Algebra Fundamentals
Visual Algebra
Shape patterns that grow step by step, and the expressions that describe them: linear, quadratic, exponential, periodic and alternating patterns, and the different ways to see one pattern.
THE SYLLABUS
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Building Patterns
A pattern that adds the same piece at every step grows by the same amount each time: with a 6-cube heart the steps hold 6, 12, 18, 24 cubes.
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Pattern Rules
A pattern's rule says what is added at each step: add 5 cubes to the previous shape, so 10, 15, 20, 25 and the 10th step has 55.
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Linear Patterns
A linear pattern grows by the same amount at each step: a marquee that gains a zigzag of 8 lights per step holds 8, 16, 24, 32 lights, so step 30 holds 30 × 8 = 240.
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Growing Patterns
A pattern can grow in several places at once: a sun whose 12 rays each gain one square per step grows by 12 every step, so step 25 holds 25 × 12 = 300 squares.
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Level Check
Fifteen questions on Level 1: the next step of a pattern, what each step adds, steps far along, and five look-back questions that evaluate an expression.
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