Chapter 1
Decimal Notation:Understanding what a decimal is, and using them in calculators, fractions, negative numbers, and estimation.
Decimals for Whole Numbers
Introduces the decimal system, and talks about place values (tens, hundreds, thousands, etc) and their names.
Decimals for Numbers Between Whole Numbers
This section discusses number lines and continues to talk about names for decimal places (tenths, hundredths, etc)
Estimating by Rounding Up or Rounding Down
This section talks about the idea of Estimation and how it can be used to check answers and find easier problems.
Estimating by Rounding to the Nearest
This section talks about which numbers should typically be rounded up(numbers ending in 5-9), and which numbers should be rounded down (numbers ending in 0-4)
Knowing Your Calculator
Talks about the basics of using a calculator
Decimals for Simple Fractions
How to convert simple fractions into decimals
Decimals for Mixed Numbers
How to convert simple fractions with a whole number part into decimals.
Negative Numbers
An introduction to negative numbers
Comparing Numbers
Talks about ordering numbers and finding numbers bigger or smaller than other numbers. Introduces inequality symbols <, >, ≤, ≥, ≠
Equal Fractions
Finding equivalent fractions
Chapter 2
Large and Small Numbers: Multiplying and dividing by various forms of 10, 100, 1000, and 0.1, 0.01, and 0.001
Multiplying by 10, 100, 1000
How to multiply by 10, 100, and 1000
Exponents and Powers
What an exponent or power is.
Scientific Notation
What Scientific Notation is and how to change numbers into this format.
Chapter 3
Measurement: Different measurement systems and how to convert between them.
Chapter 4
Variable Usage: Order of operations as well as what a variable is and how to use them.
Order of Operations
This section talks about PEMDAS and how to use it.
Describing Patterns with Variables
This section goes over patterns and how to describe them with variable. It also talks about such things as instances. Remember that an instance is an example.
Translating words into algebraic expressions
How to change words into algebra is the topic of this section. Make sure you understand what sum and product means.
Evaluating Algebraic Expressions
This section covers substitution, or how to take numbers and put them into algebraic expressions.
Parentheses
PEMDAS returns this time with a focus on the first letter:P for parentheses.
Grouping Symbols
Brackets are just a different type of parentheses.
Formulas
Formulas are mathematical expressions where the letters stand for some function. For instance, the area of a rectangle is A = l x w.
Probability
Probability is the chance of something happening, and in this section topics like biased, fair, and also the probability formula for equally likely outcomes.
Open Sentences
An Open Sentence is an equation that uses variables.
Inequalities
Inequalities are mathematical sentences that use symbols other than the equal sign(≠, >, ≥, <, and ≤). This chapter covers how to write and graph inequalities.
Chapter 5
Patterns Leading to Addition: Rules for addition and various problems related to adding such as angles and perimeter
Models for Addition
General methods and ideas to keep in mind when adding.
Zero and Opposites
Once you really start to use the number zero, things in mathematics start to get strange. Topics such as Property of Opposites, and the Opposite of Opposites Property, and the Additive Identity Property of Zero
Rules for Adding Positive and Negative Numbers
This section details some strategies when dealing with adding Negative Numbers. There are several different methods including using a number line, a calculator, and finding the Absolute Value
Combining Turns
Adding angles is no different than adding other numbers. You just have to remember certain vocabulary.
Adding Positive and Negative Fractions
This section is all about adding and subtracting with negative numbers, but this time we're using fractions! Remember that the only way to add fractions is to make sure their denominator (bottom number) is the same.
Adding Probabilities
This section extends the idea of adding fractions by adding fractional probabilities.
The Commutative and Associative Properties
Covers the Commutative Property of Addition and the Associative Property of Addition
Solving x + a = b
How to solve basic algebraic equations of the form x + a = b
Polygons
This section deals with the properties of polygons
Adding Lengths
This section talks about perimeter, distances between points, and similar problems.
Chapter 6
Problem Solving: How to solve problems and use logic to make problems easier to solve.
Being a Good Problem Solver
This talks about some simple ways on how to be a good problem solver.
Read Carefully
This is a problem solving section that focuses on word problems and strategies how to solve them.
Draw a Picture
This section shows how drawing pictures can help in solving problems
Trial and Error
When trying to solve problems, don't expect to get it right the first time. If one strategy doesn't work, try something else!
Make a Table
Sometimes making a table of all the possible solutions can point to a solution when trying to solve problems.
Use a Spreadsheet
Computers were made to solve problems easier than we could before. Spreadsheets are a type of computer software that can solve certain types of problems.
Special Cases and Simpler Numbers
This section talks about how to make a problem easier in order to solve it. For instance, trying an example and changing numbers so they simplify the problem are two good strategies for problem solving
Chapter 7
Patterns Leading to Subtraction: Rules for subtraction and various problems related to subtraction such as angles and lines.
Two Models for Subtraction
This chapter talks about certain ways to think about subtraction that will help for the section ahead. You need to be able to not only subtract numbers, but also angles
The Slide Model for Subtraction
The slide model is basically using a number line to subtract numbers.
Solving x - a = b
We delve a little into algebra here and try to solve a simple equation of the form x - a = b
Solving a - x = b
If you switch the x and the a around, you get a slightly different problem that needs to be solved, and there are different ways to do it.
Counting and Probability with Overlap
This section talks about finding the probability of multiple events when they aren't dependent on each other (they overlap). We also talk about Venn Diagrams here.
Angles and Lines
Introduces vertical angles as well as finding supplementary angles and complimentary angles.
Angles and Parallel Lines
When dealing with parallel lines, there are many properties and relationships between the angles of their transversal, or line cutting across the parallel lines.
Special Quadrilaterals
This takes the section on parallel lines and shows how the topics in section 7-7 can be used when applied to quadrilaterals.
The Triangle-Sum Property
The inside angles (otherwise known as interior angles) of a triangle add up to 180º. This section involves properties that test your knowledge of this.
Chapter 8
Displays: How to display information and read displayed information. Also there is some working with various transformations such as translations, reflections, symmetry, and tessellations.
Chapter 9
Patterns Leading to Multiplication: Rules for multiplication and the various problems related to multiplication such as volume, fractions, and negative numbers.
Chapter 10
Multiplication and Other Operations: Solving various algebra equations, finding surface area, and areas of triangles and trapezoids.
Chapter 11
Patterns Leading to Division: Rules for division and various problems related to division such as fractions, negative numbers, and proportion.
Chapter 12
Real Numbers, Area, and Volume: Square Roots, the Pythagorean theorem, circle area and circumference, cylinder Surface Area and volume, spheres.
Chapter 13
Coordinate Graphs and Equations: Graphing equations and solving equations by graphing.