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Intro To Linear Polynomials

Diagnose readiness and introduce the connection between physical patterns, functions, and straight-line graphs.

4 lessons8 concepts

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Overview

The Matchstick Problem

Hook introducing a visual pattern that requires a generalized formula.

Imagine you are building a growing chain of hexagons using matchsticks.

If it takes 6 matchsticks to make 1 hexagon, 11 matchsticks to make 2 hexagons, and 16 matchsticks to make 3 hexagons... how many matchsticks will you need to build the 100th hexagon?

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Hook

Chapter Overview Visual

Shows the big picture of how real-world sequences translate to algebraic equations.

$rich vibrant illustration, Kurzgesagt-inspired, bold shapes with subtle texturing, saturated but harmonious color palette, strong composition, professional science museum display quality. A sequence of 3 hexagons made of matchsticks transitioning seamlessly into a plotted straight line on a coordinate graph, representing the translation of physical patterns into linear equations.$

Click to zoom

Physical sequences can be modeled as linear equations and graphed as straight lines.

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checklist

I already know...

Checklist of prerequisite skills.

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Before You Start — Check What You Know

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quiz

Prerequisite Check

Diagnostic test on substituting values and solving one-step equations.

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If you start at the origin $(0,0)$ , move 3 units to the right along the x-axis, and 4 units up along the y-axis, what are your new coordinates?

Hint

Concept: prerequisites

Coordinates are always written as $(x, y)$ , where $x$ is the horizontal movement and $y$ is the vertical movement.

Concepts

01. Polynomial Basics

Define algebraic terms, variables, coefficients, and degree of one-variable polynomials.

02. Linear Polynomials And Equations

Define linear polynomials, equate them to constants to form equations, and view them as input-output functions.

03. Linear Patterns

Identify linear relationships in patterns where the difference between consecutive terms is constant.

04. Linear Growth And Decay

Distinguish between linear growth (increasing at constant rate) and linear decay (decreasing at constant rate).

05. Finding Linear Relationships

Formulate a linear relationship y = ax + b from given conditions.

06. Graphing Linear Equations

Plot a linear equation on a coordinate plane by selecting values for x and finding corresponding values for y.

07. Slope, Intercept, And Parallel Lines

Understand the roles of 'a' (slope) and 'b' (y-intercept) in the linear equation y = ax + b, and define parallel lines.

08. Chapter Review

Synthesize chapter concepts, from polynomial vocabulary to formulating and graphing linear relationships.