Unit 7: Rational Numbers

Students learn about negative numbers and ways to represent them on a number line and the coordinate plane, and they perform the four operations on rational numbers.

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What this unit covers

A Negative Numbers and Absolute Value · 5 lessons

Goals

• Interpret a rational number and the absolute value of a number in context.
• Plot rational numbers and their opposites on a number line; know that a number and its opposite have the same absolute value.
• Use words and symbols to compare rational numbers, where a rational number could also be the absolute value of a number.

Lessons

1. Positive and Negative Numbers
2. Comparing Positive and Negative Numbers
3. Ordering Rational Numbers
4. Absolute Value of Numbers
5. Comparing Numbers and Distance from Zero

B Adding and Subtracting Rational Numbers · 5 lessons

Goals

• Apply addition and subtraction of signed numbers to represent situations and solve problems.
• Calculate the sum or difference of two rational numbers.

Lessons

1. Changing Temperatures
2. Changing Elevation
3. Money and Debts
4. Representing Subtraction
5. Finding Differences

C The Coordinate Plane · 3 lessons

Goals

• Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
• Use coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
• Working in all four quadrants, plot a point given its coordinates, or identify the coordinates of a given point in the coordinate plane.

Lessons

1. Constructing the Coordinate Plane
2. Interpreting Points in a Coordinate Plane
3. Distances in the Coordinate Plane

D Multiplying and Dividing Rational Numbers · 4 lessons

Goals

• Apply multiplication and division of signed numbers to represent situations and solve problems.
• Calculate the product or quotient of two rational numbers.

Lessons

1. Multiplying Rational Numbers
2. Multiply!
3. Dividing Rational Numbers
4. Negative Rates

E Four Operations with Rational Numbers · 4 lessons

Goals

• Apply the four operations with rational numbers to solve problems.
• Solve an equation of the form x + p = q or px = q, where p, q, and x are rational numbers.
• Write an equation of the form x + p = q or px = q (where p, q, and x are rational numbers) to represent a situation.

Lessons

1. Expressions with Rational Numbers
2. Solving Problems with Rational Numbers
3. Solving Equations with Rational Numbers
4. Representing Contexts with Equations

F Let's Put It to Work · 2 lessons

Lessons

1. Drawing in the Coordinate Plane (Optional)
2. The Stock Market