1. 9/5/13 Warm-up 1.) 2.) 3.) CHALLENGE: ANSWERS 1.) 24 2.) -24 3.) 56 CHALLENGE: zero

2. ALGEBRA 1P GAME PLAN Date9/5/13 Thursday Section / Topic Notes: 1-4 & 1-5: Adding & Subtracting Real Numbers (Day 1) GoalSWBAT add & subtract real numbers using a number line model and properties of addition. Algebra California Standard 1.0 Students identify and use the arithmetic properties of real numbers 2.0 Students understand and use such operations as taking the opposite HomeworkChoose 2 problems from each set: P. 27 #5-12 P. 28 #28-35 P. 34 #1-12 P. 34 #30-37 Announcement Quiz Wednesday, 9/11

3. Vocabulary Identity Property of Addition: The sum of a number and zero is that number Example: 5 + 0 = 5Example: 0 + -5 = -5 Additive Inverse: The opposite of a number Example: The additive inverse of 7 is -7. Inverse Property of Addition: The sum of a number and its additive inverse is zero. Example: -4 + 4 = 0 or 4 + (-4) = 0

4. -3-20123456 7 89 1. 2 + 6 2. 2 + (-6) 3. -2 + 6 4. -2 + (-6) 5. -6 + 4 6.-3 + (-8) 7. -5 + 3 8. -2 + 9 Solve

5. Same sign: Simply add them together keep the sign. Example: 2 + 6 = 8-2 + -6 = -8 Different signs: Subtract the numbers and keep the sign of the number with the greater absolute value (the “bigger” one). -2 +6 = 42 + (-6) = -4

6. Double negatives!! I amhealthy unnot - (-5) 8- (-4) =12

7. Applying Addition Evaluating Expressions Evaluate -n + 8.9 Step 1 Substitute a value for the variable n = -2.3 - ( -2.3) + 8.9 Step 2 Add a line, Change the sign, bam bam = 2.3 + 8.9 11.2 Step 3 Simplify

8. Evaluate the Expression V = 7 1.v – 13 2. -2 + v 3.8 – v 4.8 + v – 6 + v - 6 5 16

9. ALGEBRA 1 Use a number line to simplify each expression. a. 3 + (–5) 3 + (–5) = –2 b. –3 + 5 –3 + 5 = 2 Start at –3. Move left 5 units. Start at –3. Move right 5 units. c. –3 + (–5) –3 + (–5) = –8 Start at –3. Move left 5 units. Adding Real Numbers LESSON 1-4 Additional Examples

10. ALGEBRA 1 Simplify each expression. a. 12 + (–23) b. –6.4 + (–8.6) The difference of the absolute values is 11. The negative addend has the greater absolute value, so the sum is negative. Since both addends are negative, add their absolute values. The sum is negative. Adding Real Numbers LESSON 1-4 Additional Examples =- 11 = -15.0

11. ALGEBRA 1 The water level in a lake rose 6 inches and then fell 11 inches. Write an addition statement to find the total change in water level. 6 + (–11) = –5 The water level fell 5 inches. Adding Real Numbers LESSON 1-4 Additional Examples

12. ALGEBRA 1 Evaluate 3.6 + (–t) for t = –1.7. 3.6 + (–t) = 3.6 + [–(–1.7)]Substitute –1.7 for t. = 3.6 + [1.7]–(–1.7) means the opposite of –1.7, which is 1.7. = 5.3Simplify. Adding Real Numbers LESSON 1-4 Additional Examples

13. ALGEBRA 1 A scuba diver who is 88 ft below sea level begins to ascend to the surface. Define:Let r = the number of feet the diver rises. a. Write an expression to represent the diver’s depth below sea level after rising any number of feet. Write:–88+r –88 + r b. Find the new depth of the scuba diver after rising 37 ft. –88 + r = –88 + 37 Substitute 37 for r. = – 51 Simplify. The scuba diver is 51 ft below sea level. Relate:88 ft below sea level plus feet diver rises Adding Real Numbers LESSON 1-4 Additional Examples

14. -3-20123456 7 89 To subtract a number, add its opposite Example: 3 – 5 = 3 + (-5) = 2Example: 3 – (-5) = 3 + 5 = 8 1.4 – 7 2. -1 – 4 3. -3 –( -8) 4. 8 + (-5) 5.-4 – (-9) 6. - 0.5 + ( -1.3) 7. 3.7 – ( -4.3) 8. -3 + 8 -4 Solve

