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Course Overview

In the Grade 6 Math course, students study the mathematical concepts that will help them as they transition through middle school and prepare for Pre-Algebra.  Mr. Rogers brings math to life, presenting compelling and engaging real-world applications.

Course topics include:

• Ratios, Rates and Proportions

• Fractions, Decimals, and Percents

• Multiplying and Dividing Decimals

• Multiplying and Dividing with Fractions and Mixed Numbers

• Common and Uncommon Denominators

• Integers and Rational Numbers

• Expressions, Exponents, and Variables

• Mathematical Properties and Expressions

• One-Step Equations

• Solving One-Step Equations with Decimals, Fractions, and Cross-Products

• Functions and Inequalities

• Two- and Three-Dimensional Figures

• Statistics

Scope and Sequence

Unit 1 – Ratios Students begin the Grade 6 Math course with a study of ratios -- identifying and writing ratio relationships and using multiplication to compare numbers.  They explore divisibility rules, factors, greatest common factors, and simplifying ratios, and practice with real-world examples.

Unit 2 - Rates and Proportions In this unit students discover what is meant by unit rates. They practice finding them, and then explore how this concept is used in the real world. Next they define proportions and practice writing them.  They solve problems using proportional relationships and explore real-world situations where proportions would be used.

Unit 3 - Fractions, Decimals, and Percent’s Students review the basics of fractions and decimals. They study converting between these two forms and practice converting fractions into decimals and decimals into fractions.

Unit 4 – Percent’s Students next explore percent. They master writing percent as fractions and as decimals and writing decimals and fractions as percent. They examine percent’s greater than 100% and less than 1%. They learn to use a bar diagram to figure percentages, and they consider how fractions, decimals, and percent are related to each other.

Unit 5 - Adding and Subtracting with Decimals This unit begins with the principles needed for adding decimals. Students study adding whole numbers to decimals and adding decimals to decimals. They consider how these skills can be used in the real world. They continue by exploring principles used in subtracting decimals and then practice subtracting decimals from whole numbers, as well as subtracting decimals from decimals. They examine how these skills can be applied to solve real-world problems.

Unit 6 - Multiplying and Dividing with Decimals Next students review whole number multiplication and then augment their understanding of decimals with multiplying decimals and whole numbers. They study multiplying decimals by decimals and multiplying and dividing decimals by powers of ten.

Unit 7 - More Division with Decimals Students examine the standard algorithm for dividing whole numbers, then consider dividing decimals by whole numbers and explore a real-world application of this skill. They further delve into dividing decimals by decimals, and then compare and contrast the four operations with decimals.

Unit 8 - Multiplying Fractions and Mixed Numbers With a focus on the multiplication of fractions, students explore multiplying fractions by whole numbers. They learn to find the percent of a number, to multiply fractions by fractions, and to simplify before multiplying fractions. They consider a real-world application of these skills, and then discuss the difference between mixed numbers and improper fractions, as well as how to convert from one to the other and back. They also investigate how to multiply mixed numbers.

Unit 9 - Dividing with Fractions In this unit students begin with dividing whole numbers by fractions and explore a real-world application of this skill. They continue with dividing fractions by fractions, dividing mixed numbers, and dividing mixed numbers and fractions. They use multiplication to ascertain that decimals and fractions are two ways of writing the same number.

Unit 10 - Common and Uncommon Denominators Beginning with a review of adding and subtracting fractions that have common denominators, students next review how to find the least common multiple. They then explore adding and subtracting fractions with uncommon denominators. They compare and contrast the four operations by performing them all on the same pair of fractions.

Unit 11 - Integers and Rational Numbers Students explore a real-world use for integers and then study graphing, absolute value, and comparing and ordering integers. Next, they define rational numbers and learn to compare and order them. They learn to locate and graph ordered pairs, and they explore rational numbers on the coordinate plane. Following this unit students are presented with the Mid-Term Review and Exam.

Unit 12 - Expressions, Exponents, and Variables In this unit students examine variables. They discuss the parts of an expression and determine how to write verbal phrases as expressions. They explore the use of exponents and study the order of operations. They discuss substituting values for variables and using substitution in algebraic expressions.

Unit 13 - Mathematical Properties and Expressions Students discuss seven properties of mathematics and learn to use the distributive property to perform mental multiplication. They study equivalent expressions and use the distributive property to rewrite and to factor expressions. They explore simplifying by combining like terms and delve deeper into equivalent expressions.

Unit 14 - One-Step Equations After reviewing equations, students investigate solving them with substitution. They learn to solve and write one-step addition, subtraction, multiplication, and division equations, and they practice solving one-step equations.

Unit 15 - Solving Equations with Decimals Continuing their study of solving equations, students consider using decimals in this operation. They study using decimals to solve addition, subtraction, multiplication, and division equations. Next, they get extra practice solving equations with decimals.

Unit 16 - Solving Equations with Fractions and Cross Products Fractions are the next number type that students study in connection with equations. They investigate and practice solving addition, subtraction, multiplication, and division equations with fractions. They also learn to solve percent problems, and to solve equations with cross products.

Unit 17 - Functions and Inequalities Students discover functions and learn about function tables. They explore geometric and arithmetic sequences and function rules and write equations representing functions. They investigate functions on the coordinate plane, graph linear functions, and study real world functions in the form of tables and graphs. Next, they consider inequalities, and learn to write and graph them.

Unit 18 - Two-Dimensional Figures Beginning with a review of polygons, students study two-dimensional figures. They learn to find area and apply this skill to parallelograms. They explore finding missing lengths of parallelograms and finding the area of triangles and trapezoids. They investigate polygons on the coordinate plane and finding their area and perimeter. They also discover how to find the area of composite figures.

Unit 19 - Three-Dimensional Figures In this unit students analyze three-dimensional figures. They learn to find the volume of rectangular and triangular prisms, and to apply these skills in the real world. They also master finding fractional side lengths.

Unit 20 - More Three-Dimensional Figures Students learn what surface area is and how to measure it. Next, they are taught what nets are, and how to use them to find surface area.  They apply these new skills with rectangular prisms, triangular prisms, and with pyramids.

Unit 21 – Statistics In this final unit students practice understanding and identifying statistical questions. They next explore dot plots, followed by the measures of center - mean, mode, and median - and the measures of variation - range. They investigate mean absolute deviation and choosing appropriate measures, and analyze line plots, histograms, box plots, and the shape of data. This unit is followed by the Final Review and Exam.