Grade 7 Math Help
Step-by-step Grade 7 math videos, unit overviews, new terminology, lesson summaries, practice support, and helpful resources for students, parents, teachers, tutors, and homeschool families.
Welcome to Grade 7 Math
This page organizes Grade 7 math support by unit. Each unit includes an overview, important vocabulary, an all-lessons practice video or playlist, and short lesson summaries to help students review the main ideas.
Unit 1 — Scale Drawings
Unit Overview
Students learn about scaled copies, scale factors, scale drawings, and how measurements change when figures are enlarged or reduced.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.1.1 | scaled copy, original, polygon | |
| 7.1.2 | correspond, scale factor, figure, segment | |
| 7.1.4 | quadrilateral, measurement, distance | correspond, scale factor, original |
| 7.1.5 | reciprocal | |
| 7.1.6 | area, one-dimensional, two-dimensional | squared |
| 7.1.7 | scale drawing, scale, represent, actual, three-dimensional | scaled copy |
| 7.1.8 | estimate, travel, constant speed | scale |
| 7.1.9 | floorplan | |
| 7.1.10 | appropriate, dimension | actual, represent |
| 7.1.11 | scale without units, ___ to ___ | scale drawing |
| 7.1.12 | equivalent scales | ___ to ___ |
Scale Drawings and Scaled Copies
Scaled Copies
Students learn how scaled copies compare to original figures and how scale factors affect lengths.
Scale Drawings
Students use scale drawings to represent real objects, maps, and floor plans.
Area and Scale
Students connect scale factors to changes in length and area.
Unit 2 — Introducing Proportional Relationships
Unit Overview
Students study proportional relationships, constants of proportionality, tables, graphs, equations, and real-world situations involving equivalent ratios.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.2.1 | equivalent ratios | |
| 7.2.2 | constant of proportionality, proportional relationship, value | equivalent ratios, row, column |
| 7.2.3 | ___ is proportional to ___, relate, constant | per, reciprocal |
| 7.2.4 | equation, quotient | ___ is proportional to ___ |
| 7.2.5 | steady, situation | |
| 7.2.6 | equation, quotient | |
| 7.2.7 | constant of proportionality, proportional relationship | |
| 7.2.8 | volume, surface area | constant |
| 7.2.10 | origin, plot, coordinate plane | |
| 7.2.11 | quantity, axes, coordinates | |
| 7.2.13 | x-coordinate, y-coordinate | origin |
| 7.2.14 | axes | |
| 7.2.15 | reasonable |
Proportional Relationships
Equivalent Ratios
Students connect equivalent ratios to proportional relationships.
Constants of Proportionality
Students identify and interpret the constant of proportionality in tables, graphs, and equations.
Graphs and Equations
Students represent proportional relationships on the coordinate plane and with equations.
Unit 3 — Measuring Circles
Unit Overview
Students learn about circles, radius, diameter, circumference, pi, and area of a circle. They use formulas and approximations to solve circle measurement problems.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.3.1 | relationship, perimeter | |
| 7.3.2 | radius, diameter, circumference, center of a circle | circle |
| 7.3.3 | pi | |
| 7.3.4 | half-circle, rotation, approximation | |
| 7.3.5 | diameter, circumference, pi, travel | |
| 7.3.6 | approximate, estimate | |
| 7.3.7 | area of a circle | |
| 7.3.8 | radius, area of a circle | formula, squared |
| 7.3.10 | center of a circle, formula, squared | |
| 7.3.11 | design |
Circles, Circumference, and Area
Circle Measurements
Students learn radius, diameter, circumference, and how these measurements are related.
Using Pi
Students use pi to estimate and calculate circumference.
Area of a Circle
Students use formulas to calculate and reason about the area of circles.
Unit 4 — Proportional Relationships and Percentages
Unit Overview
Students use proportional reasoning to solve percent problems, including percent increase, percent decrease, discounts, taxes, tips, markups, markdowns, and percent error.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.4.1 | percentage | |
| 7.4.2 | unit rate | |
| 7.4.4 | (a fraction) more than, (a fraction) less than, initial / original amount, final / new amount | distributive property, tape diagram |
| 7.4.5 | repeating decimal, long division, decimal representation | |
| 7.4.6 | percentage increase, percentage decrease | (a fraction) more than, (a fraction) less than |
| 7.4.7 | discount | initial / original amount, final / new amount |
| 7.4.10 | tax rate, sales tax, tip | percentage increase |
| 7.4.11 | interest, commission, markup, markdown | percentage decrease |
| 7.4.12 | percentage, discount | |
| 7.4.13 | measurement error | |
| 7.4.14 | percent error, temperature, degrees Fahrenheit |
Percent Problems
Percentages and Proportions
Students connect percentages to proportional relationships and unit rates.
Increase and Decrease
Students solve problems involving percentage increase and percentage decrease.
Real-World Percent Applications
Students solve problems with discounts, sales tax, tips, interest, markups, markdowns, and percent error.
