FAST Math Grade 8 study plan
FAST Math Grade 8 · Give each week a clear focus.
8 weeks · About 6 hours per week
Expressions, Equations and Inequalities (linear relationships, systems, radicals)
Solve multi-step linear equations in one variable, including equations with rational coefficients and variables on both sides, and classify each as identity, conditional, or contradiction.
Rearrange literal equations and formulas (for example, solving for a base, a rate, or a radius) by isolating any specified variable.
Solve and graph two-step and multi-step linear inequalities, correctly reversing the inequality symbol when multiplying or dividing by a negative number.
Translate word problems into a single equation or inequality and check the solution against the original context.
Your checkpoint
A timed 20-question mixed set covering equations and inequalities, scored and corrected, with a one-page error log naming the specific mistake type for each missed item.
Expressions, Equations and Inequalities (linear relationships, systems, radicals)
Solve systems of two linear equations by graphing, substitution, and elimination, and choose the most efficient method for a given system.
Classify systems as having one solution, no solution, or infinitely many solutions from their equations and from their graphs.
Write a system of equations to model a real-world situation and interpret the solution in context.
Simplify radical expressions and estimate irrational square roots to the nearest tenth without a calculator.
Your checkpoint
A set of five real-world system-of-equations word problems solved, graphed, and explained in writing, with the solution verified by two different methods.
Functions (defining, comparing and modeling linear and nonlinear functions)
Determine whether a relation given as a table, graph, ordered pairs, or verbal rule is a function, and justify the decision using the definition of function.
Identify domain and range from graphs and tables, including continuous versus discrete contexts.
Evaluate functions in function notation and interpret what f(x) represents in a real situation.
Write a linear function rule from a table, a graph, two points, or a description of a constant rate of change.
Your checkpoint
A function-sorting activity with at least 15 relations classified as function or not function, each with a one-sentence written justification.
Functions (defining, comparing and modeling linear and nonlinear functions)
Compare two functions presented in different representations (equation, graph, table, verbal description) by their rate of change and initial value.
Distinguish linear from nonlinear functions using tables, graphs, and equations, and identify examples such as parabolas and exponential growth curves.
Interpret slope and y-intercept of a linear model in the context of a real-world data set.
Sketch a qualitative graph of a situation described verbally, such as a cooling object or a filling tank.
Your checkpoint
A comparison write-up of four functions given in four different representations, ranking their rates of change and defending each ranking with computed evidence.
Geometry and Measurement (transformations, congruence/similarity, Pythagorean theorem, volume)
Perform and describe translations, reflections, rotations, and dilations on the coordinate plane, giving coordinates of image points.
Determine whether two figures are congruent or similar using sequences of transformations, and state the scale factor for dilations.
Apply the properties of rigid motions to prove that two figures are congruent.
Use the relationships among corresponding angles and sides of similar triangles to find missing measures.
Your checkpoint
A transformation portfolio of eight figures, each showing the pre-image, the image, the transformation rule, and a statement of whether congruence or similarity is preserved.
Geometry and Measurement (transformations, congruence/similarity, Pythagorean theorem, volume)
Apply the Pythagorean theorem and its converse to find missing side lengths and to classify triangles as right, acute, or obtuse.
Solve real-world distance problems on the coordinate plane using the Pythagorean theorem.
Calculate the volume of cylinders, cones, and spheres, and solve for a missing dimension given the volume.
Solve multi-step volume problems involving composite solids and explain each step in writing.
Your checkpoint
A ten-problem geometry set combining Pythagorean theorem and volume of solids, fully worked with units labeled and a score of at least 80 percent.
Number Sense and Operations (real numbers, exponents, scientific notation) & Data Analysis, Statistics and Probability (bivariate data, scatter plots, two-way tables)
Convert between scientific notation and standard form, and multiply and divide numbers expressed in scientific notation.
Apply the properties of integer exponents to simplify expressions, including negative and zero exponents.
Distinguish rational from irrational numbers and place irrational square roots approximately on a number line.
Construct and interpret scatter plots, describe association as positive or negative and linear or nonlinear, and informally fit a line of best fit.
Read and complete two-way frequency tables, computing joint, marginal, and conditional relative frequencies.
Your checkpoint
A two-part data and number-sense packet: one scatter-plot analysis with a drawn line of best fit and prediction, plus one completed two-way table with all three relative frequency types calculated.
Mathematical Thinking and Reasoning (multi-step problem solving and modeling) & Expressions, Equations and Inequalities (linear relationships, systems, radicals) & Functions (defining, comparing and modeling linear and nonlinear functions)
Solve multi-step modeling problems that combine two or more domains, showing a written plan before computing.
Justify reasoning with mathematical evidence rather than describing steps only.
Complete a full-length timed practice test under exam conditions and record the score by domain.
Analyze missed items from the practice test and rework each until correct without looking at the answer key.
Your checkpoint
A full-length timed practice test with a domain-by-domain score report and a corrected rework of every missed problem, targeting at least 75 percent overall.
Milestones
Week 2: Can solve a two-variable system by substitution and by elimination, and correctly classify a system as one solution, no solution, or infinitely many, on 8 of 10 items.
Week 4: Can compare two functions in different representations by rate of change and initial value, and distinguish linear from nonlinear, on 8 of 10 items.
Week 6: Can apply the Pythagorean theorem and compute volumes of cylinders, cones, and spheres, scoring at least 80 percent on a mixed geometry set.
Week 8: Scores at least 75 percent on a full-length timed practice test and has reworked every missed problem to correct independently.