## Course Overview

In this 6th Grade math course, students enhance computational and problem-solving skills while learning topics in algebra, geometry, probability, and statistics. They solve expressions and equations in the context of perimeter, area, and volume problems while further developing computational skills with fractions and decimals. The study of plane and solid figures includes construction and transformations of figures. Also in the context of problem solving, students add, subtract, multiply, and divide positive and negative integers and solve problems involving ratios, proportions, and percents, including simple and compound interest, rates, discount, tax, and tip problems. They learn multiple representations for communicating information, such as graphs on the coordinate plane, statistical data and displays, as well as the results of probability and sampling experiments. They investigate patterns involving addition, multiplication, and exponents, and apply number theory and computation to mathematical puzzles.

## Course Outline

### SEMESTER 1

#### Unit 1: Problem Solving

Mountain climbing involves solving different kinds of problems. Just like solving math problems, climbing requires tools and a solid strategy. In this unit, you will learn about number lines, the order of operations, and problem solving. To solve problems, you will learn how to translate between words and math symbols, and you will use strategies such as drawing figures, estimating, and breaking a problem down into smaller parts. You will also learn how to handle precision and reasonableness.

- Semester 1 Introduction
- Foundations
- On the Number Line
- Order of Operations
- Number Properties
- Translating Between Words and Math
- Translating Mixed Operations
- Problem-Solving Strategies
- Getting to the Core: Problem Solving
- Identifying Information in Word Problems
- Precision
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 2: Distance: Addition and Equations

If a farmer has painted part of a fence, how much more does she need to paint? Addition equations can help the farmer solve a problem like that one. In this unit, you'll learn how to use units to measure distance and perimeter. You'll also solve addition and subtraction equations and discover how those equations can give rise to the idea of negative numbers. Finally, you will use absolute value and operations with positive and negative numbers to solve problems.

- Foundations
- Units of Distance
- Polygons and Perimeter
- Addition and Subtraction Equations
- Applications of Addition and Subtraction Equations
- Getting to the Core: Addition and Subtraction
- Your Choice
- Negative Numbers
- Absolute Value and Distance
- Addition and Subtraction with Negative Numbers
- Getting to the Core: Negative Numbers
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1

#### Unit 3: Area: Multiplication Equations

A general contractor needs to calculate area to determine the amount of wood for a floor. In this unit, you'll learn how to compute the areas of squares, triangles, rectangles, and other polygons. You will also learn how to divide to find an unknown side length and how a square root relates a side length to the area of a square.

- Units of Area
- Areas of Rectangles
- Special Quadrilaterals
- Getting to the Core: Similar Parallelograms
- Your Choice
- Areas of Triangles
- Figures Made Up of Triangles and Parallelograms
- Unknown Side Lengths: Division
- Getting to the Core: Modeling by Restructuring
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 4: Working with Rational Numbers

Most two-by-fours are actually about 1-1/2 inches by 3-1/2 inches. Any carpenter working with lumber is also working with rational numbers.In this unit, you will learn how to change between various representations of rational numbers including equivalent fractions and decimals. You'll also add, subtract, multiply, and divide rational numbers and use these skills to solve practical problems.

- Foundations
- Primes and Composites
- Using Prime Factorization
- Equivalent Fractions
- Representing Rational Numbers
- Comparing Rational Numbers
- Your Choice
- Perimeters with Fractions
- Areas with Fractions
- Dividing Fractions
- Solving Problems with Fraction Division
- Getting to the Core: Fractions
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 5: Solids

When shipping merchandise, you need to know the volume of the container to determine how much it will hold. In this unit, you will learn how to find the volume and surface area of shapes such as prisms and pyramids. You will also find out how a cube root connects the volume of a cube to its side length.

- Foundations
- Cubes and Cube Roots
- Volumes of Prisms
- Nets of Solids
- Getting to the Core: Measuring Volume
- Your Choice
- Surface Area: Prisms and Pyramids
- Properties of Volume and Surface Areas
- Getting to the Core: Volumes and Surface Areas
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 6: Comparisons: Ratios

In southern Asia and South America, some mosquitoes carry a disease called malaria. How can you compare how efforts to fight the disease are progressing in various countries? Scientists and doctors use ratios to understand many problems. In this unit, you will use ratios and proportions to solve many different problems. For instance, you will compute interest on loans, as well as calculate taxes, tips, and discounts.