Unit 5 — Rational Number Arithmetic
Unit Overview
Students add, subtract, multiply, and divide rational numbers. They use contexts such as temperature, elevation, money, account balances, and number lines to make sense of signed numbers.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.5.1 | degrees Celsius, vertical, elevation, sea level | negative |
| 7.5.2 | absolute value, signed numbers | temperature, number line |
| 7.5.3 | sum, opposite, expression | |
| 7.5.4 | deposit, withdrawal, account balance, debt | |
| 7.5.6 | difference | distance |
| 7.5.7 | solution to an equation | x-coordinate, y-coordinate |
| 7.5.8 | velocity | absolute value |
| 7.5.11 | factor | |
| 7.5.13 | rational number | sum, difference |
| 7.5.15 | variable, additive inverse, multiplicative inverse | opposite, solution to an equation |
| 7.5.16 | operation | |
| 7.5.17 | increase, decrease |
Rational Number Operations
Signed Numbers
Students interpret positive and negative numbers using real-world contexts.
Adding and Subtracting Rational Numbers
Students use number lines and contexts to add and subtract rational numbers.
Multiplying and Dividing Rational Numbers
Students extend arithmetic rules to rational numbers and solve equations.
Unit 6 — Expressions, Equations, and Inequalities
Unit Overview
Students solve equations and inequalities, write equivalent expressions, use properties of operations, and reason about unknown amounts, variables, and relationships.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.6.2 | unknown amount | |
| 7.6.3 | commutative property, equivalent expression | |
| 7.6.4 | unknown amount, relationship | |
| 7.6.6 | variable | |
| 7.6.7 | balanced hanger, each side of an equation | |
| 7.6.8 | equivalent expression, each side of an equation | |
| 7.6.9 | operation, solve | |
| 7.6.10 | distribute, substitute | |
| 7.6.13 | inequality, less than or equal to, greater than or equal to, open / closed circle | less than, greater than |
| 7.6.14 | solution to an inequality, boundary, direction of an inequality | less than or equal to, greater than or equal to, substitute |
| 7.6.15 | open / closed circle | |
| 7.6.16 | solution to an inequality | |
| 7.6.17 | inequality | |
| 7.6.18 | term | |
| 7.6.19 | factor an expression, expand an expression | |
| 7.6.20 | combine like terms | commutative property, term |
| 7.6.21 | distribute | |
| 7.6.22 | associative property | factor an expression, expand an expression |
Equations, Inequalities, and Expressions
Equations
Students solve equations using balanced reasoning and representations.
Inequalities
Students write, solve, graph, and interpret inequalities.
Equivalent Expressions
Students use properties of operations to expand, factor, and combine like terms.
Unit 7 — Angles, Triangles, and Prisms
Unit Overview
Students explore angle relationships, triangle conditions, constructions, cross sections, prisms, pyramids, volume, and surface area.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.7.1 | straight angle, adjacent angles, degree | right angle |
| 7.7.2 | supplementary, complementary, angle measure, protractor | degrees, measurement error |
| 7.7.3 | vertical angles, intersect, vertex of an angle | |
| 7.7.4 | supplementary, vertical angles | |
| 7.7.5 | perpendicular | complementary |
| 7.7.6 | identical copy, condition | angle measure, side length, quadrilateral |
| 7.7.7 | compass, different triangle | intersect, identical copy, segment |
| 7.7.8 | condition, different triangle | |
| 7.7.9 | unique triangle, parallel | |
| 7.7.10 | protractor, compass | |
| 7.7.11 | cross section, vertex of a pyramid, base of a prism or pyramid, face | perpendicular, parallel, prism, pyramid |
| 7.7.12 | cross section, base of a prism or pyramid, volume | |
| 7.7.14 | face, perimeter | |
| 7.7.15 | surface area |
Geometry
Angles
Students use angle relationships, including complementary, supplementary, and vertical angles.
Triangles
Students investigate conditions that determine unique triangles or multiple triangles.
Prisms and Cross Sections
Students study cross sections, prisms, pyramids, volume, and surface area.
Unit 8 — Probability and Sampling
Unit Overview
Students study probability, chance experiments, sample spaces, simulations, sampling, populations, representative samples, and comparing data distributions.
New Terminology
| Lesson | Receptive | Productive |
|---|---|---|
| 7.8.1 | more likely, less likely | |
| 7.8.2 | event, chance experiment, outcome, equally likely as not | likely, unlikely, impossible, certain |
| 7.8.3 | probability, random, sample space | outcome |
| 7.8.5 | simulation | probability, random |
| 7.8.7 | event, simulation | |
| 7.8.8 | tree diagram | sample space |
| 7.8.9 | tree diagram | |
| 7.8.11 | mean absolute deviation (MAD), distribution, very different, overlap | mean, median |
| 7.8.12 | population, sample, survey | mean absolute deviation (MAD) |
| 7.8.13 | measure of center, representative sample | distribution, center, spread |
| 7.8.14 | random sample | |
| 7.8.15 | interquartile range (IQR), measure of variability | population, sample, random sample, symmetric |
| 7.8.16 | proportion | representative sample |
| 7.8.17 | interquartile range (IQR), measure of variability | |
| 7.8.18 | meaningful difference | overlap, measure of center |
| 7.8.20 | meaningful difference |
Probability and Sampling
Probability
Students learn about events, outcomes, chance experiments, and probability.
Simulations and Sample Spaces
Students use simulations and tree diagrams to organize possible outcomes.
Sampling and Data
Students study populations, samples, representative samples, and variability.
Comparing Distributions
Students compare distributions using center, spread, MAD, IQR, and meaningful differences.
Helpful Grade 7 Math Tools
Use these tools to check answers and review common Grade 7 math topics.
Printable and Digital Resources
Looking for organized notes, key ideas, practice support, or teacher-friendly resources? Visit the Resources page or the Illustrative Tutor Gumroad store.
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