​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