Grade 7 Math

Course Features
Course Details
Course Overview
In Acellus Grade 7 Math course, students develop a strong foundation in working with integers, decimals, fractions, and rational numbers, learning to order, compare, and perform operations including addition, subtraction, multiplication, and division with positive and negative values. They explore algebraic concepts such as variables, expressions, equations, and inequalities, mastering simplification, evaluation, and solving techniques while applying them to real-world scenarios. The curriculum builds skills in geometry, covering angles, triangles, 2D and 3D figures, with calculations for area, surface area, volume, and irregular shapes, enhancing spatial reasoning and problem-solving.
Students also delve into ratios, rates, proportions, and percents, including applications in finance like interest, budgets, and percent changes, as well as scale drawings and proportionality in tables and graphs. The course concludes with statistics and probability, where learners analyze data sets using measures like mean, median, mode, range, and mean absolute deviation, interpret graphs, understand sampling methods, and calculate theoretical and experimental probabilities for independent and dependent events.

Sample Lesson - Introduction
Scope and Sequence
Unit 1: Integers Part 1 Students will learn to order positive and negative integers, identify opposites and additive inverses, recognize inverse operations, understand absolute value, represent repeated multiplication with exponents, apply the order of operations to expressions with positive integers, and model addition of integers using number lines.
Unit 2: Integers Part 2 Students will simplify integer expressions by combining like terms, subtract integers using number lines and the "add the opposite" strategy, find distances between integers with absolute values, solve real-world problems involving integers and money, multiply and divide positive and negative integers, and apply the order of operations to multi-step expressions with integers.
Unit 3: Decimals Part 1 Students will identify and compare place values up to ten-thousandths, translate decimals from word to standard form, order and round decimals, estimate sums and differences, apply estimation to real-world problems with money and measurements, and add and subtract positive and negative decimals.
Unit 4: Decimals Part 2 Students will add and subtract negative and positive decimals, multiply positive and negative decimals, divide decimals using the standard algorithm, apply decimal operations to real-world scenarios, and convert between decimals and percents.
Unit 5: Fraction Basics Students will identify factors and greatest common factors, list multiples and least common multiples, define rational numbers, express fractions as parts of a whole, simplify fractions, convert between improper fractions and mixed numbers, convert fractions to terminating and repeating decimals, compare rational numbers, and order sets of rational numbers including decimals, fractions, and mixed numbers.
Unit 6: Fraction Operations Part 1 Students will find common denominators, add fractions and regroup to mixed numbers, subtract fractions from 1, add and subtract mixed numbers with uncommon denominators, regroup mixed numbers, and subtract mixed numbers requiring regrouping.
Unit 7: Fraction Operations Part 2 Students will multiply and simplify fractions, multiply fractions with whole numbers, use cross-canceling, multiply mixed numbers by converting to improper fractions, find reciprocals, divide fractions and mixed numbers, solve real-world problems with rational numbers, multiply and divide negative fractions, and calculate fractional amounts of whole numbers in applications.
Unit 8: Algebra: Expressions Part 1 Students will define parts of algebraic expressions, identify coefficients, constants, and terms, evaluate one- and multi-variable expressions using substitution, simplify expressions by combining like terms including with integers, decimals, and fractions.
Unit 9: Algebra: Expressions Part 2 Students will apply the distributive property to simplify expressions with numerical, variable, and rational terms, remove grouping symbols, factor algebraic expressions including complex ones with exponents and multiple variables, recognize equivalent expressions, translate verbal expressions to algebraic ones, identify expressions from linear patterns in tables, and interpret real-world problems through algebraic expressions.
Unit 10: Algebra: Equations Students will understand equation balance, identify inverse operations, isolate variables in one-step equations, solve one- and two-step equations, combine like terms to solve equations, handle equations with rational numbers including decimals and fractions, solve equations with variables on both sides using the distributive property, and write and solve equations from real-world scenarios.
Unit 11: Algebra: Inequalities Students will identify inequality symbols, translate verbal comparisons to inequalities, graph inequalities on number lines, solve one- and two-step inequalities including with negative integers, interpret inequality statements, and translate real-world scenarios to inequalities.
Unit 12: Angles and Triangles Students will classify angles by measure, identify adjacent, complementary, supplementary, and vertical angles, find missing angles in diagrams and triangles, calculate exterior angles, classify triangles by sides and angles, and draw triangles based on angle and side clues.
Unit 13: 2D Figures Students will classify quadrilaterals by angles and sides, calculate areas of parallelograms, triangles, trapezoids, and shapes with cutouts, identify circle parts like radius and diameter, understand pi, compute circumference and area of circles, and find areas of irregular shapes by decomposing into rectangles and triangles.
Unit 14: 3D Figures Part 1 Students will name 3D solids like prisms, cylinders, cones, spheres, and pyramids, identify measurements for surface area and volume, recognize nets and composing 2D shapes, determine cross sections, calculate surface areas using nets for prisms, pyramids, and cylinders, and compute volumes of prisms, cylinders, and pyramids.
Unit 15: Ratios and Rates Part 1 Students will represent and simplify ratios, solve proportions and word problems, calculate unit rates including with fractions, use proportions for percents, mentally find 10% and estimate percents, calculate percents of numbers, apply tips and discounts, and compute percent of change and error in real-world scenarios.
Unit 16: Ratios and Rates Part 2 Students will calculate simple interest, solve multi-step percent problems with markups, markdowns, and taxes, determine budget expenses as percentages, analyze net worth statements, find scale factors, calculate actual lengths and areas in scale drawings using linear and squared scale factors.
Unit 17: Proportionality Students will determine constants of proportionality in equations, recognize proportionality in tables and graphs, solve proportion word problems, interpret linear and non-linear graphs to predict values and identify data points from real-world scenarios.
Unit 18: Statistics and Probability Part 1 Students will calculate range, mean, median, mode, and mean absolute deviation of data sets, interpret box and whisker plots, understand random sampling methods and their strengths, and compare data sets using box plots and other graphical representations.
Unit 19: Statistics and Probability Part 2 Students will calculate theoretical probabilities for simple events, construct probability models with frequency tables, use uniform models for equally likely outcomes, analyze data with frequencies, compare experimental and theoretical probabilities, compute probabilities for independent and dependent events, and find experimental probabilities from simulations.
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