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1. Combine 2 red chips and 2 blue chips…what is their sum?

1. Combine 2 red chips and 2 blue chips…what is their sum? 2. Make the above into an addition statement …use brackets. Add & Subtract Integers (Unit 9). Red Chips = +1 Blue Chips = -1. Are integers with the same numeral, but different signs (+ or -)

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1. Combine 2 red chips and 2 blue chips…what is their sum?

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  1. 1. Combine 2 red chips and 2 blue chips…what is their sum? 2. Make the above into an addition statement …use brackets. Add & Subtract Integers (Unit 9) Red Chips = +1 Blue Chips = -1

  2. Are integers with the same numeral, but different signs (+ or -) …they are the same distance from zero, in opposite directions. Opposite Integers • For example: • (+1) and (-1) are opposite integers • (-3) and ( ) are opposite integers • (+14) and ( ) are opposite integers • (-659) and ( ) are opposite integers

  3. Zero Pair: combining (+1) with (-1) (+1) + (-1) = 0 Zero Pairs • We can combine numerous zero pairs to solve problems: • For example: • (+1) + (-1) = • (-3) + (+3) = • (+11) + (-11) =

  4. Grouping: combining “positives with positives” “positives with negatives” or “negatives with negatives” to allow us to solve Adding Integers Addition Statements: (+1) + (+2) = ______ (+5) + (- 4) = ______ • Your turn…apply “integer addition” • Draw the model for (-3) + (+ 4) • 2. Draw the model for (+11) + (-3)

  5. Using Tiles to group + and – to find the answer….(great site!) http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html Using addition equations (small to large #’s) to find the answer. http://www.berghuis.co.nz/abiator/maths/sa/saintegeradd2.htmL VARIETY of GAMES: http://classroom.jc-schools.net/basic/math-integ.html Adding Integers GAMES

  6. SOLVE FindThe Addition Statement

  7. Model the scenario and create an addition statement to find your answer… FindThe Addition Statement Ray spent $5 on bus fares to visit his Aunt. During the visit, her Aunt gave him $12 for doing some yard work. How much money did Ray gain from the visit?

  8. Page 313: # 5 abc, 8 ab, 9ac, 12 bc Page 314: # 14, 17 acef Extend Page 315: # 18, 19 Applying Integer Addition

  9. Using aNumber Lineto Add Integers Start at zero and move the direction of the first number…then move the direction of the second number! Directions: Positive (+) andNegative (-) Move the DOT to it’s correct place using the addition statements below… 1. (+4) + (+3) 2. (-2) + (+5) 3. (+5) + (-11)

  10. What is the “addition statement?” • The addition statement below is… • (+4) + (+3) • What do the colors of the arrows represent? • What do the length of the arrows represent?

  11. What is the “addition statement?” • The addition statement below is… • (+4) + (+3) • What do the colors of the arrows represent? • What do the length of the arrows represent? • What is the total?

  12. What is the “addition statement?” What are the “Addition Statements?”

  13. What is the “addition statement?” What are the “Addition Statements?”

  14. What is the “addition statement?” Create your own…come on up and test your classmates? Addition Statement…

  15. What is the “addition statement?” What are the “Addition Statements?”

  16. What is the “addition statement?” What are the “Addition Statements?”

  17. Finding Temperaturesusing a Number Line • Number lines can also be vertical (grids). • Top of the “y” axis is positive and bottom is negative. • Rightside of “x” axis is positive andleft side is negative. What are the 2 different addition statements?

  18. What is the “addition statement?” Create your own… Addition Statement…

  19. ApplyInteger Addition The temperature in Yellowknife, Northwest Territories, on morning in October was – 4°C. The temperature increased by 9°C to reach the high temperature for that day. What was the high temperature? 5°C 0°C - 5°C

  20. ApplyInteger Addition This morning it was ______°C and the temperature has gone up 12°C. What is the high temperature going to be today? 5°C 0°C - 5°C

  21. Page 320: # 5ab, 6 bc, 7 ab, 10, 12 Page 321: # 14, 18, 20ab, 21 cd Extend Page 322: # 21ab, 22, 23 Applying Integer Addition

  22. Subtract integers using integer chips… What is the subtraction expression for the model above? Take away 4 red chips from the original 6 red chips…what do you have left? Explore Integer Subtraction

  23. Subtract integers using integer chips… What is the subtraction expression for the model above? Take away 3 blue chips from the original 7 blue chips…what do you have left? Explore Integer Subtraction