- Foundations
- Ratios as Comparisons
- Percent
- Finding Percents of Numbers
- Your Choice
- Getting to the Core: Understanding Ratio and Percent
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 7: Semester Review and Test

- Semester Review
- Semester Test

### SEMESTER 2

#### Unit 8: Statistics

Every jelly bean can be described. Each one has color, flavor, mass, and number of calories. The language and tools of statistics help to describe buckets full of data. In this unit, you will learn how to create and interpret statistical graphs including circle graphs, bar graphs, line plots, line graphs, box-and-whisker plots, and histograms. You'll also learn how to calculate and interpret measures of center and variation. Finally, you will learn how sampling can help you make decisions about a population.

- Semester 2 Introduction
- Foundations
- More Statistical Graphs
- Histograms
- Getting to the Core: Understanding Data Displays
- Your Choice
- Measures of Center
- Box-and-Whisker Plots
- Getting to the Core: Distribution of Data
- Measures of Variation
- Statistical Claims
- Getting to the Core: Interpreting Data Sets
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 9: The Second Dimension

Scientists can use data to figure out how tall someone was from a single bone. When you have two variables, such as femur length and overall height, a two-dimensional plot can help you see patterns and make predictions. In this unit, you will learn how to identify and plot points on a coordinate plane. You'll then identify points that are solutions to equations with two variables and create and interpret scatter plots.

- Foundations
- Points on a Coordinate Plane
- Using Points to Solve Problems
- Equations with Two Variables
- Getting to the Core: Reflecting Points on a Coordinate Plane
- Getting to the Core: Coordinate Plane
- Your Choice
- Scatter Plots
- Interpreting Scatter Plots
- Figures on a Coordinate Plane
- Getting to the Core: Polygons on the Coordinate Plane
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 10: Rates

On average, about 1088 cubic meters of water flow over southern Africa's Victoria Falls every second. That's more than 1,000,000 liters, or enough to fill 26 Olympic-sized swimming pools every minute! In this unit, you will calculate and use rates to solve many types of problems including pricing, speed, and work problems. You'll also use direct variation and see how rates affect graphs of relationships.

- Foundations
- Rates as Comparisons
- Unit Rates
- Solving Unit-Rate Problems
- Getting to the Core: Another Look at Unit Rates
- Your Choice
- Average-Speed Problems
- Constant-Rate Problems
- Getting to the Core: Another Look at Constant Rates
- Direct Variation
- Interpreting Direct Variation
- Getting to the Core: Another Look at Direct Variation
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 11: Working with Positives and Negatives

In the stock market positive and negative numbers are key to understanding how companies stocks are valued. In this unit, you will learn how to add, subtract, multiply, and divide positive and negative numbers including decimals. You'll also work with inequalities.

- Foundations
- Adding and Subtracting Signed Numbers
- Net Gains and Losses
- Getting to the Core: Addition/Subtraction of Signed Numbers
- Your Choice
- Multiplying Signed Numbers
- Dividing Signed Numbers
- Exponents and Patterns
- Getting to the Core: Multiplication/Division of Signed Numbers
- Properties of Signed Numbers
- Inequalities
- Getting to the Core: Number Properties and Inequalities
- Unit Review 1
- Unit Review 2
- Unit Checkpoint 1
- Unit Checkpoint 2

#### Unit 12: Probability

People who play on and coach sports teams, like baseball, as well as those who follow the teams, deal with uncertainty all the time. Probability provides the tools to understand and communicate this uncertainty. In this unit, you will learn how to use Venn and tree diagrams to count the number of ways a trial can be conducted. You can use a diagram to calculate a theoretical probability. You'll also learn how to use experimental probability and the law of large numbers. Finally, you'll learn about independent, dependent, and complementary events.

- Foundations
- Counting
- Probability and Experiments
- Experimental Probability
- Theoretical Probability
- Your Choice
- The Law of Large Numbers
- Independent and Dependent Events
- Complementary Events
- Unit Review
- Unit Checkpoint

#### Unit 13: Making and Moving Figures

Two men from Southampton, England, say that they used only planks, rope, hats, and wire to make the first crop circles in the 1970s. Crop circle designs range from the simple to the complex, but anyone who makes crop circles needs to know about circles and transformations. In this unit, you will construct and transform figures. For constructions, you will use paper folding as well as a compass and a straightedge. For transformations, you will use coordinates and other methods.

- Foundations
- Folded-Paper Construction
- Compass and Straightedge Construction
- Your Choice
- Translation
- Reflection
- Rotation
- Translating with Coordinates
- Reflecting with Coordinates
- Unit Review
- Unit Checkpoint

#### Unit 14: Semester Review and Test

- Semester Review
- Semester Test