Grade 8 · printable course

Pre-Algebra: Foundations for Algebra I

Grade 8 · 456 pages · 83 lessons · PDF, print at home

A full-year grade 8 mathematics course aligned to CCSS that transitions students from proportional reasoning to the algebra of linear relationships. Students formalize exponent rules and scientific notation, extend the number system to include irrational numbers, and establish the Pythagorean theorem with proof and application. The course builds functions as a unifying concept, contrasts linear and nonlinear relationships, and culminates in systems of linear equations and bivariate statistical reasoning. Geometric transformations ground congruence and similarity in precise, testable definitions rather than visual intuition. The course hands off directly into Algebra I.

Delivered by email within minutes as a PDF stamped with your name. Print any part as often as you need for the children in your household; the link never expires.

$27.99

one household licence

Want every Grade 8 subject at once? Letters & Devotion Grade 8: The Complete Year is one PDF for $79.99.

What is inside

Every unit and lesson in this book, in order. The same lessons are taught online at lettersanddevotion.com, so a family can move between paper and screen.

Pre-Algebra: Foundations for Algebra I

83 lessons · try a lesson online free

Unit 1: Exponents, Powers, and Scientific Notation9 lessons
  1. 1.Positive integer exponent notation (base, exponent, power)
  2. 2.Laws of exponents (product, quotient, power-of-a-power rules)
  3. 3.Conditions under which the product-of-powers and quotient-of-powers rules apply
  4. 4.The zero and negative exponent extension of the integer exponent pattern
  5. 5.Scientific notation as a decimal times a power of 10
  6. 6.Arithmetic operations on numbers in scientific notation
  7. 7.Order-of-magnitude comparison of quantities in scientific notation
  8. 8.The logical necessity of the zero/negative exponent extension across all nonzero bases
  9. 9.Common exponent-rule errors embedded in a worked solution
Unit 2: The Real Number System9 lessons
  1. 10.Perfect squares up to 225 and their square roots
  2. 11.Square root and cube root notation applied to perfect squares/cubes
  3. 12.The irrationality of square roots of non-perfect squares
  4. 13.The rational/irrational classification of numbers presented in varied forms
  5. 14.Tenths-level estimation of irrational square roots using bounding perfect squares
  6. 15.Justified placement of irrational numbers on a number line
  7. 16.Ordering of mixed rational and irrational numbers
  8. 17.The rational/irrational status of a genuinely novel numeric claim
  9. 18.The limits of a finite decimal display as evidence of rationality
Unit 3: Linear Equations in One Variable10 lessons
  1. 19.One- and two-step linear equations in one variable
  2. 20.Distribution and combining like terms in multi-step equations
  3. 21.Equations with variables on both sides
  4. 22.The no-solution case as a logical outcome of equation-solving
  5. 23.The three solution-count cases (one, none, infinite) for linear equations
  6. 24.The invariant structure underlying the no-solution case across different-looking equations
  7. 25.Real-world contexts modeled by one-variable linear equations
  8. 26.Solution-count reasoning applied to a novel geometric/measurement context
  9. 27.Structural cues (coefficient and constant relationships) that determine solution count
  10. 28.Like terms in an algebraic expression
Unit 4: Functions8 lessons
  1. 29.The definition of function as one output per input
  2. 30.The vertical line test as a graphical criterion for the function definition
  3. 31.Equivalence of a function across table and graph representations
  4. 32.Rate of change as a constant difference indicating a linear function
  5. 33.Rate of change and initial value as representation-independent quantities usable for comparison
  6. 34.Construction of a function rule from an unstructured verbal description, including a non-constant rate case
  7. 35.The distinction between co-variation and a valid function rule
  8. 36.Linear versus nonlinear classification using rate-of-change evidence
Unit 5: Transformations, Congruence, Similarity, and the Pythagorean Theorem12 lessons
  1. 37.Translations described by coordinate rules, e.g. (x,y) -> (x+3, y-2)
  2. 38.Coordinate rules for reflections over axes and other lines
  3. 39.The distinction between rigid motions and dilations with respect to distance and angle preservation
  4. 40.Congruence as the existence of a rigid-motion sequence between two figures
  5. 41.Similarity as a rigid-motion sequence plus one dilation, with scale factor unknown at the outset
  6. 42.Angle pair relationships formed by a transversal crossing parallel lines
  7. 43.The triangle angle-sum theorem, justified via parallel-line angle relationships
  8. 44.An informal proof of the Pythagorean theorem based on area conservation
  9. 45.Unknown side lengths of right triangles in applied problems (ladders, screens, ramps)
  10. 46.The converse of the Pythagorean theorem as a test for a right angle
  11. 47.Distance between two coordinate points via a constructed right triangle
  12. 48.Selecting and combining transformation reasoning and the Pythagorean theorem in an unfamiliar applied context
Unit 6: Linear Relationships: Slope, Proportionality, and Systems13 lessons
  1. 49.Similar-triangle justification for constant slope on a non-vertical line
  2. 50.The slope formula (y2-y1)/(x2-x1) applied to two coordinate points
  3. 51.Proportional relationships graphed as lines through the origin, with slope equal to unit rate
  4. 52.Unit rate comparison across mixed representations of proportional relationships
  5. 53.Slope-intercept form as a graphing and interpreting tool
  6. 54.The origin test distinguishing proportional from non-proportional linear relationships
  7. 55.The intersection point of two graphed lines as the system's solution
  8. 56.The meaning of an intersection point as a shared input-output pair in a modeled context
  9. 57.The substitution method for solving a 2x2 linear system
  10. 58.Strategic variable selection prior to substitution
  11. 59.The one/none/infinite solution cases for a linear system, linked to identity and contradiction equations
  12. 60.System-of-equations modeling of a scenario from an unpracticed domain
  13. 61.Structural reasoning about simultaneous intersection using slope and intercept comparisons rather than computation
Unit 7: Systems of Linear Equations: Modeling and Application10 lessons
  1. 62.The solution of a system as a point satisfying both equations simultaneously
  2. 63.The intersection point of two graphed lines as the system's solution
  3. 64.The substitution method for solving systems
  4. 65.The relative efficiency of graphing versus substitution as solution methods
  5. 66.Translation of a two-constraint real-world context into a system of equations
  6. 67.The real-world meaning of a system's solution point
  7. 68.The relationship between slope/intercept comparison and the number of solutions of a system
  8. 69.The real-world meaning of no-solution and infinite-solution systems
  9. 70.The full modeling cycle from context to justified system solution
  10. 71.The no-solution condition extended to standard-form equations
Unit 8: Bivariate Data and Lines of Fit12 lessons
  1. 72.Patterns of association in scatter plots (positive, negative, none)
  2. 73.Linear vs. nonlinear association, clusters, and outliers in bivariate data
  3. 74.Informal line of fit placement
  4. 75.Criteria for judging quality of a line of fit
  5. 76.Slope-intercept equation of a fitted line
  6. 77.Contextual meaning of slope and intercept in a bivariate data model
  7. 78.Interpolation using a line of fit, and reasonableness of prediction
  8. 79.Two-way tables and relative frequency for categorical bivariate data
  9. 80.Association between categorical variables via relative frequency comparison
  10. 81.Complete line-of-fit modeling process applied to a novel dataset
  11. 82.Evaluation of another student's line-of-fit reasoning against data evidence
  12. 83.The distinction between a statistical trend and an exact linear rule

More for Grade 8

Everything for Grade 8 · All printable books