Mathematics

About this course

Seventh grade is a complete pre-algebra course. It opens with rational numbers, working through comparing and ordering, the sign rules for adding, subtracting, multiplying, and dividing negatives, and free conversion among fractions, decimals, and percents. From there it adds order of operations with negatives, the exponent rules including zero and negative exponents, scientific notation and calculating in it, square roots and cube roots, simplifying radicals, and the real number system with rational and irrational numbers placed on the number line. Proportional reasoning gets three units: ratios and unit rates with complex fractions, identifying proportional relationships, solving proportions by cross multiplication, the constant of proportionality found in tables, graphs, and equations, scale drawings and map scale, dimensional analysis, and the full run of percent problems including percent change, discount and markup, tax, tip, commission, and simple interest with I = Prt.

The geometry and measurement work is substantial. Your student studies angle relationships, angles formed by parallel lines and a transversal, the triangle angle sum and exterior angle theorems, the triangle inequality, the Pythagorean theorem including finding distance on the coordinate plane, circumference and area of circles and sectors, composite figures, surface area of prisms, cylinders, and pyramids, and volume of prisms, cylinders, pyramids, cones, and composite solids. A transformations unit covers translations, reflections, rotations, compositions, dilations with scale factor, congruence through rigid motion, similar triangles, and tessellations. Statistics moves past averages into range, interquartile range, mean absolute deviation, box plots, histograms, comparing distributions, sampling methods, two-way tables, and how statistics can mislead, and a probability unit adds sample space, complementary and compound and dependent events, the counting principle, and combinations. The algebra units cover writing and rewriting expressions, the distributive property and factoring, one-step through multi-step equations, equations with variables on both sides including the no-solution case, equations with fractional coefficients, one- and two-step and compound inequalities, and then relations, functions, linear and nonlinear functions, rate of change, and solving systems of linear equations by graphing and substitution.

The course is 180 lessons across 15 units, one per school day, at about 50 minutes each. Lessons are written directly to your student in textbook style: a definition, a step-by-step strategy, three to five fully worked examples with checks, and applications, followed by a ten-question quiz that grades itself. To be ready, your student should be comfortable with fractions, decimals, and percents, understand what a variable is, and be able to solve a two-step equation. Integers, exponent rules, and functions are all developed from the beginning here. Pencil, paper, and an eraser are the listed materials; a ruler, protractor, and graph paper are useful for the geometry and function units.

What the course covers

• Rational numbers and the sign rules for all four operations
• Exponent rules, scientific notation, square roots, and cube roots
• Proportional relationships and the constant of proportionality
• Percent change, discount, markup, tax, tip, and simple interest
• Angle relationships, transversals, and triangle theorems
• Circumference, area of circles and sectors, and composite figures
• Surface area and volume of prisms, cylinders, pyramids, and cones
• Translations, reflections, rotations, dilations, and similarity
• IQR, MAD, box plots, sampling, two-way tables, and probability
• Multi-step equations, inequalities, functions, and systems of equations

What your student will be able to do

• Compute confidently with positive and negative rational numbers
• Apply exponent rules and write and calculate in scientific notation
• Recognize a proportional relationship and find its constant of proportionality
• Find surface area and volume of prisms, cylinders, pyramids, and cones
• Solve multi-step equations and inequalities, including variables on both sides
• Perform transformations on the coordinate plane and solve a system of linear equations

Scope and sequence

All 15 units of Mathematics for Grade 7, in the order they are taught.

Every lesson, by title

All 180 lesson titles are listed here — nothing is withheld until you download. Open a unit to read its contents.

One whole lesson, exactly as it comes

This is a real lesson taken from the middle of the course — the teaching text, the practice, the homework, and the first three quiz questions with their answers. It is not a marketing excerpt.

What you will need

Drawn from the materials named across all 180 lessons of this course. Most families already own most of it.