Grade 6 Math Help
Step-by-step Grade 6 math videos, unit overviews, new terminology, lesson summaries, practice support, and helpful resources for students, parents, teachers, tutors, and homeschool families.
Welcome to Grade 6 Math
This page organizes Grade 6 math support by unit. Each unit includes an overview, important vocabulary, an all-lessons practice video, and short lesson summaries to help students review the main ideas.
Unit 1 — Area and Surface Area
Unit Overview
Students build on earlier work with area, shapes, and geometric measurement. They learn how to find the area of triangles, parallelograms, and polygons by decomposing and rearranging shapes.
Students also explore surface area by studying three-dimensional figures, including prisms, pyramids, polyhedra, and nets.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.1.1 means Grade 6, Unit 1, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.1.1 | area region plane gap | |
| 6.1.2 | compose decompose rearrange two-dimensional | |
| 6.1.3 | shaded strategy | |
| 6.1.4 | parallelogram opposite sides or angles | quadrilateral |
| 6.1.5 | base height corresponding expression represent | |
| 6.1.6 | horizontal vertical | |
| 6.1.7 | identical | parallelogram |
| 6.1.8 | base height compose decompose rearrange | |
| 6.1.9 | opposite vertex | |
| 6.1.10 | vertex edge | |
| 6.1.11 | polygon | horizontal vertical |
| 6.1.12 | face surface area | area region |
| 6.1.13 | polyhedron net prism pyramid three-dimensional | polygon vertex edge face |
| 6.1.15 | volume | prism pyramid |
| 6.1.16 | appropriate quantity | two-dimensional three-dimensional |
| 6.1.17 | squared cubed exponent edge length | |
| 6.1.18 | value of an expression | squared cubed net |
| 6.1.19 | estimate description | surface area volume |
Reasoning to Find Area
Lesson 1 — Tiling the Plane
Students review area and learn that matching figures have the same area.
Lesson 2 — Finding Area by Decomposing and Rearranging
Students break apart and rearrange shapes to find area.
Lesson 3 — Reasoning to Find Area
Students use multiple strategies to find the area of unfamiliar figures.
Parallelograms, Triangles, Polygons, and Surface Area
Lessons 4–6 — Parallelograms
Students study parallelograms and use base-height relationships to calculate area.
Lessons 7–10 — Triangles
Students connect triangles to parallelograms and develop the triangle area formula.
Lesson 11 — Polygons
Students learn that polygons can be decomposed into triangles to find area.
Lessons 12–16 — Surface Area
Students use nets and three-dimensional figures to understand surface area.
Lessons 17–18 — Squares and Cubes
Students connect exponents to square area and cube volume.
Unit 2 — Introducing Ratios
Unit Overview
Students learn how ratios describe relationships between quantities. They use recipes, mixtures, tables, tape diagrams, and double number line diagrams to represent equivalent ratios and solve ratio problems.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.2.1 means Grade 6, Unit 2, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.2.1 | ratio __ to __ __ for every __ | |
| 6.2.2 | diagram | |
| 6.2.3 | recipe batch same taste | ratio __ to __ __ for every __ |
| 6.2.4 | mixture same color check an answer | batch |
| 6.2.5 | equivalent ratios | |
| 6.2.6 | double number line diagram tick marks representation | diagram |
| 6.2.7 | per | |
| 6.2.8 | unit price how much for 1 at this rate | double number line |
| 6.2.9 | meters per second constant speed | |
| 6.2.10 | same rate | equivalent ratios |
| 6.2.11 | table row column | |
| 6.2.14 | calculation | per table |
| 6.2.15 | tape diagram parts suppose | |
| 6.2.16 | tape diagram |
Equivalent Ratios
Lesson 1 — The Burj Khalifa
Students begin using ratio language to compare quantities.
Lessons 3–5 — Equivalent Ratios
Students use recipes and mixtures to understand equivalent ratios.
Lessons 6–10 — Representing Equivalent Ratios
Students use double number lines, tables, unit rates, and constant speed situations.
Lessons 11–14 — Solving Ratio Problems
Students solve ratio and rate problems using tables and diagrams.
Lessons 15–16 — Part-Part-Whole Ratios
Students solve problems involving sums and relationships between ratio parts.
