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UNIT 4 LESSON 16
Objective: Today we will learn how to solve for numbers
      in a sequence using Singapore Bar Models
FIRST THE
PRELIMINARIES

  Noticing Patterns
Try to follow this story and draw a
      picture to represent the story
 A bathtub full of Jello is traveling on a plane, 6 miles
  above the city
 There is a man sitting in the park feeding birds
 The jello is tipped out of the bathtub and fell out of the
  door of the plane
 After falling 1 mile the jello splits into 2 parts
 After falling the second mile, each of the 2 pieces splits
  into another 2 pieces.
 If this pattern continues all the way down, how many
  little jello pieces will fall on the man?
 Will it hurt very much?
Mile 1


         Mile 2

    Mile 3

  Mile 4          16

Mile 5        32

           Mile 6      64   Whats the pattern?


                                   2n
CONSECUTIVE NUMBERS

Numbers in a sequence are called
consecutive numbers

The age you were in 6th grade, now in 7th, and
will be in 8th grade are considered to be
consecutive numbers
WHAT ARE
CONSECUTIVE
 NUMBERS?
EXAMPLES OF
 CONSECUTIVE NUMBERS

 2, 3, 4



 12, 13, 14



 100, 101, 102



 999, 1000, 1001
TAKE THE CHALLENGE!
 Consecutive Even numbers

 2,4,6

 Consecutive Odd numbers

 3,5,7

 Consecutive Prime numbers

 7,11,13

 Consecutive Perfect squares

 4,9,16
   10,11,and 12 are consecutive numbers
                    that add up to 33. Another three
                    consecutive numbers add up to 99.
                    Find the three numbers.

1st #       ?



2nd #       ?         +1
                                              99
3rd #       ?         +1   +1
                                        99 - 3 = 96
 Example #1                             3N = 96
 The three numbers are 32, 33, and 34    1N = 32
   15, 16, and 17 are consecutive numbers
                    that add up to 48. Another three
                    consecutive numbers add up to 87.
                    Find the three numbers.

1st #       ?



2nd #       ?         +1
                                               87
3rd #       ?         +1   +1
                                        87 - 3 = 84
 Example #2                              3N = 84
 The three numbers are 28, 29, and 30    1N = 28
   5, 6, 7, 8 are four numbers that
        add up to 26. Another 4
        numbers add up to 86. Find
        the four numbers

    (take 5 minutes)


Take the challenge!
Partner Practice Rules
    {                             {   When you finish
                                         Work independently to
   Must stay on task with your           complete the in-class work
    assigned partner                      on Evaluating Expressions
   Must use level one voice             Your teacher will monitor
    (almost a whisper)                    your progress while you
   Go back to previous                   work
    problems to help with                When you finish, please
    current problems                      work on Math
   Be sure that BOTH partners            Minutes, Complete
    understand BEFORE                     corrected homework, or
    moving to the next problem            Read your choice book
   Keep your work organized!            Do Not raise your hand.
                                          Look at your notes for help
                                          or skip the question and
                                          work on a different
                                          question until your teacher
Partner Practice                          comes to your desk.

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Unit 4 lesson 17

  • 1. UNIT 4 LESSON 16 Objective: Today we will learn how to solve for numbers in a sequence using Singapore Bar Models
  • 2. FIRST THE PRELIMINARIES Noticing Patterns
  • 3. Try to follow this story and draw a picture to represent the story A bathtub full of Jello is traveling on a plane, 6 miles above the city There is a man sitting in the park feeding birds The jello is tipped out of the bathtub and fell out of the door of the plane After falling 1 mile the jello splits into 2 parts After falling the second mile, each of the 2 pieces splits into another 2 pieces. If this pattern continues all the way down, how many little jello pieces will fall on the man? Will it hurt very much?
  • 4. Mile 1 Mile 2 Mile 3 Mile 4 16 Mile 5 32 Mile 6 64 Whats the pattern? 2n
  • 5. CONSECUTIVE NUMBERS Numbers in a sequence are called consecutive numbers The age you were in 6th grade, now in 7th, and will be in 8th grade are considered to be consecutive numbers
  • 7. EXAMPLES OF CONSECUTIVE NUMBERS 2, 3, 4 12, 13, 14 100, 101, 102 999, 1000, 1001
  • 8. TAKE THE CHALLENGE! Consecutive Even numbers 2,4,6 Consecutive Odd numbers 3,5,7 Consecutive Prime numbers 7,11,13 Consecutive Perfect squares 4,9,16
  • 9. 10,11,and 12 are consecutive numbers that add up to 33. Another three consecutive numbers add up to 99. Find the three numbers. 1st # ? 2nd # ? +1 99 3rd # ? +1 +1 99 - 3 = 96 Example #1 3N = 96 The three numbers are 32, 33, and 34 1N = 32
  • 10. 15, 16, and 17 are consecutive numbers that add up to 48. Another three consecutive numbers add up to 87. Find the three numbers. 1st # ? 2nd # ? +1 87 3rd # ? +1 +1 87 - 3 = 84 Example #2 3N = 84 The three numbers are 28, 29, and 30 1N = 28
  • 11. 5, 6, 7, 8 are four numbers that add up to 26. Another 4 numbers add up to 86. Find the four numbers (take 5 minutes) Take the challenge!
  • 12. Partner Practice Rules { { When you finish Work independently to Must stay on task with your complete the in-class work assigned partner on Evaluating Expressions Must use level one voice Your teacher will monitor (almost a whisper) your progress while you Go back to previous work problems to help with When you finish, please current problems work on Math Be sure that BOTH partners Minutes, Complete understand BEFORE corrected homework, or moving to the next problem Read your choice book Keep your work organized! Do Not raise your hand. Look at your notes for help or skip the question and work on a different question until your teacher Partner Practice comes to your desk.

Editor's Notes

  • #10: Have students fold paper vertically and write model on one side and equation on the other side