Adding and subtracting integers Mrs. Landon

Goal: add integers with the same sign How do you add integers with the same sign? When in real life do you use integers? Integer: Any whole number that is positive, negative, or zero

Lesson 1.1 Adding and Subtracting Integers Integer: Any whole number that is positive, negative, or zero Non-integers consist of fractions that can be written as terminating or repeating decimals. A terminating decimal comes to a complete stop. A repeating decimal continues the same digit or block of digits forever.

Rational Number: any number that can be written as ratio in the form of a / b where a and b are both integers and b is NOT zero. In order to be a rational number, the decimal form of the number either terminates or has a repeating pattern. (Define: terminates and repeats)

Let’s Explore With your partner go through page 7 and answer the few questions you are presented with. Raise your hand when you are finished. Then complete page 8!

Adding integers with like signs STEP 1: Find the absolute value of each number Absolute value: a distance of the number from zero on the number line. Written as || Practice |8|= |-8| = |-2| = |4| =

STEP 1: Find the absolute value of each number Absolute value: a distance of the number from zero on the number line. Written as || STEP 2: Find the sum of the absolute values 7 + 6 = 13 -7 + (-6) = -13 STEP 3: Use the sign of the integers to write the sum. 5 + 4 = 9 -5 + (-4) = -9

Commutative property of addition Does this property apply when adding two negative integers? Definition of Commutative Property of Addition: The Commutative Property of Addition states that changing the order of addends does not change the sum, i.e. if a and b are two real numbers, then a + b = b + a. So does -5 + (-4) = -4 + -5 ?

Critical Thinking Choose any two negative integers. Is the sum of the integers less than or greater than the value of either of the integers? Will this be true no matter which two negative integers?

Using a number line -2 + -1 = 1 + 4 =

Your Turn 1. -8 + (-6) = 2. 102 + 18 = 3. -42 + (-16) = 4. -8 + (-8) = 1. -8 + (-6) = 2. 102 + 18 = 3. -42 + (-16) = 4. -8 + (-8) = 5. 12 + 19 =

Your Turn Page 9 # 7-14

1-2 Goal: Adding integers with different signs How do you add integers with different signs? Example: At the school fundraiser for the band, your class raised $300, but you spent $28 on supplies to raise the money. How can you express the actual amount you earned as the SUM of two integers with DIFFERENT signs?

Adding on a number line Example: 4 + (-3) Start at 4. Move 3 units to the left (in the negative direction) 4 + (-3) = _________

Let’s Try -4 + 2 -4 + 2 = _______ Page 13 practice Start at -4 Move to the right 2 spaces -4 + 2 = _______ Page 13 practice

Modeling sums of integers with different signs Each yellow represents a positive integer and each red represents a negative integer. 4 + (-1) Start with 4 positive counters Add 1 negative counter Form zero pairs (add a negative and a positive to get a zero) What is left when you remove the zero pairs is the sum. 3 positive counters are left so 4 + (-1) = 3 Page 14 practice

Numerical Step 1: Find the absolute value of each addend. Step 2: Subtract the lesser absolute value from the greater absolute value. Step 3:Use the sign of the integer with the greater absolute value for the sum Practice – 11 + 6

Adding Integers Adding Integers Example Same signs Add the absolute value of the integers. Use the common sign for the sum 3 + 5 =8 -2 + (-7) = -9 Different signs Subtract the lesser absolute value from the greater absolute value. Use the sign of the integer with the greater absolute value for the sum -3 + 5 = 2 -10 + 1 = -9 A number and its opposite The sum is 0. The opposite of any numbers is called its additive inverse 4 + (-4) = 0 -11 + 11 = 0

Choose your method 1. - 37 + 37 = 2. 12 + (-4) = 3. 10 + (-15) = 1. - 37 + 37 = 2. 12 + (-4) = 3. 10 + (-15) = 4. -23 + 4 = 5. -4 + (-6) =

Answer 1. - 37 + 37 = 0 2. 12 + (-4) = 8 3. 10 + (-15) = -5 1. - 37 + 37 = 0 2. 12 + (-4) = 8 3. 10 + (-15) = -5 4. -23 + 4 = -19 5. -4 + (-6) = -10

Your Turn Page 15 # 3-10 Individual practice page 16 ODD 1, 3, 5, 7, 9, 11, 13 (CHECK) Homework: EVENS

1.3 Subtracting integers Goal: How do you subtract integers? Consider the following: you have $10 but you want to buy something that costs $15, so you borrow $5 and have a $5 debt. You can write this as 10-15 = -5. How would you subtract a great number from a lesser number?