Unit 3 — Unit Rates and Percentages
Unit Overview
Students deepen their understanding of rates, unit rates, and percentages. They compare prices, speeds, and percentages using tables, double number lines, tape diagrams, and real-world contexts.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.3.1 means Grade 6, Unit 3, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.3.1 | at this rate | |
| 6.3.3 | order | |
| 6.3.5 | good / better / best deal rate per 1 | unit price same speed |
| 6.3.6 | unit rate | gallon |
| 6.3.7 | result | unit rate |
| 6.3.8 | pace | speed |
| 6.3.9 | meters per second good / better / best deal | |
| 6.3.10 | percentage __% of | |
| 6.3.11 | tick marks | |
| 6.3.12 | __% as much | tape diagram __% of |
| 6.3.14 | __% of | |
| 6.3.15 | regular price sale price | percentage |
Unit Conversion, Rates, and Percentages
Lessons 1–4 — Unit Conversion
Students use ratios and unit conversions to connect measurement and rate ideas.
Lessons 5–9 — Rates
Students compare speeds, prices, and unit rates in real-world situations.
Lessons 10–16 — Percentages
Students learn what percentages mean and solve percent problems using diagrams and reasoning.
Unit 4 — Dividing Fractions
Unit Overview
Students make sense of division situations, especially fraction division. They interpret division as “how many groups?” and “how much in each group?” before developing and using an algorithm for dividing fractions.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.4.1 means Grade 6, Unit 4, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.4.1 | divisor dividend | quotient |
| 6.4.2 | equation interpretation | How many groups of ___? How many ___ in each group? |
| 6.4.3 | unknown equal-sized | |
| 6.4.4 | whole | |
| 6.4.5 | relationship | |
| 6.4.6 | equal-sized | |
| 6.4.7 | times as ___ fraction of ___ | |
| 6.4.8 | container | unknown fraction of ___ |
| 6.4.9 | whole | |
| 6.4.10 | reciprocal observations | times as ___ numerator denominator |
| 6.4.11 | evaluate | |
| 6.4.13 | gaps | |
| 6.4.14 | packed | |
| 6.4.17 | assumption | packed |
Making Sense of Division
Lessons 1–3 — Division Situations
Students connect multiplication and division and interpret division problems in context.
Lessons 4–9 — Meanings of Fraction Division
Students use diagrams and contexts to understand what it means to divide fractions.
Lessons 10–11 — Algorithm for Fraction Division
Students develop and use an algorithm to divide fractions.
Lessons 12–15 — Fractions in Geometry
Students apply fraction division to lengths, areas, and volumes.
Unit 5 — Arithmetic in Base Ten
Unit Overview
Students extend their understanding of operations to decimals. They add, subtract, multiply, and divide decimals while using place value, diagrams, and algorithms.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.5.1 means Grade 6, Unit 5, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.5.1 | digits budget at least | |
| 6.5.2 | base-ten diagram bundle vertical calculation | place value digits |
| 6.5.3 | unbundle | |
| 6.5.4 | method | |
| 6.5.5 | powers of 10 | product decimal point |
| 6.5.7 | partial products | method |
| 6.5.9 | partial quotients | remainder |
| 6.5.10 | long division | divisor |
| 6.5.13 | long division | |
| 6.5.14 | precision accuracy | |
| 6.5.15 | operation |
Decimals and Operations
Lessons 1–4 — Adding and Subtracting Decimals
Students use place value and diagrams to add and subtract decimals accurately.
Lessons 5–8 — Multiplying Decimals
Students reason about decimal products using diagrams, place value, and powers of ten.
Lessons 9–13 — Dividing Decimals
Students use partial quotients and long division to divide decimals.
Unit 6 — Expressions and Equations
Unit Overview
Students write, interpret, and solve equations and expressions. They use diagrams, variables, balanced hanger models, equivalent expressions, exponents, and relationships between quantities.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.6.1 means Grade 6, Unit 6, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.6.1 | value of a variable | operation |
| 6.6.2 | variable coefficient solution to an equation true equation / false equation | value of a variable |
| 6.6.3 | each side balanced hanger | |
| 6.6.4 | solve an equation | each side |
| 6.6.6 | equation | |
| 6.6.7 | true equation / false equation | |
| 6.6.8 | equivalent expressions | |
| 6.6.9 | distributive property area as a product area as a sum | |
| 6.6.12 | to the power | |
| 6.6.13 | base of an exponent | to the power exponent |
| 6.6.14 | solution to an equation | |
| 6.6.16 | independent variable dependent variable | variable relationship |
| 6.6.17 | coordinate plane coordinates | |
| 6.6.18 | horizontal axis vertical axis plot |
Equations, Expressions, and Relationships
Lessons 1–5 — Equations in One Variable
Students use tape diagrams and equations to represent and solve situations.
