The Keystone School · grades 6–12
Middle-School Math
Ratios, negative numbers, and the first equations — the arithmetic of childhood widening into the algebra of adolescence.
How two quantities travel together — the idea beneath recipes, maps, speed, and every scale drawing.
Syllabus · 3 units · ~18 hours
Unit I — Reading a Ratio
Ratios as a comparison of two quantities · Part-to-part and part-to-whole · Equivalent ratios and the ratio table · Unit rates and price comparison
Unit II — Proportional Relationships
Recognizing proportionality in tables and graphs · The constant of proportionality · Solving proportions with cross-products · Scale drawings and maps
Unit III — Percent in the World
Percent as a rate out of one hundred · Percent increase and decrease · Tax, tip, and discount · Simple interest
The number line grows in both directions, and fractions fill every gap between the whole numbers.
Syllabus · 3 units · ~20 hours
Unit I — Below Zero
Negative numbers as opposites · Absolute value as distance from zero · Ordering and comparing integers · Integers in temperature, elevation, and money
Unit II — Operating with Signed Numbers
Adding integers with a number line · Subtraction as adding the opposite · Multiplying and dividing signed numbers · Order of operations with negatives
Unit III — Fractions, Decimals & Their Kin
Converting between fractions, decimals, and percents · Adding and subtracting rational numbers · Multiplying and dividing fractions · Terminating versus repeating decimals
Where arithmetic learns to hold its breath and let a letter stand in for a number.
Syllabus · 4 units · ~24 hours
Unit I — Expressions
Variables and algebraic expressions · Combining like terms · The distributive property · Evaluating expressions by substitution
Unit II — One- and Two-Step Equations
Equations as a balance to keep level · Inverse operations · Solving two-step equations · Checking a solution
Unit III — Inequalities & the Coordinate Plane
Writing and graphing inequalities · Solving one-step inequalities · Plotting ordered pairs in four quadrants · Reading a linear pattern from a table
Unit IV — Exponents & Roots
Powers and exponent notation · Perfect squares and square roots · Scientific notation for large and small numbers · Estimating irrational values
Shapes stop being pictures and start being quantities you can measure, compare, and predict.
Syllabus · 3 units · ~20 hours
Unit I — Angles & Lines
Naming and measuring angles · Complementary, supplementary, and vertical angles · Parallel lines cut by a transversal · Triangle angle sums
Unit II — Area & Perimeter
Area of triangles and quadrilaterals · Circumference and area of a circle · Composite figures · Perimeter in real layouts
Unit III — Surface Area & Volume
Nets of three-dimensional solids · Volume of prisms and cylinders · Surface area from a net · The Pythagorean theorem in measurement
How to summarize a pile of numbers honestly — and how a graph can quietly mislead.
Syllabus · 3 units · ~16 hours
Unit I — Describing Data
Statistical versus non-statistical questions · Mean, median, and mode · Range and interquartile range · Choosing a measure that fits the data
Unit II — Displaying Data
Dot plots and histograms · Box plots and the five-number summary · Reading and building a bar chart · How scale can distort a graph
Unit III — Chance
Probability as a number from zero to one · Experimental versus theoretical probability · Simple compound events · Simulating chance with a spinner or die