# Grade 7 Math

#### Course Features

#### Course Details

Course Overview

In the Acellus Grade 7 Math course, after a thorough review of basic operations, Mr. Mark Rogers demonstrates how to solve real-world problems by applying basic concepts of Algebra and Geometry and by using proportional relationships. Students are also shown how to use statistical data to make inferences and how to use and evaluate probability models.
### Course Objectives & Student Learning Outcomes

Upon completion of Acellus Grade 7 Math, students will be able to: compare integers; choose opposites; use absolute value; add integers on integer Hill, using a Chip Model and on a number line; subtract, multiply, and divide integers; use order of operations including with integers; interpret, compare, estimate, round, add, subtract, multiply, and divide decimals by a whole number, by a decimal; and converting percents to decimals; find greatest common factor and least common multiple; identify and reduce fractions; convert mixed to improper fractions, improper to mixed fractions, fractions to terminating decimals, fractions to repeating decimals; order rational numbers; find common denominator; add and subtract simple fractions; add and subtract mixed numbers; add and subtract mixed numbers with regrouping; multiply simple fractions and mixed numbers; divide simple fractions and mixed numbers; add and subtract rational numbers; and multiply and divide negative fractions. Students will also be able to read and write expressions and equations; evaluate expressions; simplify expressions with integers; add and subtract rational coefficients; simplify, expand, factor, identify, and translate expressions; write equations; solve one-step and two-step equations; solve equations with rational numbers and with variables on both sides; write and graph inequalities; solve inequalities; solving inequality in word problems; identify and find adjacent complementary, supplementary, reflex, and vertical angles and angles that share a vertex; draw triangles and angels; find area of parallelograms, triangles and trapezoids; define circle vocabulary; find circumference, radius, diameter, and area of circles; find area of irregular figures; identify 3D figures, and nets; relate cross sections; calculate surface area of prisms, pyramids, cylinders and composite figures; calculate volume of prisms, cylinders, pyramids and composite figures. Finally, students will be able to calculate ratios, proportions, unit rate, proportions with fractions, proportions and percents, percent of error, percent of change, and simple interest; implement scale factor; calculate length given a scale; calculate areas in scale drawings; calculate proportionality in tables, graphs, verbal descriptions and equations; interpret graphs; calculate inverse proportionality in tables, in graphs, and in verbal descriptions; calculate mean, mode, median, and range; create Box and Whisker Plots; identify random sampling and compare data sets; utilize probability models of categorized data and with frequencies; calculate theoretical and experimental probability; use a uniform probability model, identify, compare, and contrast independent and dependent events, use simulation tools.**Scope and Sequence**

**Unit 1 – Adding Integers**Students begin the Acellus Grade 7 Math course by comparing integers. They study working with opposites and absolute value. They explore adding integers using additive inverse, using the chip model, and using a number line.

**Unit 2 - Integers and the Four Operations**In this unit students continue studying integers. They investigate the applications of adding, subtracting, multiplying, and dividing integers. They explore the order of operations rule.

**Unit 3 - Decimals**Students investigate interpreting, comparing, rounding, and estimating with decimals. They practice adding and subtracting decimals.

**Unit 4 - More Decimals**Continuing their study of decimals, students explore multiplying with decimals. They examine dividing decimals by whole numbers and by decimals, as well as dividing positive and negative decimals. They investigate converting decimals into percents.

**Unit 5 - Fractions**Delving into a study of fractions, students begin with greatest common factors and least common multiples. They gain understanding of what fractions are and how they can be reduced. They learn to convert mixed numbers to improper fractions, and improper fractions to mixed numbers. They explore how decimals eventually repeat or terminate. They discuss how to convert fractions to terminating and to repeating decimals. They consider how rational numbers are ordered.

**Unit 6 - More Fractions**Students continue their study of fractions. They learn to find a common denominator. They grasp how to add and subtract simple fractions, mixed numbers, and mixed numbers with regrouping.

**Unit 7 - Mixed Numbers**In this unit students explore multiplying and dividing simple fractions and mixed numbers. They investigate adding and subtracting rational numbers. They study multiplying and dividing negative fractions. The consider real-world applications of these skills.

**Unit 8 - Expressions and Coefficients**Beginning their preparation for algebra, students learn about expressions and equations. They study how to evaluate an expression and to simplify expressions with integers. They discuss adding and subtracting rational coefficients involving decimals and involving mixed numbers. They simplify expressions involving rational numbers.

**Unit 9 - Expanding, Factoring, and Translating Expressions**Students learn to expand expressions with integers and with rational numbers. They factor algebraic expressions. They discuss recognizing equivalent expressions. They study how to translate expressions and explore real-world applications using expressions.

**Unit 10 - Equations**Next, students learn to write, simplify, and solve one- and two-step equations. They investigate equations with rational numbers and with variables on both sides. They consider real-world applications using variable equations.

**Unit 11 - Inequalities**In this unit students study writing, graphing, and solving inequalities. They practice inequality word problems. Following this unit, students are presented with the Mid-Term Review and Exam

**Unit 12 - Angles**Students explore angles, including adjacent, complementary, supplementary, reflex, and vertical angles. They also study angles that share a vertex. They investigate the relationship between triangles and angles. They analyze exterior angles. They delve into types of triangles and drawing triangles.

**Unit 13 - Two-Dimensional Figures**Building on their study of angles, students learn to find the area of parallelograms, triangles, and trapezoids. They explore circle vocabulary and circumference and investigate how to find C, r, and d. They analyze the area of circles and finding A, r, and d. They consider the area of irregular figures.

**Unit 14 - Three-Dimensional Figures**In this unit students learn to identify 3-D figures and nets. They study cross sections. They explore finding the surface area of prisms, pyramids, and cylinders.

**Unit 15 - Volume of Three-Dimensional Figures**Continuing their investigation of three-dimensional figures, students learn to find the volume of prisms, cylinders, pyramids, and composite figures. They also explore finding the surface area of composite figures.

**Unit 16 - Rates, Ratios, and Proportions**Students investigate ratios. They study the basics of proportion and practice proportion word problems. They examine unit rate. They analyze proportions with fractions and with complex fractions. They consider the relationship between proportions and percents. They explore percent of change and percent of error.

**Unit 17 - Interest and Scale**In this unit students discuss simple interest. They explore multi-step percent problems. They investigate scale factor and learn to calculate length, given a scale. They study area in scale drawings. They consider scale factor with perimeter and area.

**Unit 18 - Statistics Part 1**Turning to the subject of statistics, students explore direct proportionality in tables, graphs, verbal descriptions, and equations. They learn to interpret linear and non-linear graphs.

**Unit 19 - Statistics Part 2**Continuing to explore statistics, students discuss mean, mode, median, and range. They study box and whisker plots. They learn about random sampling. They compare data sets.

**Unit 20 - Probability**Students discuss theoretical probability. They explore probability models of categorical data. They consider using a uniform probability model. They analyze probability models with frequencies as well as experimental probability. They examine independent and dependent events. They learn to use simulation tools.

Following this unit, students are presented with the Final Review and Exam.