Lessons 6–11 — Equal and Equivalent
Students write expressions, identify equivalent expressions, and use the distributive property.
Lessons 12–15 — Expressions with Exponents
Students interpret and evaluate expressions with exponents.
Lessons 16–18 — Relationships Between Quantities
Students represent relationships using equations, graphs, and coordinate planes.
Unit 7 — Rational Numbers
Unit Overview
Students extend the number line to include negative numbers, compare rational numbers, work with absolute value, solve inequalities, and use all four quadrants of the coordinate plane.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.7.1 means Grade 6, Unit 7, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.7.1 | positive number negative number temperature degrees Celsius elevation sea level | number line below zero |
| 6.7.2 | opposite numbers rational number location distance from zero | |
| 6.7.3 | sign inequality closer to 0 farther from 0 | greater than less than |
| 6.7.4 | from least to greatest | temperature elevation sea level |
| 6.7.5 | positive change negative change context | |
| 6.7.6 | absolute value | positive number negative number distance from zero |
| 6.7.7 | closer to 0 farther from 0 | |
| 6.7.8 | maximum minimum | |
| 6.7.9 | requirement solution to an inequality | |
| 6.7.10 | unbalanced hanger | inequality |
| 6.7.11 | quadrant x-coordinate y-coordinate | |
| 6.7.12 | line segment | axis |
| 6.7.13 | degrees Fahrenheit | degrees Celsius |
| 6.7.14 | absolute value x-coordinate y-coordinate | |
| 6.7.16 | factor common factor greatest common factor (GCF) | |
| 6.7.17 | multiple common multiple least common multiple (LCM) |
Negative Numbers, Inequalities, and the Coordinate Plane
Lessons 1–7 — Negative Numbers and Absolute Value
Students use number lines and contexts to understand positive numbers, negative numbers, and absolute value.
Lessons 8–10 — Inequalities
Students write, graph, and interpret inequalities.
Lessons 11–15 — Coordinate Plane
Students plot points and work with shapes in all four quadrants.
Lessons 16–17 — Factors and Multiples
Students review common factors, greatest common factors, common multiples, and least common multiples.
Unit 8 — Data Sets and Distributions
Unit Overview
Students study data, statistical questions, dot plots, histograms, measures of center, measures of spread, mean, median, MAD, IQR, quartiles, and box plots.
New Terminology
These terms are organized by grade, unit, and lesson. For example, 6.8.1 means Grade 6, Unit 8, Lesson 1.
| Lesson | Receptive Vocabulary | Productive Vocabulary |
|---|---|---|
| 6.8.1 | numerical data categorical data dot plot | |
| 6.8.2 | statistical question variability | |
| 6.8.3 | distribution frequency | bar graph |
| 6.8.4 | typical | |
| 6.8.5 | center mode spread | variability |
| 6.8.6 | histogram bins | distribution center |
| 6.8.7 | statistical question spread | |
| 6.8.8 | symmetrical peak cluster unusual value | numerical data categorical data gap |
| 6.8.9 | average mean fair share | |
| 6.8.10 | measure of center balance point | |
| 6.8.11 | measure of spread mean absolute deviation (MAD) | symmetrical mean |
| 6.8.12 | typical mean absolute deviation (MAD) | |
| 6.8.13 | median | measure of center |
| 6.8.14 | peak cluster unusual value | |
| 6.8.15 | range quartile interquartile range (IQR) five-number summary | measure of spread minimum maximum |
| 6.8.16 | box plot whisker | median interquartile range (IQR) |
| 6.8.17 | range quartile | |
| 6.8.18 | dot plot histogram box plot |
Data, Variability, and Statistical Questions
Lessons 1–2 — Statistical Questions
Students collect data and learn how statistical questions involve variability.
Lessons 3–8 — Dot Plots and Histograms
Students represent and describe data using dot plots and histograms.
Lessons 9–12 — Mean and MAD
Students interpret mean as fair share and use MAD to describe spread.
Lessons 13–17 — Median, IQR, and Box Plots
Students use median, quartiles, interquartile range, and box plots to analyze data.
Helpful Grade 6 Math Tools
Use these tools to check answers and better understand common Grade 6 math topics.
Printable and Digital Resources
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