7th Grade Math Number System

1. 7th Grade Math Number System Unit 1: The Number System

2. Number System Unit Topics Click on the topic to go to that section • Number System, Opposites & Absolute Value • Comparing and Ordering Rational Numbers • Adding Rational Numbers • Turning Subtraction Into Addition • Adding and Subtracting Rational Numbers Review • Multiplying Rational Numbers • Dividing Rational Numbers • Operations with Rational Numbers • Converting Rational Numbers to Decimals Common Core Standards: 7.NS.1, 7.NS.2, 7.NS.3 Unit 1: The Number System

3. Number System, Opposites & Absolute Value Return to Table of Contents Unit 1: The Number System

4. 1 Do you know what an integer is? Yes No Unit 1: The Number System

5. Number System Rational Real 1/3 Integer 5/2 Whole 0.22 Natural 1,2,3... Irrational 1/5 -3/4 0 ...-4, -3, -2, -1 8.3 -1/11 -2.756 Unit 1: The Number System

6. Define Integer Definition of Integer: The set of whole numbers, their opposites and zero. X Examples of Integer: {...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...} Unit 1: The Number System

7. Define Rational Definition of Rational: A number that can be written as a simple fraction (Set of integers and decimals that repeat or terminate) X Examples of rational numbers: , ½ 9 0, -5, 8, 0.44, -0.23, Unit 1: The Number System

8. Define Irrational Definition of Irrational: A real number that cannot be written as a simple fraction X Examples of irrational numbers: Unit 1: The Number System

9. Classify each number as specific as possible: Integer, Rational or Irrational 5 ¾ 3.2 -6 -21 1 ½ π 9 3¾ 5 0 -6.32 -65 2.34437 x 103 integer rational irrational Unit 1: The Number System

10. Rational Numbers on a Number Line Negative Numbers Positive Numbers Zero -5 -4 -3 -2 -1 1 2 0 3 4 5 Numbers to the right of zero are greater than zero Numbers to the left of zero are less than zero Zero is neither positive or negative Unit 1: The Number System

11. 2 Which of the following are examples of integers? -5 A B 0 -3.2 C D 12 1 2 E Unit 1: The Number System

12. 3 Which of the following are examples of rational numbers? 1 3 A B -3 10 C D 0.25 E 75% Unit 1: The Number System

13. Numbers In Our World Unit 1: The Number System

14. Numbers can represent everyday situations You might hear "And the quarterback is sacked for a loss of 5 yards." This can be represented as an integer: -5 Or, "The total snow fall this year has been 6 inches more than normal." This can be represented as an integer: +6 or 6 Unit 1: The Number System

15. Write a number to represent each situation: Spending $6.75 Gain of 11 pounds Depositing $700 10 degrees below zero 8 strokes under par (par = 0) feet above sea level Unit 1: The Number System

16. 4 Which of the following numbers best represents the following scenario: The effect on your wallet when you spend $10.25. A -10.25 B 10.25 C 0 D +/- 10.25 Unit 1: The Number System

17. 5 Which of the following integers best represents the following scenario: Earning $50 shoveling snow. A -50 B 50 C 0 D +/- 50 Unit 1: The Number System

18. Which of the following numbers best represents the following scenario: You dive feet to explore a sunken ship. 6 A B C 0 D Unit 1: The Number System

19. Opposites The numbers -4 and 4 are shown on the number line. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 9 8 10 Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero. The numbers -4 and 4 are opposites. Opposites are two numbers which are the same distance from zero. Unit 1: The Number System

20. 7 What is the opposite of -7? Unit 1: The Number System

21. 8 What is the opposite of 18.2? Unit 1: The Number System

22. What happens when you add two opposites? Try it and see... Click to Reveal A number and its opposite have a sum of zero. Numbers and their opposites are called additive inverses. Unit 1: The Number System

23. Jeopardy • Integers are used in game shows. • In the game of Jeopardy you: • gain points for a correct response • lose points for an incorrect response • can have a positive or negative score Unit 1: The Number System

