Reveal Math, Accelerated

In Lesson 2-1 of Reveal Math, Accelerated for Grade 7, students learn how to connect ratios, rates, and proportions by writing and solving proportions using equivalent ratios and unit rates. The lesson uses real-world contexts such as aquarium salinity and a leaky faucet to show how ratio reasoning can be applied to find unknown quantities. Students practice setting up proportional equations and computing unit rates to solve multi-step problems.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to use tables of equivalent ratios to determine whether two quantities share a proportional relationship. They practice identifying the constant of proportionality by comparing ratios across multiple scenarios, such as trail mix ingredients and popcorn seasoning measurements. The lesson builds foundational understanding of Unit 2: Proportional Relationships by connecting constant ratios to unit rates in real-world contexts.

In this Grade 7 Reveal Math Accelerated lesson from Unit 2, students learn how to use coordinate plane graphs to determine whether a relationship is proportional by identifying whether the line passes through the origin and has a constant ratio of y to x. Students practice finding the constant of proportionality from a graph by locating the point where x equals 1, applying these skills to real-world contexts like SONAR depth measurement and bike share pricing. The lesson builds on proportional relationship concepts to help students distinguish proportional from non-proportional linear relationships visually.

In Lesson 2-4 of Unit 2 from Reveal Math, Accelerated, 7th grade students learn how to represent proportional relationships with equations using the form y = kx, where k is the constant of proportionality. Students practice identifying the constant of proportionality from real-world contexts, such as clay animation photo rates and fuel-to-air ratios, and use it to write equations that model the relationship between two quantities.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 2: Proportional Relationships), students learn how to apply proportional reasoning to solve multi-step ratio problems by setting up and solving proportions across sequential steps. Using real-world contexts like Earth's rotation rate and video game scoring systems, students practice converting units, chaining proportions, and checking whether their solutions are reasonable.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 3), students learn how to connect percentages and proportional reasoning by writing and solving proportions using part-to-whole ratios. Using tape diagrams, they practice setting up proportions in the form part/whole = n/100 to find unknown percentages or quantities in real-world contexts such as soccer save rates, election results, and sales tax. The lesson builds fluency with cross-multiplication and percentage calculations across a range of applied problems.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to apply the percent equation — part = percent × whole — to solve real-world problems involving sales tax, gratuity, commissions, and convenience fees. Using tape diagrams to set up and solve for unknown parts, percents, or wholes, students practice isolating variables within the percent equation across a variety of consumer math contexts. The lesson builds fluency with percent reasoning as part of Unit 3's focus on solving problems involving percentages.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to calculate percent change — both percent increase and percent decrease — using the percent equation (amount of change = percent change × original amount) and tape diagrams. The lesson applies these skills to real-world contexts such as Arctic sea ice loss, social media growth, and changes in wealth distribution. Students practice identifying the original amount and the amount of change to solve for an unknown percent change, rounding results to the nearest tenth of a percent.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to solve markup and markdown problems by applying the percent equation to calculate price increases above manufacturing cost and price reductions from an original selling price. Using tape diagrams and two solution strategies, students practice finding customer cost after a markup percentage and the discounted price after a markdown percentage. The lesson connects these concepts to real-world retail scenarios such as pricing jeans, bird feeders, and sunglasses.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to solve simple interest problems by applying the percent equation to calculate interest, principal, and interest rate. Using real-world scenarios like savings accounts and payment plans, students practice finding annual interest earned or charged and determining account balances after interest is applied. The lesson builds on Unit 3's focus on percentages, giving students tools to evaluate financial decisions involving borrowing and saving.

