Discovering Algebra

Learn to convert fractions to decimals by multiplying numerator and denominator to reach a 100 or 10000 denominator, placing the decimal as in 3/4 = 0.75 and 3/16 = 0.1875.

Convert decimals to fractions by writing the decimal as a numerator over a power of ten, then simplify with the greatest common factor; e.g., 0.25 = 25/100 = 1/4.

Explore how to evaluate square roots and interpret the radical symbol, with examples like the square root of 36 is 6, and solving x^2 = 25 yields ±5.

Explore cube roots and their relation to volume, showing how the cube root of 8 equals 2 and how odd and even indices affect the radical.

Explore how to add, subtract, multiply, and divide variable expressions, ensuring like variables, handling coefficients, and combining or simplifying terms such as x, x^2, and xy.

Explore the commutative property of addition and the identity property with zero, showing that order does not affect the sum, unlike subtraction; also review the associative property.

Master the distributive property of multiplication by applying it to a(b + c) = ab + ac and to subtraction, with examples 5(x+2) = 5x+10 and 4(x-4) = 4x-16.

explore the reflexive, symmetric, and transitive properties of equality, showing that a value equals itself, equal quantities swap, and equality transmits through linked values.

Explore the coordinate plane by identifying the x axis, the y axis, and the origin at (0,0), and locate the four quadrants I, II, III, and IV.

Explore plotting ordered pairs on a coordinate plane by starting at the origin, moving along the x and y axes, and graphing examples like (1,2) and (2,-1).

Explore the reflexive, symmetric, and transitive properties of equality with simple examples, showing that a value equals itself and equality is transitive.

Identify linear functions by examining tables for constant changes in x and y; a straight line confirms linearity, while nonconstant y increments indicate nonlinearity.

Learn to find the slope of a line by calculating delta y over delta x, using the example y=2x with points (1,2) and (3,6) to show slope equals 2.

Learn to compute slope from two points by dividing the change in y by the change in x; examples (3,6) and (6,7) yield 1/3, and (-1,4) and (2,6) yield 2/3.

Explore slope-intercept form y = mx + b, where m is the slope and b the y-intercept, and relate x and y with example points, a table, and plotted line.

Find the x- and y-intercepts of a line in standard form by setting y to zero for the x-intercept and x to zero for the y-intercept, as shown with 3x+4y=12.

Learn how to graph horizontal and vertical lines by drawing x=5 and y=2 across the plane, extending into multiple quadrants.

Derive a line's equation from a graph using point-slope form by computing the slope from two points and substituting into y − y1 = m(x − x1).

Learn to factor two-term polynomials by extracting the greatest common factor, applying difference of squares, and factoring sum or difference of cubes using a simple sign guide.

Master factoring three-term trinomials by identifying a perfect square, using the double product check for the middle term, and expressing the result as a binomial square.

Discovering algebra teaches you the short factoring method for trinomials in general form. Find two numbers that multiply to ac and sum to b, then factor into binomials.

Discover how to factor three-term polynomials by grouping: extract a common factor, form matching binomials, and construct a product that yields all terms.

Master the three-term factoring using the easy long method. Apply the AC method and split the middle term, then use grouping to reach a factorized form.