Grade 7: Math
Start with a unit whose prerequisites fit. Work through the lessons, use the study guide to review, and try the new cases before continuing.
- Unit 1 · 4 lessons
Fractional Rates and Proportional Relationships
Proportional relationships compare multiplicative changes rather than fixed additions. Rates connect two labeled quantities, and a proportional graph must be consistent with a zero starting amount as well as a constant ratio.
Before you begin: Divide positive fractions; read ordered pairs; interpret a ratio with named units.
- Unit 2 · 4 lessons
Reason with Signed Changes
Combine, multiply, divide, and solve for signed changes in supplied situations.
Before you begin: Locate negative numbers relative to zero. · Use whole-number multiplication, division, and equality.
- Unit 3 · 4 lessons
Rational Numbers as Fractions, Decimals, and Locations
Rational numbers can be represented as ratios of integers with nonzero denominator. Their decimal forms terminate or repeat, and negative quantities can be compared by their positions to the left of zero.
Before you begin: Add fractions with common denominators; understand place value and negative number-line positions.
- Unit 4 · 4 lessons
Percent Changes, Reverse Percents, and Simple Interest
A percent is a ratio per hundred, but its base quantity matters. Successive percent operations act on successive amounts; reverse problems recover the original base rather than simply adding back a percentage.
Before you begin: Convert percents to decimals; multiply decimals; solve a one-step multiplication equation.
- Unit 5 · 4 lessons
Expression Structure and Equivalent Forms
An expression names a quantity without asserting equality to another quantity. Equivalent expressions give the same output for every allowed input, and their structures can reveal repeated groups, fixed extras, or shared factors.
Before you begin: Use whole-number multiplication and signed addition; recognize a variable and a coefficient.
- Unit 6 · 4 lessons
Equations and Inequalities with Rational Structure
Solving means finding inputs that make a relationship true. Balanced operations preserve equality, whereas inequality direction must reverse when multiplication or division by a negative number reverses number-line order.
Before you begin: Use fraction arithmetic; interpret equalities, strict inequalities and at-most language.
- Unit 7 · 4 lessons
Scale Drawings and Connected Angle Relationships
A scale drawing links represented and actual lengths through a fixed factor. Geometric relationships connect angles through straight lines and triangles, so a justified equation can replace guessing from a sketch.
Before you begin: Multiply decimals or whole numbers; understand area, a straight angle and triangle interior angles.
- Unit 8 · 4 lessons
Circle and Prism Measures
Geometric measures answer different questions: circumference is boundary length, area covers a region, and volume counts space. A formula works only when its input dimensions and output units match the question being asked.
Before you begin: Multiply decimals; square a whole number; recognize radius and rectangle dimensions.
- Unit 9 · 4 lessons
Sampling and Compound Chance
A complete population, a selected sample and a probability model are different sources of information. Sampling supports estimates, observed trial counts support experimental proportions, and explicit independence permits multiplication of model probabilities.
Before you begin: Use ratios and percent proportions; identify equally likely outcomes.
Check what you can explain
The subject test uses additional supplied cases across these units. Its feedback links back to the relevant lessons. Use it to plan practice; a score on these questions is not a school grade or proof of complete subject mastery.
Open the subject test