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What is an integer?

What is an integer?. Integers. Integers : all positive and negative whole numbers and 0 Opposites: integers that are the same distance from zero on a number line. Comparing Integers : The greatest number is the one furthest to the right on the number line. Which is greater -7 or -2?.

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What is an integer?

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  1. What is an integer?

  2. Integers • Integers: all positive and negative whole numbers and 0 • Opposites: integers that are the same distance from zero on a number line

  3. Comparing Integers: The greatest number is the one furthest to the right on the number line. • Which is greater -7 or -2? Greater Than (Increasing) Less Than (Decreasing) -2 0 2 -6 -8 -4

  4. Comparing Integers • Which is greater -5 or -10? • Which is greater 2 or 5? • Which is greater -3 or 7?

  5. Comparing Integers Card Game • You will play the game with a partner. • Each person will receive 20 cards and each pair will get a page to record the results • Each person will flip over the top card at the same time and the person with the highest integer wins! • Record the numbers and a greater than or less than symbol on your page

  6. Warm-Up • Use the data set to answer the following questions: 6, 5, 14, 9, 7, 12, 17 • What is the median? • What is the mean? • What is the mode?

  7. What are some real world examples of positive and negative integers? Positive Integers Negative Integers a bank withdrawal an elevation below sea level a drop in temperature • a bank deposit • an elevation above sea level • a rise in temperature

  8. What does zero represent? • A bank deposit or withdrawal • Having no money in your bank account • An elevation above or below sea level • Being at sea level • A rise or drop in temperature • No change in temperature

  9. Think Fast! • Which point represents -7? • What integer is represented by point D? • Which 2 points represent opposites? A E D B C      0 5 -5 -10

  10. Absolute Value • The absolute value of a number is its distance from zero. • Distance is always positive!! • Absolute value is represented by 2 lines surrounding the number. -2 and 2 are both a distance of 2 units from zero! = = 2 -2 2 2

  11. Magnitude • You can use absolute value to describe the magnitude of a situation. • Hannah wrote a check for more money than she has in her bank account. The balance in her account is now -$60. How much money does Hannah owe the bank? Hannah owes the bank $60. -60

  12. Less than or greater than • A team of mountaineers climbed to the summit of Mt. Everest. The temperature at the summit is less than -15°F. Describe how many degrees Fahrenheit below zero the temperature is. • How could you graph the temperature it could have been at the summit on a number line?  -10 -5 -15 -20

  13. Example Lori’s checking account has a balance of less than -$200. Which of the following statements is true about how much money Lorraine owes the bank? • She owes exactly $200. • She owes exactly -$200. • She owes less than $200. • She owes more than $200.

  14. Warm-Up • There are 15 students in a math class and 6 of the students are boys. What is the ratio of boys to girls in simplest form? • Abigail is going shopping this weekend because Target is having a 30% off sale. She is buying a pair of sunglasses that cost $14. How much will she have to pay? • Write down the following definitions • Bivariate Data: data for two variables or two types of related data; example: ice cream sales versus the temperature of the day. The two sets of data are ice cream sales and temperature. • Univariate Data: just one set of data; example: temperature

  15. The Opposite of… • If you see a number written like, -(-5) that means the opposite of -5 which would be 5. • The same if true with an absolute value sign. • What does –(-56) equal? • What does -|5| equal? = -2 - -2

  16. Rational Numbers • Rational Number: a number that can be expressed as the ratio of two integers in the form a/b where b is not equal to zero. • Rational numbers can be positive or negative. • Integers, fractions, mixed numbers, percents, terminating decimals, and repeating decimals • http://www.brainpop.com/math/numbersandoperations/rationalandirrationalnumbers/

  17. Plotting Rational Numbers • Plot the rational numbers ⅗ and -⅖ on a number line. • What intervals do you need to use on your number line? • Plot your points 0

  18. What do the points represent? • What value does each of the points represent? B A D C     -1 1 0

  19. More Practice • What are the intervals of this number line? • What values do the points represent? B A C    -1 -2 2 1 0

  20. Warm-Up • The trip costs at least $200. Write an inequality to represent the situation. • What is the surface area of the following shape? Use the formula SA = 2(wl) + 2(hl) + 2(hw)

  21. Quick Review! • Convert Fraction to Decimal: Top dog goes in the house (divide) • What is ⅘ as a decimal? • Convert percent to decimal: move the decimal to the left 2 times! • What is 25% as a decimal?

  22. Which of these rational numbers is the greatest? ⅞ 5 7 ¼ -7.5 6.25 10%

  23. Ordering Rational Numbers • Khan Academy: http://www.youtube.com/watch?v=VZOHWaw5dqM&edufilter=fU9N1e_9JCp4rAvc4PaVkQ • To put rational numbers in order, you need to plot them on a number line! • Or you can turn your numbers into decimals because they are the easiest to compare. • Put these numbers in order from least to greatest: 0.5, ¾, -1½, |0.8| • Correct order: -1½, 0.5, ¾, |0.8|

  24. Example • #8 on your packet! • Put the following numbers in order from least to greatest: -3⅓, 3.3, -3¾, 3.5

  25. Warm-Up • Mary is 3 years more than 5 times as old as Paula. If p represents Paula’s age, write an expression to represent Mary’s age. • Mrs. Perry hires a landscaper that charges 15 dollars per hour. The landscaper says that the total charge for the work Mrs. Perry wants done will cost at least 120 dollars. Write an inequality for the situation where h represents the number of hours worked.

  26. Warm-Up • What is the area of a triangle with a base of 5.3 m and a height of 2.5 m? • What is the volume of a block that is 5 meters long, 3 meters wide, and 2 meters high? • What is the height of a triangle that has an area of 120 square feet and a base of 12 feet?

  27. Coordinate Plane ( - , + ) ( + , + ) Quadrant II Quadrant I ( - , - ) ( + , - ) Quadrant III Quadrant IV When plotting points, x is first and y is second. (x,y)

  28. Plotting Coordinates • http://www.khanacademy.org/partner-content/pixar/pixar-planes/v/the-coordinate-plane • http://www.brainpop.com/math/geometryandmeasurement/coordinateplane/

  29. Plot the coordinates on the coordinate plane. (-4 , 5) (-3, -2) (2, 1) (6, -3)

  30. Reflections • Reflection: When a point is flipped over the x or y axis. • If a point (x,y) is reflected across the x-axis, the sign of the y-coordinate changes. • (x , y)  (x, -y) • If a point (x,y) is reflected across the y-axis, the sign of the x-coordinate changes. • (x , y)  (-x, y) • If a point (x,y) is reflected across both axes, the sign of both its coordinates changes. • (x , y)  (-x, -y)

  31. Reflect the point (4,5) across the x-axis. Reflect the point (-2,3) across the y-axis.

  32. CRCT Review • What is the surface area of the rectangular prism? SA = 2(wl) + 2(hl) + 2(hw) • What is the surface area of a rectangular prism with a width of 7 cm, a height of 4 cm, and a length of 8 cm?

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