In Lesson 3-6 of Reveal Math Accelerated, 7th grade students learn how to calculate percent error by finding the difference between an estimated or claimed value and an actual value, then applying the percent equation to express that difference as a percentage. Students work through real-world examples such as seed counts on sunflowers and acceptable word counts in an essay to understand how percent error measures the inaccuracy of a value relative to a reference value. The lesson also explores how percent error applies in practical contexts like federal speedometer compliance standards.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to distinguish between populations and samples, and between parameters and statistics, understanding that a parameter is calculated from every member of a population while a statistic is calculated from a sample to estimate that parameter. Using real-world contexts like tongue-rolling studies and voter surveys, students practice identifying which type of value a given percentage represents and explaining their reasoning. This lesson builds foundational vocabulary and concepts for Unit 4's broader study of sampling and statistics.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to distinguish between biased and unbiased samples by examining whether a sampling method is representative, randomly selected, and large enough to produce valid inferences. Using real-world scenarios like school surveys and community events, students identify why certain samples favor specific subgroups and how to correct flawed survey methods. The lesson builds foundational statistical reasoning skills covered in Unit 4: Sampling and Statistics.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to draw inferences about a population by using sample data and proportional reasoning. They practice setting up and solving proportions to estimate percentages and scale sample results to the full population size. The lesson uses real-world contexts like student elections and school club surveys to help students understand how statistics from a random sample can be used to make reasonable predictions.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 4: Sampling and Statistics), students learn how to use multiple samples of the same size to describe the accuracy of a sample mean by analyzing the variation among sample means. They explore real-world contexts — including shark egg-case lengths and airline water bottle usage — to understand how the spread of sample means can be used to estimate the expected error for a given sample size. By the end of the lesson, students can evaluate whether a statistic calculated from a single sample is a reliable estimate of a population parameter.

In this Grade 7 Reveal Math, Accelerated lesson, students learn how to assess visual overlap between two data distributions by comparing their centers using IQR and MAD as measures of variability. Students practice analyzing box plots and histograms to determine whether the difference between medians or means is greater or less than 1 IQR or 2 MADs, which signals how noticeably the distributions differ. Real-world contexts such as rice yield data and adult height distributions are used to draw meaningful conclusions about two populations.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 5, Lesson 5-1), students learn to add integers and rational numbers with the same sign and with different signs using two methods: number lines and absolute values. Real-world contexts like ocean depths and underground dens help students understand how to determine the sign of a sum based on the absolute values of the addends. By the end of the lesson, students can apply these rules to solve problems involving positive and negative rational numbers.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 5), students learn about additive inverses and the Additive Inverse Property, which states that for any number p, p + (−p) = 0. Using number lines, algebra tiles, and real-world scenarios like drone movement and submarine depth, students explore how opposite numbers always sum to zero and share the same absolute value. The lesson builds foundational understanding of integer operations needed for solving more complex rational number problems.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to subtract integers and rational numbers by applying the additive inverse property, rewriting expressions like p − q as p + (−q). Students also use number lines to visualize subtraction and calculate the distance between two values using absolute value. Real-world contexts, including temperature ranges on Mars and competition point totals, give students practice applying these skills across Unit 5.

In Lesson 5-4 of Unit 5 in Reveal Math, Accelerated, Grade 7 students learn how to multiply integers and rational numbers, including the rules for determining the sign of a product when multiplying numbers with the same or different signs. The lesson covers multiplying a positive and a negative integer, multiplying two negative integers, and applying these skills to decimals and real-world contexts such as loan payments and waste reduction.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to divide integers and rational numbers, including how to determine the sign of a quotient based on whether the dividend and divisor have the same or different signs. The lesson covers dividing a positive by a negative, a negative by a positive, and two negatives, using number lines, algebra tiles, and standard division. Students also practice placing the negative sign in equivalent positions within a fraction and apply these skills to real-world problems involving money and other contexts.

In this Grade 7 lesson from Reveal Math, Accelerated, students apply the order of operations to evaluate expressions involving integers and rational numbers, including fractions, decimals, and negative exponents. Using the Fahrenheit-Celsius conversion formula as a real-world context, students practice substituting values into algebraic expressions and simplifying step by step. The lesson is part of Unit 5 and builds fluency with mixed operations across all rational number types.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 6: Congruence and Similarity), students explore translations as a type of rigid motion transformation in which a figure slides a given distance in a given direction without changing its size, shape, or orientation. Students practice identifying pre-images and images, applying translations on a coordinate plane by shifting vertices horizontally and vertically, and using prime notation to label translated figures. Real-world contexts like building relocation and park design help students understand how translations preserve corresponding side lengths and angle measures.

In this Grade 7 Reveal Math Accelerated lesson, students explore reflections as a type of rigid motion, learning that a reflection flips a figure across a line of reflection while preserving the size and shape of the original figure. Students practice identifying and drawing reflections on the coordinate plane, including reflections across the x-axis and y-axis, by analyzing how the coordinates of vertices change to produce the image. The lesson connects geometric concepts to real-world contexts such as furniture arrangement and symmetry in decorative art.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 6: Congruence and Similarity), students explore rotations as a type of rigid motion transformation, learning how figures are turned a specified angle and direction about a fixed center of rotation. Students practice rotating figures 90°, 180°, and 270° clockwise and counterclockwise, including applying coordinate rules to map triangle vertices after rotation about the origin. The lesson connects rotational symmetry to real-world contexts such as furniture arrangement and wind turbine design.