Modeling subtraction You can use counters to find the difference of two integers Model -3 – (-2) Start with 3 negative counters to represent -3 Take two negative counters away to represent subtracting -2 What is left? 1 negative counter So -3 – (-2) = -1

Your turn -5 – (-3) Start with 5 negative counters to represent -5 Take three negative counters away to represent subtracting -3 What is left? 2 negative counter So -5 – (-3)= -2

Subtract using model method Start with 6 positive counters to represent 6 You need to take away 3 negative counters, so add 3 zero pairs. What is left? 9 positive counters So 6 – (-3) = 9

Your turn: 4 – (-2) = Model 4 – (-2) = Start with 4 positive counters to represent 4 You need to take away 2 negative counters, so add 2 zero pairs. What is left? 6 positive counters So 4 – (-2) = 6

Your turn 1. -2 – (-4) = 2. -5 – (-4) = 3. 6 – (-4) = 4. 7 – (-2) = 1. -2 – (-4) = -2 – (-4) = 2 2. -5 – (-4) = -5 – (-4) = -1 3. 6 – (-4) = 6 – (-4) = 10 4. 7 – (-2) = 7 – (-2) = 9

Subtracting on a Number line To model the difference of 5-3 , you start at 5 and move 3 units to the left. NOTICE: 5 - 3 = 5 + (-3) . Subtracting 3 is the same as adding its opposite, -3 You can use the fact that subtracting a number is the same as adding its opposite to find the difference of two integers.

Number Line: -1 – 5 Practice Rewrite subtraction as addition of the opposite -1 – 5 = -1 + (-5) Practice 1. -4 – 6 = -4 + (-6) 2. -6 – 2 = -6 + (-2) 3. -7 – (-3) = -7 + 3 = 4. -6 – (-2) = -6 + 2 =

To graph on a number line Example: -1 – 4 Rewrite subtraction as addition of the opposite -1 + 4 Start at -1 and move 4 units to the left. The difference is 3

Practice -5 – (-2) Rewrite subtraction as addition of the opposite - 5 – (-2) = -5 + 2 Start at _____ and move _____ units to the _________. The difference is _________

Your Turn Complete page 19, 20 and the top of page 21 to practice modeling integer subtraction and subtracting on a number line

Subtracting integers by adding the opposites Step 1: Write the subtraction expression Step 2: find the difference by adding the opposite. The temperature on Monday was -5 °Celsius. By Tuesday the temperature rose to -2 °Celsius. Find the change in temperature. Final temperature – Monday’s temperature = change in the temperature. -2 °C – (-5 ° C) = the change -2 + 5 = 3 ° C

Complete page 21 and the top of page 22 GET IT CHECKED Complete page 22

1.4 Applying addition & Subtraction of Integers Goal: How do you solve multistep problems involving addition and subtraction of integers? Over a period of four hours, the temperature rose 3°F, rose 2°F, dropped 4° F, and dropped 1°F. IF the starting temperature was -2 °F, what was the temperature after four hours?

What is the total change in Mei’s checking account if she writes a $35 check for shoes, deposits $50, and then writes a $55 check for a sweater?

In Round 1 of a game, a student loses 5 points, loses 3 points, gains 17 points, and loses 7 points. What is the students score at the end of the Round 1?

Let’s look at page 25 and work through the problem Complete page 25 # 1

Property Review When would we use the Commutative Property? The Commutative Property of Addition states that two or more numbers can be added in any order without changing the sum. 8 + 20 = 20 + 8 When would we use the Associative Property? The Associative Property of Addition states that for all real numbers, a, b, and c, the sum is always the same, regardless of the grouping. 2 + 3+ 8 = (2 +3) + 8 = 2 + (3+8)

How can you use the Properties to Solve? What is the total change in Mei’s checking account if she writes a $35 check for shoes, deposits $50, and then writes a $55 check for a sweater?

How can you use the Properties to Solve? In Round 1 of a game, a student loses 5 points, loses 3 points, gains 17 points, and loses 7 points. What is the students score at the end of the Round 1?

Work on page 26 and complete #2 and 3 with your math partner. Read page 27 and complete #4

Guided Practice time Work through page 28 with your math partner. Checkpoints: 3, 9, and 12 Then work on selected level of 1.4 worksheet A/B: I get this! C: I’m bored and need a challenge! D: I’m having a little trouble