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Thursday, August 26

Thursday, August 26. Bell Work. Fill in planner Pr. 1-4/1-5 (EVENS) Agenda for Today Grade Practice 1-3 Notes Group Work Assignment. Bell Work Answers. Sample Map Item. Objective. SWBAT Add and subtract real numbers using models and rules. Real Number Addition Rules. Rule #1.

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Thursday, August 26

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  1. Thursday, August 26 Bell Work • Fill in planner • Pr. 1-4/1-5 (EVENS) • Agenda for Today • Grade Practice 1-3 • Notes • Group Work • Assignment

  2. Bell Work Answers

  3. Sample Map Item

  4. Objective • SWBAT • Add and subtract real numbers using models and rules

  5. Real Number Addition Rules Rule #1 • If the signs are the same, pretend the signs aren’t there. Add the absolute values and then put the sign of the addends in front of your answer. 9 + 3.5 = 12.5 -9 + -3.5 = -12.5

  6. Rule #2 • If the signs are different, subtract the smaller absolute value from the larger one. Then, put the sign of the real number with the larger absolute value in front of your answer. -9 + 2 = Larger abs. value 9 – 2 = 7 Answer = - 7

  7. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Using a Number Line to Add Integers When the number is positive, count to the right. When the number is negative, count to the left. - +

  8. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 3 + -5 = -2 + -

  9. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 6 + -4 = +2 + -

  10. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 3 + -7 = -4 + -

  11. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -3 + 7 = +4 - +

  12. Use your number line to solve -8 • -3 + -5 = • -4 + 7 = • 3 + 4 = • -6 + 7 = • 5 + 9 = • -9 + -9 = 3 7 1 14 -18

  13. Adding Integers Matching

  14. Adding Integers Song

  15. Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!

  16. -3 - 2 is the same as -3 + (-2) -3+(-2)=-5

  17. 5 - 7 is the same as 5 + (-7) 5 + -7 = -2

  18. Try a few… 1. 8 – (-12) = ? 2. 22 – (-30) =? 3. – 17 – (-3) = ? 4. –52 – 5 = ?

  19. Check Your Answers 1. 8 – (-12) = 8 + 12 = 20 2. 22 – (-30) = 22 + 30 = 52 3. – 17 – (-3) = -17 + 3 = -14 4. –52 – 5 = -52 + (-5) = -57

  20. Adding Fractions with common denominators

  21. Adding Fractions with different denominators Problem: You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators Solution: Turn fractions into equivalent fractions with a common denominator that is find the Least Common Multiple (LCM) of the two denominators

  22. Finding the Lowest Common Denominator • The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples Multiples of 2 are 2, 4, 6, 8, 10…… Multiples of 3 are 3, 6, 9, 12, ……… What is the lowest common multiple?

  23. Finding the Lowest Common Denominator • The lowest common multiple of two numbers is the lowest number they will BOTH divide into 2 divides into 2, 4, 6, 8….. 3 divides into 3, 6, 9…. What is the lowest number 2 and 3 both divide into?

  24. You can’t add fractions with different denominators + The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths Special form of 1

  25. Lowest common denominator is 10 so make all fractions tenths

  26. Turn both fractions into twelfths

  27. Finally the fractions are READY to add. I just have to add the numerators 9+14=23 It is 3/3 So I multiply 3/7 by 3/3 It is 7/7 So I multiply 2/3 by 7/7 What is the lowest number BOTH 3 and 7 divide into? Hmmmmm?????? What special form of 1 will change 7 to 21. Hmmmm? What special form of 1 will change 3 to 21. Hmmmm? It is 21. So that is my common denominator Now 3x3=9 and 2x7=14 Now I know the new numerators

  28. Adding Mixed Numbers • Separate the fraction and the whole number sections, add them separately and recombine at the end

  29. Decimal and Fraction Examples Think: I have different signs, so I need to subtract the absolute values. Think: Which number had the larger absolute value in my given problem? Think: My answer is positive because 4.5 has a larger absolute value than 2.3

  30. Decimal and Fraction Examples Think: I have the same signs, so I will add the absolute values. Think: I will keep the sign of the numbers in the expression Think: My answer is negative because both numbers in the expression were negative!

  31. Decimal and Fraction Examples Think: I’m going to change this to addition by adding the opposite of -1.4 Think: I better line up my decimal points.

  32. Decimal and Fraction Examples Think: I need to find a common denominator before I can add these fractions. Think: Ok, I have different signs, so I need to subtract the absolute values. Think: I have to take the sign of the number with the higher absolute value, so my answer will be positive.

  33. Decimal and Fraction Examples Think: I need to find a common denominator before I can add these fractions. Think: I’m going to end up with a negative result. I’m going to change this problem to adding a negative fraction. Think: My denominator will stay the same. 1 + (-6)= -5, so that is my numerator.

  34. What is a matrix? • A rectangular arrangement of rows and numbers. Weight Loss/Gain

  35. Adding Matrices

  36. Who Won?

  37. 6 -2 -2 -11 -11 -17.4 Don’t Do #3 -4 1.5 -16 -9 -1/8 5/4 -1

  38. Subtraction practice • (Do these on the back of your quick check) [ ] ] 3 -1 ] -4 7 - 2 3 -4 2

  39. Objective • SWBAT • Add and subtract real numbers using models and rules How did we do?

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