In this Grade 7 Reveal Math Accelerated lesson, students learn to define and identify congruent figures using sequences of rigid motion transformations, including translations, reflections, and rotations. Students practice mapping figures such as quadrilaterals and triangles onto one another on a coordinate grid to determine congruence. The lesson builds understanding that two figures are congruent only when a series of rigid motions can map one figure exactly onto the other, preserving both size and shape.

In this Grade 7 lesson from Reveal Math, Accelerated, students explore dilations as a type of transformation that changes the size of a figure using a scale factor, distinguishing them from rigid motion transformations. Students practice applying dilations to figures on and off the coordinate plane, including enlargements and reductions, by multiplying side lengths or coordinates by a given scale factor with the origin as the center of dilation. The lesson covers identifying whether a dilation is an enlargement or reduction and determining unknown scale factors from pre-image and image dimensions.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 6: Congruence and Similarity), students learn to define similar figures as shapes with proportional corresponding sides and the same shape but not necessarily the same size. Students practice identifying similarity by comparing ratios of side lengths and by describing sequences of transformations — including dilations, rotations, and translations — that map one figure onto another. The lesson connects scale factor to real-world contexts such as architectural drawings and video game programming.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to apply the Angle-Angle (AA) Similarity theorem to determine whether two triangles are similar by identifying pairs of congruent corresponding angles. Students practice using AA Similarity to find missing angle measures and solve real-world problems involving roof trusses and proportional side lengths. The lesson is part of Unit 6: Congruence and Similarity and builds on students' understanding of transformations and proportional relationships.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to use scale drawings to find real-world measurements by applying equivalent ratios and the perimeter formula. They practice interpreting map scales, calculating actual distances and dimensions, and adjusting scale drawing measurements when the scale changes. The lesson draws on contexts like Central Park and the Tappan Zee Bridge to build fluency with proportional reasoning in Unit 6: Congruence and Similarity.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to simplify linear expressions by identifying and combining like terms using the Commutative Property and the concept of additive inverses. The lesson covers writing expressions with multiple variables and constants in simplest form, recognizing that an expression is fully simplified when it contains no like terms and no parentheses. Real-world contexts such as electric vehicle motor dimensions, game scoring, and song lengths are used to apply these skills.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to expand linear expressions by applying the Distributive Property to eliminate parentheses, including cases involving subtraction rewritten using the additive inverse. Through real-world contexts like calculating pool fencing perimeters and craft box tape lengths, students practice distributing constants over binomials and combining like terms to write expressions in simplest form. The lesson is part of Unit 7: Work with Linear Expressions and reinforces the concept of equivalent expressions.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to add and subtract linear expressions by combining like terms and applying the additive inverse property. Using algebra tiles and properties of operations, they simplify expressions such as (2x + 3) + (5x − 5) and (x + 150) − (0.05x + 50) in real-world contexts like mosaic design and budgeting. The lesson builds fluency with rewriting subtraction as addition and regrouping terms to produce expressions in simplest form.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to factor linear expressions by identifying the Greatest Common Factor (GCF) of the terms and applying the Distributive Property to rewrite expressions as a product of the GCF and the remaining factors. The lesson uses real-world contexts, such as splitting ticket costs and movie expenses, to build understanding of what factored forms represent. Students practice factoring multi-term expressions like 24x + 18y and 3x + 3y + 3z − 30 as part of Unit 7's focus on working with linear expressions.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to write and solve two-step equations in the form px + q = r by applying Properties of Equality to isolate the variable. Using real-world contexts like marching band costs and airplane cruising time, students practice defining variables, setting up equations, and solving by performing inverse operations in the correct order. The lesson also addresses unit analysis, helping students understand how each term in an equation must represent the same unit of measurement.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to solve two-step equations in the form p(x + q) = r using two methods: dividing both sides by the coefficient p first, or applying the Distributive Property to eliminate parentheses. Real-world contexts such as diluting a bleach solution and calculating kennel dimensions help students practice writing and solving these equations. The lesson is part of Unit 8: Solve Problems Using Equations and Inequalities.

