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Mathematics 8

Build algebra readiness through real numbers, slope, linear equations, functions, the Pythagorean theorem, geometric transformations, data analysis, and personal financial literacy. TEKS §111.28 aligned.

14 Units

30-45 minutes per unit

What You Will Learn

Linear Relationships

Master slope, y = mx + b, systems of equations, and function concepts — the core of algebraic thinking.

Pythagorean Theorem & Geometry

Prove and apply the Pythagorean theorem. Explore transformations, volume, and coordinate geometry.

TEKS §111.28 Aligned

Covers Texas Essential Knowledge and Skills for Grade 8 Mathematics.

All Units

The Real Number System

Explore the full real number system — rational and irrational numbers — and learn how to locate and approximate irrational numbers on the number line.

•Distinguish between rational and irrational numbers using decimal expansions
•Classify real numbers within the nested hierarchy of the number system
•Approximate irrational numbers to the nearest tenth and hundredth
+1 more objectives

Scientific Notation

Master scientific notation to express, compare, and compute with very large and very small numbers used across science and engineering.

•Convert numbers between standard form and scientific notation
•Compare and order numbers written in scientific notation
•Perform multiplication and division with numbers in scientific notation
+1 more objectives

Proportional Relationships

Deepen your understanding of proportional relationships by identifying the constant of proportionality and representing these relationships in multiple ways.

•Identify the constant of proportionality in tables, graphs, equations, and verbal descriptions
•Write equations of the form y = kx to represent proportional relationships
•Distinguish proportional from non-proportional relationships
+1 more objectives

Slope and Rate of Change

Develop a deep understanding of slope as a rate of change, calculate slope from graphs, tables, and equations, and connect slope to real-world contexts.

•Calculate slope using the slope formula from two points
•Interpret slope as a unit rate and rate of change in context
•Identify slope from graphs, tables, and equations in slope-intercept form
+1 more objectives

Linear Relationships and Equations

Explore linear relationships in all their forms — slope-intercept, proportional, and non-proportional — and connect equations, graphs, and tables.

•Write linear equations in slope-intercept form y = mx + b
•Graph linear equations using slope and y-intercept
•Distinguish between proportional (y = mx) and non-proportional (y = mx + b) linear relationships
+1 more objectives

Writing and Solving Equations

Write and solve multi-step linear equations with rational coefficients, including equations that require combining like terms and applying the distributive property.

•Write equations to represent real-world and mathematical situations
•Solve multi-step equations using properties of equality
•Solve equations with rational coefficients and variables on both sides
+1 more objectives

Systems of Equations: An Introduction

Introduce simultaneous equations and explore graphical and substitution methods to find the solution to a system of two linear equations.

•Identify the solution to a system of linear equations as the point of intersection on a graph
•Solve systems of equations using graphing
•Solve systems of equations using substitution
+1 more objectives

Introduction to Functions

Understand the function concept, identify functions from multiple representations, and distinguish linear from non-linear functions.

•Define a function and identify functions from tables, graphs, and mapping diagrams
•Apply the vertical line test to determine if a graph represents a function
•Identify the domain and range of a function
+1 more objectives

The Pythagorean Theorem

Prove and apply the Pythagorean theorem to find unknown side lengths, determine distances on the coordinate plane, and classify triangles.

•State and apply the Pythagorean theorem to find unknown side lengths in right triangles
•Identify Pythagorean triples and use them to recognize right triangles
•Calculate the distance between two points on the coordinate plane
+1 more objectives

Volume of Cylinders, Cones, and Spheres

Derive and apply volume formulas for cylinders, cones, and spheres to solve real-world problems involving three-dimensional shapes.

•Apply the formula V = πr²h to find the volume of cylinders
•Apply the formula V = (1/3)πr²h to find the volume of cones
•Apply the formula V = (4/3)πr³ to find the volume of spheres
+1 more objectives

Transformations on the Coordinate Plane

Explore translations, reflections, rotations, and dilations on the coordinate plane, and classify figures as congruent or similar based on the transformation applied.

•Perform translations, reflections, and rotations and identify coordinates of image points
•Perform dilations from the origin and calculate scale factors
•Distinguish between transformations that produce congruent figures and those that produce similar figures
+1 more objectives

Scatterplots and Data Trends

Construct and interpret scatterplots, draw trend lines, assess the strength and direction of associations, and use linear models to make predictions.

•Construct a scatterplot and describe the association between two quantitative variables
•Draw and write an equation for a trend line (line of best fit)
•Use a trend line equation to make predictions and evaluate their reasonableness
+1 more objectives

Personal Financial Literacy

Apply mathematical reasoning to personal financial decisions, including calculating simple and compound interest, understanding the cost of credit, and comparing loan options.

•Calculate simple interest using I = Prt and solve for any missing variable
•Calculate compound interest and explain why it grows faster than simple interest
•Identify and calculate the total cost of credit including fees and interest
+1 more objectives

Algebra Readiness Capstone

Synthesize the major strands of 8th grade mathematics — number systems, linear relationships, geometry, and data — through integrated, multi-step problem solving that builds readiness for high school algebra.

•Connect linear equations, slope, and functions across representations (graph, table, equation, context)
•Apply proportional reasoning and the Pythagorean theorem in multi-step geometric contexts
•Interpret and use scatterplot trend lines alongside algebraic models
+1 more objectives

Grade 8 Mathematics. Designed for Texas homeschool families. TEKS §111.28 aligned.