MGSE7.NS.1

Number Systems: Operations with Rational Numbers (1)

MGSE7.NS.1a Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00. 

​Learning Targets

I can explain subtraction using additive inverse representing it with two-sided counters, number lines, algebra tiles, and equations.

I can represent the distance between two rational numbers on a horizontal or vertical number line.

I can estimate the difference between two rational numbers (e.g. the difference of -33 and 10 is about 40 rather than about 20).

I can apply the properties of operations to add and subtract rational numbers (e.g. The Associative Property can be used to reorder addends for efficiency, -13 + 27 - 7 can be thought of as -13 + -7 + 27 or -20 + 27).

I can solve real-world and mathematical problems with rational numbers and absolute value.

COPY THE NOTES IN YOUR NOTEBOOK!!!

​Essential Vocabulary

​Additive Inverse ● Multiplicative Inverse ● Absolute Value ● Integers ●Irrational Numbers ● Long Division ● Natural Numbers ● Negative Numbers ● Opposite Numbers ● Positive Numbers ● Rational Numbers ● Repeating Decimal ● Terminating Decimal ●Whole Number● Zero Pair

​Essential Questions

● What strategies are most useful in helping develop algorithms for adding, subtracting, multiplying, and dividing positive and negative rational numbers?

● What are the steps to converting a rational number to a repeating or terminating decimal?

Types of Numbers

• Natural Numbers ( 1, 2, 3, 4, 5...)

• Whole Numbers ( 0,1,2,3,4,5...) Includes 0 and all natural numbers

• Integers (..., -3, -2, -1, 0, 1, 2, 3...)

• Rational Numbers ( All Natural, Whole, Integers, fractions, and decimal numbers) can be written as a ratio

• Irrational Numbers- Can not be written as a ratio. Ex. Pi

Absolute Value

• distance a number is from zero along a number line

• Simply put, is just asking you how far away -4 is from zero.

• Since distance is always a positive number (you can't travel "negative" steps, just steps in a different direction), the result of absolute value is always positive.

Additive Inverse

• Another name for Additive Inverse is "Opposite"

• Example 3 and -3

• Opposites are an equal distance from zero.

• Their sums are zero

Open Ended

Choose one word from the image that describes a negative number.

Open Ended

Choose one word from the image that describes a positive number.

Multiple Choice

The lowest recorded temperature in Antarctica was about 90°F below zero. The highest recorded temperature in Antarctica was about 15°F. Which integer represents the highest recorded temperature in Antarctica?

• -90

• 15

• -15

• 90

Multiple Choice

What is the result of adding 3 to −3?

• -6

• 0

• 9

• -9

Multiple Choice

What is the result of adding 20 to −20?

• -40

• 20

• 0

• -20

Multiple Choice

An elevator is on the 10th floor. It goes down 6 floors and then up 4 floors. What floor is the elevator on now?

• 6th floor

• 7th floor

• 8th floor

• 9 floor

Fill in the Blanks

A car is traveling at a speed of 65 mph. The car slows down 18 mph because of traffic, and then increases its speed by 13 mph. What is the car's speed now?

Fill in the Blanks

What is the absolute value of -5

Fill in the Blanks

What is the absolute value of 2

Poll

When it comes to the lesson for today, I am

• An expert

• Proficient

• Unsure

• Need Help