In Lesson 8-3 of Unit 8 from Reveal Math, Accelerated, Grade 7 students learn to solve linear equations with variables on both sides by applying the distributive property and combining like terms. The lesson uses balance scale models and real-world contexts, such as budgeting party costs, to build understanding of inverse operations and maintaining equality. Students practice setting up and solving multi-step equations in the form ax + b = cx + d.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 8), students learn to identify and describe the three types of solutions to linear equations: one solution, no solution, and infinitely many solutions. By simplifying multi-step equations and analyzing the resulting structure, students determine whether an equation produces a unique value, a contradiction, or an identity. The lesson builds algebraic reasoning skills that connect equation structure to the nature of its solution set.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to write and solve one-step addition and subtraction inequalities using the Addition and Subtraction Properties of Inequality. They practice defining variables, setting up inequalities from real-world scenarios, and graphing solution sets on a number line with open or closed circles. The lesson is part of Unit 8: Solve Problems Using Equations and Inequalities.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to write and solve one-step multiplication and division inequalities using the Multiplication and Division Properties of Inequality. A key focus is understanding why the inequality symbol must reverse direction when multiplying or dividing both sides by a negative number. Students practice applying these skills to real-world problems and graphing solution sets on a number line.

In Lesson 8-7 of Reveal Math Accelerated, Grade 7 students learn to write and solve two-step inequalities of the form px + q > r using the Properties of Inequality, including reversing the inequality symbol when multiplying or dividing by a negative number. The lesson covers defining variables, applying inverse operations, and graphing solution sets on a number line. Real-world contexts such as raffle ticket sales and wildlife research are used to practice translating word problems into two-step inequalities.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 9), students learn to describe and calculate the slope of a line as the ratio of rise to run using the formula slope = (y₂ − y₁) / (x₂ − x₁). Through real-world contexts like weekly savings and cycling speed, students connect slope to unit rate and the constant of proportionality in proportional relationships. The lesson builds students' ability to interpret the steepness of a line on a graph and apply slope to solve problems involving constant rates of change.

In this Grade 7 Reveal Math Accelerated lesson from Unit 9, students learn how to compare proportional relationships by analyzing slope across multiple representations, including tables, graphs, and equations. Using real-world contexts like roller coaster lift hills and wheelchair-accessible ramps, students calculate and compare unit rates and slopes to determine which relationship is steeper. The lesson builds skills in interpreting proportional relationships flexibly across different formats and applying slope comparisons to practical situations.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 9: Linear Relationships), students learn how to use similar triangles, called slope triangles, to determine and verify the slope of a line. Students discover that similar triangles with hypotenuses on the same line produce proportional vertical and horizontal changes, resulting in a constant slope ratio anywhere along the line. The lesson applies this concept to real-world contexts such as calculating roof slope using rise over run.

In Lesson 9-4 of Reveal Math, Accelerated, 7th grade students learn to identify and distinguish proportional linear relationships (y = mx) from nonproportional linear relationships (y = mx + b) using slope, constant of proportionality, and y-intercepts. Students practice writing equations in slope-intercept form and interpreting what the slope and y-intercept represent in real-world contexts such as weight on the Moon and advertising income. The lesson builds understanding of how a line's position relative to the origin determines whether a relationship is proportional or nonproportional.

