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Exploring Integers and Transformations: Adding, Subtracting, and Coordinate Geometry

This comprehensive guide covers fundamental operations with integers, including addition, subtraction, multiplication, and division. It also delves into the coordinate plane, transformations like translations and reflections, and practical applications within real-world scenarios. Key examples illustrate the concept of positive and negative integers through various situations, such as depths below sea level and helicopter ascents. Lastly, it discusses the properties of geometric figures, helping learners understand transformations on a coordinate grid through interactive exercises.

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Exploring Integers and Transformations: Adding, Subtracting, and Coordinate Geometry

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  1. Intro to Integers Adding/Subt. Integers Mult./ Divide Integers Coordinate Plane Transformations 1pt 1 pt 1 pt 1pt 1 pt 2 pt 2 pt 2pt 2pt 2 pt 3 pt 3 pt 3 pt 3 pt 3 pt 4 pt 4 pt 4pt 4 pt 4pt 5pt 5 pt 5 pt 5 pt 5 pt

  2. Write an integer to describe the situation: The Dead Sea is 1,312 feet below sea level.

  3. -1,312

  4. Write an integer to describe the situation: A helicopter rises 75 feet.

  5. 75 or +75

  6. What is the sum of two opposite integers?

  7. ZERO

  8. Which is greater -45 or -42?

  9. -42

  10. Order 0, 41, 3, -20, -10, and 10 from greatest to least.

  11. 41, 10, 3, 0, -10, -20

  12. Find the sum. -11 + -18

  13. -29

  14. Find the difference. -12 - 12

  15. Use Leave, Change, Opposite: -12 – 12 -12 + (-12) = -24

  16. What is -3 plus -6 plus 4?

  17. -3 + -6 + 4 -9 + 4 = -5

  18. Solve. 3 + (-6) – (-3)

  19. 3 + (-6) – (-3) -3 – (-3) Using Leave, Change, Opposite: -3 + 3 = 0

  20. Find the value of x – y if x = 9 and y = -16.

  21. 9 – (-16) 9 + 16 = 25

  22. Find the product of -4 and -8.

  23. -4 x -8 = 32

  24. Find the quotient of 45 and -9.

  25. 45 ÷ (-9) = -5

  26. A submarine is at the surface of the water. It starts to descend at a rate of 4 meters per second. How far below the surface will the submarine be after 5 seconds?

  27. -4 x 5 = -20 meters

  28. EVALUATE. 3(-4 - 7)

  29. 3(-4 – 7) 3(-4 + (-7)) 3(-11) = -33

  30. EVALUATE.

  31. Which quadrant contains the points B and X?

  32. Quadrant III

  33. The point (0,0) is called the _____________.

  34. Origin

  35. Name the ordered pair for the point V.

  36. (-2, 0)

  37. What points are located in the first quadrant?

  38. R and X

  39. Write the letter for the point named by the ordered pair.

  40. What is the difference between a translation and a reflections?

  41. A translation is a slide, and a reflection is a flip.

  42. What type of transformation is shown in the picture below?

  43. Reflection

  44. Working Backwards Problem Pam has money in her savings account. She made withdrawals of $100, $45, and $63. Her balance is now $245. How much did she have in her account before the three withdrawals?

  45. $453

  46. The vertices of triangle ABC are (-1,2), (0,5), and (3,1). On the coordinate grid, draw the triangle and then complete the following transformation: Translate the image 6 units down and 2 right.

  47. The vertices of triangle ABC are (-1,2), (0,5), and (3,1). On the coordinate grid, draw the triangle and then complete the following transformation: Reflection about the x-axis

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