  24. Model the equations below… (-5) – (-2) (+8) – (+3) Model it… Subtraction

  25. Model the equations below… (-5) – (-2) (+8) – (+3) Model it… Subtraction What do you notice about each equation?

  26. Model the equations below… (-5) – (+2) (+1) – (+4) CAN THESE BE SOLVED??? Model it… Subtraction

  27. STRATEGY #1 “Move in – Move out” Model it… Subtraction

  28. (+ 2) – (+5) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model the first integer • Move in enough to model the second integer • 3.Remove the chips asked in the subtraction statement • 4. What is left

  29. (-1) – (-6) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model the first integer • Move in enough to model the second integer • 3.Remove the chips asked in the subtraction statement • 4. What is left

  30. (-1) – (+4) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model the first integer • Move in enough to model the second integer • 3.Remove the chips asked in the subtraction statement • 4. What is left

  31. (-3) – (-7) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model the first integer • Move in enough to model the second integer • 3.Remove the chips asked in the subtraction statement • 4. What is left

  32. (+2) – (-6) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model the first integer • Move in enough to model the second integer • 3.Remove the chips asked in the subtraction statement • 4. What is left

  33. STRATEGY #2 “Zero Pairs” Model it… Subtraction

  34. (+ 2) – (- 4) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • Model what the question is asking • ZERO PAIRS: 2nd integer reversing the (+) or (-) of number… • 3.Remove the chips asked in the subtraction statement • 4. Then group the chips left over!

  35. (- 2) – (- 3) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • 1. Model what the question is asking • ZERO PAIRS: 2nd integer reversing the (+) or (-) of number… • 3.Remove the chips asked in the subtraction statement • 4. Then group the chips left over!

  36. (+5) – ( -3) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • 1. Model what the question is asking • ZERO PAIRS: 2nd integer reversing the (+) or (-) of number… • 3.Remove the chips asked in the subtraction statement • 4. Then group the chips left over!

  37. (-4) – ( -8) What if the Integer #’s are different? Step 1 Step 2 Step 3 Step 4 • Steps to follow: • 1. Model what the question is asking • ZERO PAIRS: 2nd integer reversing the (+) or (-) of number… • 3.Remove the chips asked in the subtraction statement • 4. Then group the chips left over!

  38. ( ) – ( ) Method #1: Finding the “Higher Minus Lower” • The morning temperature is - 5°C. This afternoon it will reach a • temperature of +6°C. How much higher is the afternoon • temperature than (difference) the morning temperature? • Model it… • Use the steps (Zero Pair, Remove, and then Group)

  39. ( ) – ( ) Method #1: Finding the “Lower Minus Higher” • The morning temperature is - 5°C. This afternoon it will reach a • temperature of +6°C. How much lower is the morning • temperature than (difference) the afternoon temperature? • Model it… • Use the steps (Zero Pair, Remove, and then Group)

  40. Page 328: # 7, 9ab, 10cd, 11ac Page 329: # 14, 16 Applying Integer Subtraction

  41. STRATEGY #3 “Sub to Add” Model it… Subtraction

  42. Use integer chips to find the answer to the subtraction statement below… (+4) – (+ 2) What happens when we change the subtraction statement to an addition statement? (+4) + (- 2) The answers are ____________________. Which of the two methods above are easier? Subtracting Integers

  43. (- 5) – (- 3) (- 5) + (+ 3) The answers are ____________________. Which of the two methods above are easier? Do you see a pattern? Try it again!

  44. (- 12) – (+ 5) (- 12) + (- 5) The answers are ____________________. Which of the two methods above are easier? Do you see a pattern? Try it again!

  45. Use a number line to add & subtract. Subtract: (- 2) – (- 5) = ( ) + ( ) Solution…change the above statement into an addition statement. Then use the number line below to find your answer. Applying Integer Operations

  46. Use a number line to add & subtract. Subtract: (+7) – (+3) = ( ) + ( ) Solution…change the above statement into an addition statement. Then use the number line below to find your answer. Applying Integer Operations

  47. What do you notice about the signs (+ or -) when you change the subtracting statement to an adding statement? Changing subtraction to “addition”

  48. Find the difference of the Caspian Sea (+ 217 m) elevation from the elevation of Lake Winnipeg (- 28 m)? Steps: Would you use chips or a number line? Change the subtraction statement to an addition statement. Model your answer. You may use a calculator to help find your answer. Changing subtraction to “addition” + 28 m + 245 m + 217 m 0 m

  49. Page 333: # 5ab, 6bc, 7a, 8b, 9cd, 14 Page 334: # 19, 22 Changing subtraction to “addition”

  50. Use the golf score chart below to find the addition or subtraction statements. Prize…what does the term “albatross” mean in a golf score? Applying Integer Operations • On hole #1 Rosa made an eagle and Samantha made a bogey. • How many more strokes did Samantha take than Rosa? • Would subtract or add? • Find the answer!

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