Bridge to Algebra 1

Pre-Algebra · Axiom Academy

A preview of coming attractions: watch each pre-algebra idea you already know grow into the Algebra 1 tool it becomes. In pre-algebra you solved equations like x + 5 = 12 by keeping a scale balanced — do the same thing to both sides until x stands alone. Algebra 1 keeps that exact rule , but now the unknown can appear on both sides : 3x + 5 = 2x + 9 . The animation grows the simple equation into the harder one, then balances it. 2. From Ratio Tables to Functions You filled in ratio tables — months across the top, cost underneath — and spotted the constant rate. Algebra 1 turns that rule into a function , a machine you feed an input x to get an output f(x) . Watch a phone-plan table become the line f(x) = 5x + 20 , then compare two plans and read the break-even straight off the graph. Pre-algebra: a constant rate in a ratio table Algebra 1: the same rule, written as a function Build a ratio table for one plan. Read off the rate. Answer one question at a time. Model both plans as f(x) and g(x) , graph them, and find exactly where they cross — Plan A and Plan B both cost 40 at 4 months . 3. When the Line Bends: Parabolas Every graph you drew in pre-algebra was a straight line . Algebra 1 adds one new ingredient — an x^2 term — and the line curves into a parabola . The animation starts at the line y = 4x and bends it, as -x^2 turns on, into f(x) = -x^2 + 4x — revealing a highest point (the vertex ) and the spots where it crosses the axis (the roots ).

This is the written version of the interactive lesson above. See the full Pre-Algebra course.