In this Grade 7 Reveal Math, Accelerated lesson, students learn to define probability as a ratio of favorable outcomes to total possible outcomes, with values ranging from 0 (impossible) to 1 (certain). Using real-world contexts like weather forecasts and a ten-sided die, students practice expressing probability as a fraction, decimal, or percent and classifying events as unlikely, neither unlikely nor likely, or likely. The lesson builds foundational understanding of probability language and calculation that supports further study of chance and data analysis in Unit 10.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to calculate experimental probability of simple events by finding the ratio of the number of times an event occurs to the total number of trials. Students also use experimental probability to predict relative frequency through proportional reasoning, and explore why an experimental probability of zero does not mean an event is impossible.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to calculate the theoretical probability of simple events using the ratio of favorable outcomes to total possible outcomes. The lesson introduces the uniform probability model and guides students through real-world examples, such as determining the probability of choosing scissors in rock, paper, scissors or selecting a specific shirt color from a closet. Students also practice expressing probability as a fraction, decimal, and percent across a variety of contexts.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to compare experimental probability and theoretical probability for simple events. Using real-world examples like Rock, Paper, Scissors, they calculate each type of probability, convert fractions to common denominators or decimals, and analyze how closely the two values align. Students also explore how increasing the number of trials improves the accuracy of experimental probability.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to find the theoretical probability of compound events by identifying all possible outcomes in a sample space. Students practice using organized tools such as tree diagrams and tables to list outcomes when two or more simple events are combined, such as multiple coin flips or spinning two spinners. The lesson reinforces the concept that probability is the ratio of favorable outcomes to total outcomes in the sample space.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to design and use simulations to find experimental probability when real-world experiments are not practical. Using tools like spinners and multi-sided dice, students model chance events such as selecting left-handed students or predicting eye color outcomes, then calculate experimental probability as the ratio of favorable outcomes to total trials. The lesson connects simulation design to real-world probability scenarios, reinforcing how models can mimic the likelihood of an event's occurrence.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to draw and analyze triangles using side lengths and angle measures, including the Triangle Inequality Theorem — the rule that the sum of the two shorter sides must be greater than the longest side. Students also explore whether given sets of measurements produce a unique triangle, discovering that three side lengths determine a unique triangle while three angle measures alone do not. The lesson connects these concepts through real-world contexts like constructing borders and creating geometric art designs.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to solve real-world problems using vertical angles, supplementary angles, complementary angles, and adjacent angles. They apply equations such as m∠ABC + m∠ABD = 90° and m∠AEB + m∠BEC = 180° to find unknown angle measures in contexts like road intersections and aerobatic flight. The lesson is part of Unit 11: Angles and builds students' ability to identify angle relationships and use them to justify solutions.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to identify and apply angle relationships formed when a transversal intersects parallel lines, including corresponding angles, alternate interior angles, and alternate exterior angles. Students explore how these angle pairs are congruent and practice using angle measures to solve real-world problems involving parallel structures. The lesson builds key geometry vocabulary and reasoning skills within Unit 11: Angles.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 11), students learn that the interior angles of a triangle always sum to 180 degrees and that an exterior angle of a triangle equals the sum of its two remote interior angles. The lesson uses parallel lines and alternate interior angles to prove these relationships, then extends them to show that the exterior angles of a triangle sum to 360 degrees. Students apply these concepts to real-world problems involving parallel streets and intersecting transversals.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to identify and describe cross sections formed by slicing three-dimensional figures such as rectangular prisms, square pyramids, and cones. Students explore how the orientation of the slice — parallel, perpendicular, or angled — determines whether the resulting two-dimensional shape is a square, rectangle, triangle, or other polygon. The lesson also applies cross section area calculations using formulas for squares and triangles in real-world contexts.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to identify perfect squares, calculate square roots of perfect squares, and estimate the square roots of non-perfect squares using benchmark values. The lesson connects square roots to the area formula for squares and applies the concept to real-world contexts such as finding side lengths and calculating voltage. Students practice distinguishing between squares and square roots and develop strategies for narrowing decimal approximations of irrational square roots.

In this Grade 7 lesson from Reveal Math, Accelerated, students apply area and surface area formulas to solve real-world problems involving composite two-dimensional and three-dimensional figures. Using skills such as decomposing trapezoids, rectangles, and triangles and summing their areas, students work through multi-step problems like calculating roofing material for a pagoda-style roof and determining how much paint is needed for a multi-tier planter. The lesson builds on Unit 12 concepts by connecting geometric formulas to practical, context-driven scenarios.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 12), students learn how to solve problems involving the circumference of circles by exploring the constant ratio of circumference to diameter known as pi (π ≈ 3.14) and applying the formulas C = πd and C = 2πr. Using real-world contexts like circular horse training pens and Ferris wheels, students practice calculating circumference given either the radius or diameter. The lesson builds conceptual understanding of the relationships between radius, diameter, and circumference before applying those skills to multi-step problems.

In Lesson 12-5 of Reveal Math, Accelerated, Grade 7 students learn how to apply the area of a circle formula A = πr² to solve real-world problems, including finding exact and approximate areas using both π and 3.14 as an approximation. The lesson builds conceptual understanding by connecting the circle area formula to the area of a parallelogram through rearranging circular sections. Students practice calculating area from given radius and diameter measurements and distinguish between exact and approximate results.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 12), students learn to understand and apply cube roots as the inverse operation of cubing a number, using the relationship s = ∛V to find the side length of a cube from its volume. Students identify perfect cubes, estimate cube roots of non-perfect cubes between consecutive whole numbers, and simplify cube roots of fractions. The lesson also connects cube roots to real-world contexts, including applying Kepler's Third Law to calculate planetary distances using the equation T² = r³.

