1. Unit 3 Simplifying Expressions

2. Let’s start with the number line: Number lines are infinite (they go on and on forever in both directions) Zero is in the center of the number line. It separates the negative integers from the positive integers. Zero is neither positive or negative. The negative integers are on the left, and the positive integers are on the right. The greater the negative number, the smaller its value (example: -16 is smaller than -15) Negative numbers that are closer to zero are higher in value than those farther away from zero. The left side of the number line is a reflective mirror image to the right side of the number line.

4. Your Task: Draw a number line that ranges from -10 to +10. Make sure to include all integers in between including zero. If you finish early … extend your number line to show values -20 to +20 and all numbers in between, including zero. *Remember, each integer should be evenly spaced on the number line, because the distance between each integer is the same, 1)*

5. Now knowing what a number line looks like, let’s compare integers 1) -5 4 2) 3 7 3) -16 -11 4) -8 4 5) 10 20 6) -7 -3 7) -5 -6 8) 2 0 9) -19 -18 10) -12 -10 Use > (greater than) or < (less than)

6. Let’s create a Human Number Line! Your Task: Using the number I gave you, SILENTLY put yourselves in order from smallest to greatest. Next… whoever is zero will stay where they are. All other numbers will move to form two lines so they are facing their opposite integer. (+1 will be facing -1 and so forth). Which integer is your opposite?

7. Name each integer’s opposite! 1) 1 2) -9 3) -30 4)18 5) 91 6) -15 7) 60 8)45 9) -54 10) -82

8. Adding positive and negative integers When adding positive and negative integers, it’s a battle!! -5 + 2 Look at the two numbers you are adding. Looking solely at the digits, not the numbers, determine which is bigger. 5 and 2, 5 is bigger The sign of your answer will be the sign of your larger digit. In this case 5 is greatest, so my answer will be negative since our problem is working with a negative 5. -5 + 2 = - ____ Now since the signs are different, we will subtract the two digits we have. 5-2 = 3 So… -5 +2 = -3

9. You can also use your number lines to simplify numeric expressions. -If you move left on your number line, you are subtracting. If you move right on your number line, you are adding. -We have the expression -5 + 2 -The first number in our expression is the number we start with on our number line. So you will start on the number -5. It then says to +2, so we will move right 2 places, which will put us at -3. -7 -6 -5 -4 -3 -2 -1 0 1 2 Adding

10. Subtracting positive and negative integers. Rules are similar to that of adding positive and negative integers. If you are subtracting a negative and a positive integer, such as -5 – 2, you will take the sign of the larger digit. Since 5 is greater than 2, our answer will be negative. Since we are subtracting 2 from -5, we are getting even smaller. We will do the opposite operation and add 5 and 2 to get 7. Therefore, our answer is -7. If we are subtracting a negative number from a negative number, we will do the following. We have -5 - -2. Take the sign of the larger digit. 5 is greater than 2, so our answer will be negative. Since we are subtracting a negative 2, the two negative signs cancel each other out, and we end up adding 2. -5 + 2 Then do the opposite operation, 5 -2 is 3 so our answer is -3.

11. You can also use your number lines to subtract!! -7 -6 -5 -4 -3 -2 -1 0 1 2 Subtracting -5 – 2 = -7 -7 -6 -5 -4 -3 -2 -1 0 1 2 -5 - -2 = -5 + 2 = -3 Adding

12. Multiplying Rules! A positive times a positive equals a positive ( 5 x 4 = 20) A negative times a negative equals a positive (-5 x -4 = 20) A negative times a positive equals a negative (-5 x 4 = -20) A positive times a negative equals a negative (5 x -4 = -20) ***When the signs are the same, the answer will be a positive integer ***When the signs are different, the answer will be a negative integer

13. Dividing Rules! ( Same as Multiplying) A positive divided by a positive equals a positive ( 20 ÷ 4 = 5) A negative divided by a negative equals a positive (-20 ÷ -4 = 5 ) A negative divided by a positive equals a negative (-20 ÷ 4 = -5) A positive divided by a negative equals a negative (20 ÷ -4 = -5) ***When the signs are the same, the answer will be a positive integer ***When the signs are different, the answer will be a negative integer

14. Transcribing written text into numeric expressions 1. Take out a piece of paper. 2. Divide it into 4 sections ( +, -, x, and ÷) 3. You have 2 minutes to think of as many mathematical words as possible that mean each of the four different operations (adding, subtracting, multiplying, and dividing). Read, Set… At the end of 2 minutes, we will go over your answers and you will fill in a notes page with all potential possibilities.

15. Adding

16. Subtracting

17. Multiplying

18. Dividing

19. Write the numerical expression for each situation. 1)The product of five and two 2) The sum of three and six 3) six less than ten 4) Two times eleven 5) The quotient of twenty and four 6) ten below thirty

20. Half of a number multiplied by 3. 3 multiplied by x subtracted by 4. April went to the grocery store and bought apples and bananas. Write an expression showing the total cost she paid for 3 pounds of bananas and 6 pounds of apples? Sydney went to the mall. She bought 4 tubes of chapstick and a pair of shoes that cost $20. Write an expression showing the total that Sydney spent at the mall. Brooke drove across the country. She drove 55 miles per hour. Write an expression showing how far she traveled.

21. GamesFlyers 312 416 520 n? What is an expression that shows that relationship between games and flyers?

22. PhotosAlbum Pages 279 3612 4515 n? What is an expression that shows the relationship between the number of photos and the number of album pages?

23. Position1234n Value of Term 57911? What is an expression that shows the relationship between the position and the value of term? Challenge!

24. Distributive Property –Let’s use distributive property to make solving these expressions easier!! 3 (45) 5(255) 8(32)

26. What is a variable? In this next section, we will be simplifying expressions with variables! Don’t be afraid! It’s a lot of fun! A couple things to remember… 1)When two numbers are separated with a dot or parenthesis, that means they are being multiplied. 52 = 52 5(2) = 10 52 = 10 2) YOU NEED TO USE YOUR ORDER OF OPERATIONS!!!

27. A couple examples! X = 5 y = 1 z = 2 Look to see what the variables equal! 1)Example: X + 3 5 + 3 8 Plug in 2) 5 – y 3) 9 + z 4) 2x 5) x+zy 2 3 45 Let’s see whatcha did!