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Warm-Up 8/8/12

Warm-Up 8/8/12. Order the following numbers from least to greatest by first plotting them on a number line: -5, 2, -8, 4, 5/2, 4/3

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Warm-Up 8/8/12

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  1. Warm-Up 8/8/12 Order the following numbers from least to greatest by first plotting them on a number line: -5, 2, -8, 4, 5/2, 4/3 2. The number “5” is a rational number, an integer, a whole number, and a natural number. The number “-0.5” is a rational number (not an integer, whole, or natural number). Categorize the number “-4/2” Which number is greater, 1.2 or 1.1472? Which number is smaller, -4.54 or -4.19938?

  2. Let’s Practice Categorizing some more… -9 : 4/2: 1.5: 0:

  3. –8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 Additional Example 3: Ordering Integers Using a Number Line. Use a number line to order the integers from least to greatest. –3, 6, –5, 2, 0, –8 The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

  4. VOCABULARY Integers: All whole numbers and their opposites. i.e. -4, -2, 0, 1, 5 Positive: any real number greater than 0 i.e. 3, 1.24, 8, 0.77 Negative: any real number less than 0 i.e. -0.4, -5, -7.3, -4/3

  5. Opposite: an opposite of a number is the number with the opposite sign. i.e. The opposite of 4 is -4. The opposite of 10 is -10. –4 and 4 are opposites –4 4 • • 1 2 3 4 5 –5–4–3–2–1 0 Positive integers Negative integers 0 is neither positive nor negative

  6. –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Take out your homework!!! WARM –UP 8/9/12 Yes, you have to graph the numbers too! Use a number line to order the integers from least to greatest. –5, 4, –3, 2, –1, –2 The numbers in order from least to greatest are –5, –3, –2, –1, 2, and 4.

  7. 1-4 you should have graphed, but their opposites are shown below: -2 2) 9 3) 1 4) -6 5) > 6) > 7) < 8) < 9) -5, -3, -1, 4, 6 10) -8, -2, 1, 7, 8 11) -6, -4, 0, 1, 3 45) Decreased by “about” 9% 46) Increased by about 27% 47) -12 < -3, so it was actually getting colder outside

  8. 1st, 3rd, and 4th period: Put everything under your desk or away for the next few minutes……

  9. The opposite of 8 is…. The opposite of -9 is… The opposite of -4.87 is… The opposite of 0 is….?

  10. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Graphing Integers and Their Opposites on a Number Line Graph the integer -7 and its opposite on a number line. 7 units 7 units The opposite of –7 is 7.

  11. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Check It Out: Example 1 Graph the integer -5 and its opposite on a number line. 5 units 5 units The opposite of –5 is 5.

  12. You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

  13. Remember! –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 The symbol < means “is less than,” and the symbol > means “is greater than.” Additional Example 2A: Comparing Integers Using a Number Line Compare the integers. Use < or >. 4 -4 > 4 is farther to the right than -4, so 4 > -4.

  14. -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Additional Example 2B: Comparing Integers Using a Number Line Compare the integers. Use < or >. -15 -9 > -9 is farther to the right than -15, so -15 < -9.

  15. -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Check It Out: Example 2B Compare the integers. Use < or >. > -4 -11 -4 is farther to the right than -11, so -4 > -11.

  16. How are integers useful? • By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet. • negative/positive bank accounts

  17. The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the distance from the top of Mt. McKinley to the bottom of Death Valley?

  18. “0” represents sea level The distance from the top of Mt. McKinley to sea level is 20,320 feet and the distance from sea level to the bottom of Death Valley is 282 feet. The total distance is the sum of 20,320 and 282, which is 20,602 feet.

  19. The problem uses the notion of opposites: “above sea level” is the opposite of “below sea level.” Here are some more examples of opposites: Top, bottom increase, decrease forward, backward positive, negative

  20. Let’s revisit the problem from earlier… The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level. The lowest elevation is Death Valley, which is 282 feet below sea level. What is the distance from the top of Mt. McKinley to the bottom of Death Valley?

  21. WARM-UP 8/10/12 Monday the temperature was 23 degrees below zero and Friday the temperature was 77 degrees, (above zero) how much did the temperature increase from Monday to Friday? Antarctica is 2,538m below sea level. Mount Rushmore is 1745m above sea level. What is the distance from the top Mount Rushmore to Antarctica? If the top of the Eiffel tower is 324 m above sea level, then what is the total distance from the top of Mount Rushmore to the top of the Eiffel tower?

  22. Write an integer to represent each situation: 1) +10 10 degrees above zero A loss of 16 dollars A gain of 5 points 8 steps backwards 14 degrees below zero 70 ft below sea level 2) -16 3) +5 4) -8 5) -14 6) -70

  23. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 Do you remember doing this yesterday?? Remember, a number and its opposite are the same distance to zero…. Graph the integer -5 and its opposite on a number line. 5 units 5 units

  24. A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero. The symbol I Iis read as “the absolute value of.” For example I -3 I is “the absolute value of -3.”

  25. 8 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Additional Example 4A: Finding Absolute Value Use a number line to find each absolute value. |8| 8 is 8 units from 0, so |8| = 8.

  26. 12 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Additional Example 4B: Finding Absolute Value Use a number line to find each absolute value. |–12| –12 is 12 units from 0, so |–12| = 12.

  27. 3 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 Check It Out: Example 4A Use a number line to find each absolute value. |3| 3 is 3 units from 0, so |3| = 3.

  28. 9 units –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Check It Out: Example 4B Use a number line to find the absolute value. |–9| –9 is 9 units from 0, so |–9| = 9.

  29. Finish workbook page 13 if you haven’t already done so…

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