15. ALGEBRA 1 Find –3 – 2 using a number line. –3 – 2 = –5 Start at –3. Move left 2 units Subtracting Real Numbers LESSON 1-5 Additional Examples

16. ALGEBRA 1 Simplify each expression. a. –11.6 – (–14) = 2.4 Add. = + Use common denominators. 4949 6969 = Add. 10 9 = or 1 Write in simplest form. 10 9 1919 10 9 b. – (– ) 2323 4949 = –11.6 + 14 The opposite of –14 is 14. 2323 4949 4949 4949 = + The opposite of – is. Subtracting Real Numbers LESSON 1-5 Additional Examples

17. ALGEBRA 1 Simplify | –13 – (–21) |. | –13 – (–21) | = | –13 + 21 | The opposite of –21 is 21. = | 8 |Add within absolute value symbols. = 8Find the absolute value. Subtracting Real Numbers LESSON 1-5 Additional Examples

18. ALGEBRA 1 Evaluate x – (–y) for x = –3 and y = –6. x – (–y) = –3 – [–(–6)]Substitute –3 for x and –6 for y. = –3 – 6The opposite of –6 is 6. = –9Subtract. Subtracting Real Numbers LESSON 1-5 Additional Examples

19. ALGEBRA 1 The temperature in Montreal, Canada, at 6:00 P.M. was –8°F. Find the temperature at 10:00 P.M. if it fell 7°F. Find the temperature at 10:00 P.M. by subtracting 7°F from the temperature at 6:00 P.M. –8 – 7 = –8 + (–7)Add the opposite. = –15Simplify. The temperature at 10:00 P.M. was –15°F. Subtracting Real Numbers LESSON 1-5 Additional Examples

20. More Real World Examples A football team gains 2 yd and then loses 7yd in two plays. You express a loss of 7 yd as -7. Use addition to find the result of the two plays. 2 + (-7) = -5 The result of the two plays is a loss of 5 yd

21. Try this The temperature falls 15 degrees and then rises 18 degrees. Use addition to find the change in temperature. -15 + 18 = 3 There is a rise of 3 degrees

22. ALGEBRA 1 –511–12 –17 Simplify each expression. 1. 7 – 122. 3 – (–8)3. –7 – 5 Evaluate each expression for x = 3 and y = 4. 4. x – y5. | – y – x|6. | y – x – 5| 4 Subtracting Real Numbers LESSON 1-5 Ticket Out The Door (TOD)

23. ALGEBRA 1 Simplify. 1.15 + (– 10)2. – 57 + (– 11)3. – 42 + 19 4. – 1 + (– 3 ) Evaluate each expression for x = –5. 5. – 11 + (– x) 6. 25 + 4x 5 –68–23 –4 7 15 1515 4 15 5 – 6– 6 Adding Real Numbers LESSON 1-4 9/6/13 Warm Up

24. ALGEBRA 1P GAME PLAN Date9/6/13 Friday Section / Topic Notes: 1-4 & 1-5: Adding & Subtracting Real Numbers (Day 2) GoalSWBAT add & subtract real numbers with fractions & decimals. Algebra California Standard 1.0 Students identify and use the arithmetic properties of real numbers 2.0 Students understand and use such operations as taking the opposite HomeworkChoose 2 problems from each set: P. 27 #13-24 P. 28 #25-27, 36, & 37 P. 34 #13-20 P. 34-36 #38, 51, 55 & 61 Announcement Quiz Wednesday, 9/11

25. Find the sum. 1) -2.304 + (-0.26) Line up the decimals and add (same signs). -2.564 2) + Get a common denominator and subtract. +

26. Find the difference. 3) Change subtraction to adding the opposite. Get a common denominator. Subtract and keep sign of the larger number. +

27. Find the difference. 4) Get a common denominator and subtract. Change subtraction to adding the opposite. _ + -

28. Substitute for y: 6.32 - (-3.42) 6.32 + 3.42 9.74 5) Evaluate 6.32 – y for y = -3.42

29. Find the solution 6.5 – 9.3 = ? Answer Now A.-3.2 B.-2.8 C.2.8 D.3.2

30. Find the solution Answer Now A. B. C. D.