1 | Ratios and Rates | - How do we know when two ratios are equivalent?
- How can we use a table to represent a ratio relationship?
- How can we use rates to make comparisons? | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. |
2 | Rational Numbers | -How do we identify the opposite of a number?
- How do we put numbers in order?
-How do we know if a quantity should be labeled as positive or negative?
-How do we graph a point in a four quadrant coordinate plane?
-How do we find the distance between two points?
-How do we identify decimals, fractions and percents that represent a situation?
-How do we make a model to represent a part, whole and percent of a situation? | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Understand ordering and absolute value of rational numbers.
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. |
3 | Expressions and Equations |
- What is the correct order of operations to evaluate an expression?
- How can we use multiplication to represent repeated addition?
- How can we use exponents to represent repeated multiplication?
- How can we determine whether two expressions are equivalent?
- How can we work backwards to solve an equation?
- How do the rules of arithmetic apply to expressions with variables? | Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
Apply the properties of operations to generate equivalent expressions.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. |
