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

Poll

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