24. When a contestant gets a $100 question correct: Score = $100 Then a $50 question incorrect: Score = $50 Then a $200 question incorrect: Score = -$150 How did the score become negative? Let's take a look... Unit 1: The Number System

25. Let's organize our thoughts... Question Answered Integer Representation New Score When a contestant gets a $100 question correct Then a $50 question incorrect Then a $200 question incorrect 100 Correct 100 100 50 Incorrect 50 -50 200 Incorrect -200 -150 Unit 1: The Number System

26. Now you try... Question Answered Integer Representation New Score When a contestant gets a $150 question incorrect Then a $50 question incorrect Then a $200 question correct 150 Incorrect -150 -150 50 Incorrect -200 -50 200 Correct 200 0 Unit 1: The Number System

27. Now you try... Question Answered Integer Representation New Score When a contestant gets a $50 question incorrect Then a $150 question correct Then a $200 question incorrect Unit 1: The Number System

28. 9 After the following 3 responses what would the contestants score be? $100 incorrect $200 correct $50 incorrect Unit 1: The Number System

29. 10 After the following 3 responses what would the contestants score be? $200 correct $50 correct $300 incorrect Unit 1: The Number System

30. 11 After the following 3 responses what would the contestants score be? $150 incorrect $50 correct $100 correct Unit 1: The Number System

31. 12 After the following 3 responses what would the contestants score be? $50 incorrect $50 incorrect $100 incorrect Unit 1: The Number System

32. 13 After the following 3 responses what would the contestants score be? $200 correct $50 correct $100 incorrect Unit 1: The Number System

33. To Review • An integer is a whole number, zero or its opposite. • A rational number is a number that can be written as a simple fraction. • An irrational number is a number that cannot be written as a simple fraction. • Number lines have negative numbers to the left of zero and then positive numbers to the right. • Zero is neither positive nor negative. • Numbers can represent real life situations. X Unit 1: The Number System

34. Absolute Value of Numbers The absolute value is the distance a number is from zero on the number line, regardless of direction. Distance and absolute value are always non-negative (positive or zero). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 What is the distance from 0 to 5? 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7 -2 What is the distance from 0 to -5? Unit 1: The Number System

35. Absolute value is symbolized by two vertical bars |4| This is read, "the absolute value of 4" 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 What is the | 4 |? Unit 1: The Number System

36. Use the number line to find absolute value. Move to check |9.6| = 9.6 Move to check |-9| = 9 4 Move to check |-4| = 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Unit 1: The Number System

37. 14 Find Unit 1: The Number System

38. 15 Find |-8| Unit 1: The Number System

39. 16 What is ? Unit 1: The Number System

40. 17 What is ? Unit 1: The Number System

41. 18 Find Unit 1: The Number System

42. 19 What is the absolute value of the number shown in the generator? (Click for web site) Unit 1: The Number System

43. 20 Which numbers have 15 as their absolute value? -30 A B -15 0 C D 15 30 E Unit 1: The Number System

44. 21 Which numbers have 100 as their absolute value? -100 A B -50 0 C D 50 100 E Unit 1: The Number System

45. Comparing and Ordering Rational Numbers Return to Table of Contents Unit 1: The Number System

46. Use the Number Line To compare rational numbers, plot points on the number line. The numbers farther to the right are larger. The numbers farther to the left are smaller. 7 4 8 -1 -10 -7 -5 -4 -2 10 -9 -8 -6 -3 9 6 0 3 5 2 1 Unit 1: The Number System

47. Place the number tiles in the correct places on the number line. Unit 1: The Number System

48. Now, can you see: Which integer is largest? Which is smallest? Unit 1: The Number System

49. Where do rational numbers go on the number line? Go to the board and write in the following numbers: Unit 1: The Number System

50. Put these numbers on the number line. Which number is the largest? The smallest? Unit 1: The Number System