators, and simplify to lowest terms.

Learn to simplify complex fractions by converting them to simple fractions using reciprocal multiplication, with worked examples such as three fifths over one third and four ninths over five.

Explore the three types of fractions: proper, unit, and improper—and how the numerator and denominator determine values; learn about like and unlike fractions and zero numerator or undefined denominator.

Discover how mixed numbers express shaded circle parts, convert between improper fractions and mixed numbers, and see how a whole plus a proper fraction forms a mixed number.

Learn to convert between mixed numbers and improper fractions with a fixed denominator. Multiply the whole number by the denominator, add the numerator, and use long division for mixed numbers.

Learn to add and subtract mixed numbers by rewriting as whole numbers plus fractions, using the least common multiple for common denominators, and converting results between mixed and improper fractions.

Convert mixed numbers to improper fractions, multiply across, then convert the result back to a mixed number using long division; learn division by flipping the second fraction.

Explore decimals and place values, learning how digits after the decimal point represent tenths, hundredths, and thousandths, and how decimals express parts of a whole using the decimal point.

Distinguish like decimals from unlike decimals by decimal digits; convert unlike decimals to like decimals; and understand equivalent decimals and that zeros after the last digit do not change value.

Learn to add and subtract decimals by aligning decimal points, stacking numbers, and applying carry and borrow rules through example problems.

Explore how decimals relate to fractions, convert between mixed numbers and improper fractions, and master moving the decimal point when dividing by ten, hundred, or thousand.

Learn to multiply decimals by turning them into whole numbers with tenfold shifts, multiply, then reinsert the decimal; master dividing decimals via long division and by converting to whole numbers.

Convert fractions to decimals using long division; treat fractions as division, then multiply the numerator by ten (eventually by 100 or 1000) and move the decimal point.

Identify the difference between pure numbers and denominate numbers with units. Compare like denominate numbers by subtraction and unlike denominate numbers by division, with unit cancellation rules.

Explore ratios and proportions, recognizing equivalent two to three relationships and simplify with the greatest common factor to lowest terms, including part-to-part and part-to-whole ratios.

Learn to identify and test proportions by confirming equal ratios through cross multiplication, and solve for unknowns in proportional problems using real examples.

Master ratios, rates, and proportions by comparing like vs. unlike denominators, reading them as fractions, reducing them, and recognizing equivalent expressions.

Explore real-world applications of proportions by solving cross-multiplication problems involving map scales, solution ratios, shadow lengths, and population ratios.

Explore ratios and proportions, understand extremes and means, and master percent as a ratio out of one hundred with practical examples.

Convert fractions to percentages using a denominator of 100 and cross-multiplication, then convert percentages back to fractions and decimals, including fractions of a percent.

Explore practical percentage problems, learn to compute percent of numbers using fractions, ten percent breakdowns, and step-by-step methods for discounts, commissions, and salary changes.

Learn to find what percent a number is of another using the formula percent = (part/whole) times 100, with examples like 15 is 30 percent of 50.

Explore solving various percent problems by converting percentages to fractions, solving for the unknown X, and applying percent concepts to discounts, taxes, and original versus final prices.

Solve percent problems by finding X when 30 percent of X is 225 and compute 76 percent of X, with applications to salary increases and compound interest.

Explore how percent decreases and increases work with real examples, showing why a 20% cut followed by a 25% rise on the new salary returns to the original amount.

Explore exponents and exponential notation, learn how the base and exponent describe repeated multiplication, and read examples like three to the fourth power and seven squared.

Explore how exponents behave with different bases, including ten, one, negative numbers, zero, and fractions; learn how even or odd exponents affect signs and how (a/b)^n equals a^n/b^n.

examine how exponents with various bases work, including exponent one where the result equals the base, and exponent zero where non-zero numbers equal one; zero to zero is undefined.

Explore negative exponents and the reciprocal pattern a^(-n) = 1 / a^n, including signs for negative bases and odd/even cases.

Master the multiplication rule for exponents: when bases match, add the exponents (including zero and negative), and convert to a common base when bases differ, with practical examples.

Learn to divide exponents with the same base by subtracting exponents: a^m/a^n = a^(m-n). Convert negative powers to reciprocals and work through examples, including zero-to-zero undefined cases.

Explore the power rule of exponents, show (a^m)^n = a^(m*n), handle negative exponents by flipping the base, and confirm that any number to the zero is one.

Learn the exponent rule for same powers: when bases are equal, add the exponents; when the powers are equal, multiply the bases and raise to that common power.

Explore dividing exponential expressions with the same power and different bases by dividing the bases and raising the result to that power, illustrated with 10^2/5^2 and similar examples.

Review exponent rules and apply the product, quotient, zero, power, expanded power, and negative power rules to simplify expressions and practice exponent problems.

Explore solving exponent expressions by factoring numbers into prime factors and applying the expanded power rule with product and quotient rules to simplify complex expressions.

Explore how square roots yield two values for positive numbers, the principal and secondary square roots, and how to use radicals with examples like 9, 16, and 25.

Learn to find square roots using prime factorization by breaking numbers into primes and multiplying one factor from each pair.

Explore cube roots as the single-valued counterpart to square roots, using the index notation to find numbers whose cubes equal a given value, including negative cases and perfect cubes.

Learn to compute square, cube, and higher roots with radical signs and indices, and distinguish that even indices yield two real roots while odd indices yield one real root.

Explore how to simplify square roots using exponent rules, cancel out powers with radicals, and divide exponents by the root index to convert between radical and exponential forms.

Convert fractional exponents to radical form to simplify expressions using the cube root and the power rule, and apply the power expanded property to combine exponents.

Learn to simplify radicals and surds by factoring into perfect squares or cubes, pulling out outside roots and keeping the rest inside, with examples like sqrt 12.

Learn to add and subtract surds by grouping like surds with the same index and radical end, then simplify by factoring out square roots and combining like terms.

Learn to multiply and divide surds, simplify by combining outside and inside radical parts, and apply index rules to produce simplified roots with clear examples.

Rationalize the denominator by multiplying by the same radical over itself to convert an irrational denominator into a rational number, with examples using square, cube, and higher roots.

Explore radicals through general examples: simplify square roots by factoring into perfect squares, rationalize ninth roots, and combine like radicals to add expressions.

Learn how to find the mean, or average, by adding numbers and dividing by how many numbers there are, illustrated with examples including negative values.

Learn to find the median by arranging data and selecting middle value, or averaging two middle values for even sets, especially when data contain outliers rather than the mean.