COMPARING INTEGERS 6.1.1.1 Locate positive rational numbers on a number line & plot pairs of positive rational numbers on a coordinate grid. 6.1.1.7 Convert between equivalent representations of positive rational numbers.

11.1 Notes Comparing Integers Integers – whole numbers, including zero Opposites – numbers that are the same distance from zero on a number line, but in opposite directions The further a number is to the right on the number line, the greater it’s value. When ordering integers from least to greatest follow the order on the number line from left to right. Absolute Value – a number’s distance from zero on the number line (Always Positive)

I can… Self Assessment Locate integers on a number line Compare and order integers Find the absolute value of a number Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Rational Numbers (#s that can be written as a fraction) Integers Fractions/Decimals Whole Numbers (Positive Integers) Negative Integers

VOCABULARY… Integers – whole numbers, including zero Opposites – numbers that are the same distance from zero on a number line, but in opposite directions -3 -2 -1 0 1 2 3

…-3, -2, -1, 0, 1, 2, 3… Negative Numbers Positive Numbers …-3, -2, -1, 0, 1, 2, 3… Opposites = same distance from 0 on a number line. The opposite of -3 is 3. To the left of 0 = Negative #s get smaller To the right of 0 = Positive #s get larger

THE VALUE OF OUR NUMBERS… Numbers increase in value from left to right on a number line. Negative Positive Zero (0) is neither negative nor positive. Zero (0) is a neutral number. Zero (0) has no opposite number.

Comparing Integers The further a number is to the right on the number line, the greater it’s value. < Ex: -3 ___ -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . -1 is on the right of -3, so it is the greatest.

Comparing Integers The farther a number is to the right on the number line, the greater it’s value. > Ex: 2 ___ -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . 2 is on the right of -5, so it is the greatest.

Comparing Integers The farther a number is to the right on the number line, the greater it’s value. Ex: 0 ___ -2 > -5 -4 -3 -2 -1 0 1 2 3 4 5 . . 0 is on the right of -2, so it is the greatest.

Your Turn… < a. -13 ___ 4 b. -4 ___ -7 < c. -156 ___ 32 <

Ordering Integers When ordering integers from least to greatest follow the order on the number line from left to right. Ex: 4, -5, 0, 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . . . Least to greatest: -5, 0, 2, 4

Ordering Integers When ordering integers from greatest to least follow the order on the number line from right to left. Ex: -4, 3, 0, -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . . . Greatest to least: 3, 0, -1, -4

Your Turn… -5, -1, 4 Graph –1, 4, and –5 on a number line. Order the numbers from least to greatest -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5, -1, 4

Your Turn… Order -8, 2, -3, 0, -9 from least to greatest. Order -67, 40, 2, -4, -24 from greatest to least -9, -8, -3, 0, 2 40, 2, -4, -24, -67

VOCABULARY… Absolute Value – a number’s distance from zero on the number line 2 The result from an absolute value will always be positive!

It takes two jumps from 0 to 2. Absolute Value The distance a number is from zero on the number line. Symbols: |2| = the absolute value of 2 Start at 0, count the jumps to 2. -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes two jumps from 0 to 2. |2| = 2

Start at 0, count the jumps to -4. It takes four jumps from 0 to -4. Absolute Value The distance a number is from zero on the number line. Ex: |-4| = Start at 0, count the jumps to -4. -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes four jumps from 0 to -4. |-4| = 4

Try This: |15| = _____ b. |-12| = _____ c. |-9| + 4 = _____ d. |13 - 5| = _____ 15 12 13 8

I can… Self Assessment Locate integers on a number line Compare and order integers Find the absolute value of a number Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

11.1 Notes Comparing Integers Integers – whole numbers, including zero Opposites – numbers that are the same distance from zero on a number line, but in opposite directions The further a number is to the right on the number line, the greater it’s value. When ordering integers from least to greatest follow the order on the number line from left to right. Absolute Value – a number’s distance from zero on the number line (Always Positive)