Lesson 1.25.23

Reasoning with Rational Numbers

Positive and Negative Rational Numbers

Multiple Choice

Today we will be working with

• Positive and negative numbers

• Negative numbers

• Positive numbers

Introduction

After a day of shopping, you realized that you spent more money than what you had in your bank! How much money do you need to ask your relatives in order to cover what you spent? Is there a way mathematically to keep this situation from happening again?

In this module, you will apply what you learned in sixth grade concerning the four operations--multiplication, division, addition, and subtraction--and expand it to work with rational numbers. Rational numbers are what we use in almost every area of life, especially in shopping!

• Evaluate expressions the involve adding and subtracting rational numbers

• Calculate the value of positive and negative rational numbers

• Evaluate the addition and subtraction of rational numbers to describe real-world contexts

By the end of this lesson the student will be able to:

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.

NC.7.NS.1

Standard & Objective

Open Ended

If you go out in the morning and the weather report says that the temperature will drop and rise throughout the day, how do you know if you’ll need a sweater or not?

You can decide on the sweater if you know how to add and subtract rational numbers.

In this lesson, we will review from sixth grade by building a model of the number system and expand it to work with rational numbers.

Specifically, in this lesson, we will build by applying what we already know about adding and subtracting to positive and negative values.

Match

Use the time to go to Canvas and review Unit 5 Key Terms and then match the following.

• rational numbers

• integers

• absolute value

• number line

• complex fraction

A number that can be written as a fraction by dividing two integers

Positive numbers and their opposites. No fractions or decimals allowed.

The non-negative value of a number or a number's distance from zero on a number line.

A visual tool that shows the location of numbers

A fraction in which the numerator, denominator, or both contain fractions

• A number that can be written as a fraction by dividing two integers

• Positive numbers and their opposites. No fractions or decimals allowed.

• The non-negative value of a number or a number's distance from zero on a number line.

• A visual tool that shows the location of numbers

• A fraction in which the numerator, denominator, or both contain fractions

What is a Rational Number?

• A real number that can be made by dividing two integers (an integer is a positive or negative whole number, like -4, 0, 2, etc.).

• Rational numbers include integers, fractions, and most decimals (finite or repeating).

• Natural numbers 1,2,3, etc.

• Whole numbers are natural numbers with the addition of 0

Some Examples of Rational Numbers

Multiple Select

Select all that are rational numbers

• 0.24

• -14.2

• $$2\ \frac{1}{5}$$

• $$-\frac{5}{6}$$

• $$0.\overline{3}$$

Positive & Negative Numbers

Rational numbers that are on a number line (Integers)

Another way to explain whole numbers and their opposites

Numbers less than zero are negative integers and Numbers more than zero are positive integers.

Multiple Choice

How are positive numbers represented on a number line?

• an arrow to the right

• an arrow to the left

• An arrow at 0

Open Ended

How does the diagram represent the situation?

Multiple Choice

How can we represent an increase in temperature on a number line?

• an arrow pointing to the left

• an arrow at 0

• an arrow pointing to the right

Draw

Start: +40

Change: 5 degrees colder

Multiple Choice

How can we represent a decrease in temperature on a number line?

• an arrow to the right

• an arrow at

• an arrow to the left

​Adding Integers

​1. -5 +9

​

​2. 8 + -19

​

​3. -13 + -4

Multiple Choice

-16 + -8

• -8

• 24

• -24

• 8

Multiple Choice

-14 + 8

• -6

• 6

• 22

• -22

Open Ended

After completing the last two problems: -16 + -8 and -14 + 8, what do you notice and what do you wonder?

Keep in Mind throughout upcoming lessons:

INTEGER SONG (ROW ROW ROW YOUR BOAT)

• SAME SIGNS ADD & KEEP

• DIFFERENT SIGNS SUBTRACT

• USE THE SIGN OF THE LARGER NUMBER

• THEN YOU'LL BE EXACT