Level 6: Systems and polynomials

Algebra · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

In level 5 every equation had one unknown and every expression was a straight line in disguise. This level opens two new doors. The first is polynomials: expressions with \(x^2\), \(x^3\) and beyond, which you learn to multiply with an area picture and then to factor, running the picture backwards. The second is systems: two equations with two unknowns, solved by drawing two lines and finding where they cross, then by substitution and elimination. The level ends by learning to tell straight-line relations from curved ones, which leads into the parabolas of level 7.

Lesson	You will be able to
Exponent laws with variables	Explain and use the laws for \(x^a x^b\), \((x^a)^b\) and \((xy)^n\), and simplify \((2x^3y)^2 \div 4x^2y\)
Polynomials	Name the parts of a polynomial, add and subtract them, and multiply two brackets with an area model
Factoring	Factor common factors, \(x^2 + bx + c\), \(ax^2 + bx + c\), differences of squares and perfect squares, and check by expanding
Linear systems by graphing	Solve two equations by drawing two lines, and explain why there is one solution, none or infinitely many
Linear systems by substitution and elimination	Solve systems exactly with either method, choose the better one, and solve mixture and speed problems
Linear and non-linear relations	Tell linear from non-linear by table, graph and equation, and choose a line or a curve to model real data

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