In Grade 7 Reveal Math Accelerated, Lesson 12-7 teaches students how to apply the volume formulas V = πr²h for cylinders and V = ⅓πr²h for cones to solve real-world problems. Students explore the relationship between the two formulas, discovering that the volume of a cone is one-third the volume of a cylinder with the same base and height. Practice problems involve calculating volumes using given radius, diameter, and height measurements and finding missing dimensions from known volumes.

In this Grade 7 Reveal Math Accelerated lesson from Unit 12, students learn to calculate the volume of spheres using the formula V = 4/3πr³ and apply it to real-world problems. Students practice finding a sphere's radius from its circumference before computing volume, and compare volumes across different-sized spheres. The lesson builds on prior knowledge of cone volume to derive the sphere volume formula and reinforces unit tracking throughout multi-step calculations.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to convert fractions to their decimal equivalents by dividing the numerator by the denominator, distinguishing between terminating decimals and repeating (nonterminating) decimals. Students also practice writing repeating decimals using bar notation, such as expressing 0.333… as 0.3̄. The lesson applies these concepts through real-world contexts like pie charts and relay race times.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to convert rational numbers between fraction and decimal form, including identifying repeating and terminating decimals using bar notation. The lesson also teaches the algebraic method of multiplying by a power of 10 to rewrite repeating decimals as fractions. Real-world contexts like baseball batting averages help students apply these skills within Unit 13 on Irrational Numbers, Exponents, and Scientific Notation.

In Lesson 13-3 of Reveal Math, Accelerated, Grade 7 students learn to identify and approximate irrational numbers, including non-perfect square roots such as √19 and √44, by locating them between consecutive integers and testing decimal values on a number line. Students distinguish irrational numbers from rational numbers by understanding that irrational numbers are nonrepeating, nonterminating decimals that cannot be expressed as a ratio of two integers. The lesson applies these skills to real-world contexts, such as estimating perimeter and radius using square roots.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to compare and order rational and irrational numbers — including fractions, repeating decimals, square roots, and pi — by converting each to its decimal approximation and plotting the values on a number line. The lesson applies these skills to real-world contexts such as calculating and comparing pizza areas using irrational expressions like 16π. Part of Unit 13 on Irrational Numbers, Exponents, and Scientific Notation, this lesson builds fluency with inequality symbols and decimal approximation as tools for ordering mixed number types.

In this Grade 7 lesson from Reveal Math, Accelerated, students explore patterns of exponents by investigating the zero exponent rule and the negative exponent rule, learning that any nonzero number raised to the zero power equals 1 and that a negative exponent represents the multiplicative inverse of the corresponding positive power. Students connect these rules to real-world contexts like metric system unit conversions and exponential growth through paper folding. The lesson builds fluency in evaluating and comparing expressions with zero and negative exponents, including fractional bases.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to apply the Product of Powers Property and the Quotient of Powers Property to simplify expressions involving exponents with the same base. They practice adding exponents when multiplying powers and subtracting exponents when dividing powers, using both numerical and algebraic examples. The lesson is part of Unit 13 on Irrational Numbers, Exponents, and Scientific Notation and includes real-world applications such as sound intensity and area problems.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to apply the Power of a Power Property and the Power of a Product Property to simplify expressions with exponents, including those with negative and zero exponents. They practice rewriting expressions such as (4²)³ as 4⁶ and (2⁻³ · 5)² as 5²/2⁶ using both expansion and algebraic rules. The lesson is part of Unit 13 on Irrational Numbers, Exponents, and Scientific Notation and includes a real-world application estimating the volume of spherical bacteria using scientific notation.

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to use powers of 10 and scientific notation to estimate and compare very large and very small quantities. Using real-world examples like smartphone storage and insect mass, students practice converting measurements to the same unit, expressing values in the form a × 10ⁿ, and finding how many times greater one quantity is than another. The lesson is part of Unit 13, which covers irrational numbers, exponents, and scientific notation.

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 13), students learn how to add, subtract, multiply, and divide numbers written in scientific notation by applying properties of exponents and the Distributive Property. The lesson emphasizes aligning powers of ten before performing addition or subtraction and converting results into proper scientific notation form. Real-world contexts such as text message totals and population density give students practice interpreting and comparing very large and very small quantities.