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Part 1: Thinking about the meaning of Division

Part 1: Thinking about the meaning of Division. 6.NS.1 (From 21 st Century Lesson 1-3 of 3). Launch 1 – Division: Larger Dividend. Dividend. Divisor. Quotient. Once. Twice. Concept 1 When the dividend is larger than the divisor, the quotient is always greater than 1. 2.

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Part 1: Thinking about the meaning of Division

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  1. Part 1: Thinking about the meaning of Division 6.NS.1 (From 21st Century Lesson 1-3 of 3)

  2. Launch 1 – Division: Larger Dividend Dividend Divisor Quotient Once Twice Concept 1 When the dividend is larger than the divisor, the quotient is always greater than 1. 2

  3. Student Work (SW #1) *In your notebook, write what you think Concept 1 means in your own words. If needed, you can use the number example, 4 ÷ 2, to help in your explanation. Please use either the words "fits into" or "holds" in your explanation. Once finished, share your explanation with a table partner. (Everyone must share) 2 Minutes of Work Time ! Write your thoughts in your notebook… Click on the timer for internet timer window to open! Agenda 3

  4. Launch 2 – Division, smaller dividend Won’t Fit Dividend Divisor Quotient Concept 2 When the dividend is smaller than the divisor, the quotient is always less than 1. 4

  5. Student Work (SW #2) *In your notebook, write what you think Concept 2 means in your own words. If needed, you can use the number example, 2 ÷ 4, to help in your explanation. Please use either the words "fits into" or "holds" in your explanation. Once finished, share your explanation with a table partner. (Everyone must share) 2 Minutes of Work Time ! Write your thoughts in your notebook… Click on the timer for internet timer window to open! 5

  6. (SW #3) Don’t freak out if not whole numbers… … the concepts still apply to fractions and decimals !! Greater than 1 Less than 1 Concept 1 or 2 (write out) Dividend Divisor Dividend Divisor Greater than 1 Less than 1 Concept 1 or 2 (write out) Agenda 6

  7. (SW #3) Don’t freak out if not whole numbers… … the concepts still apply to fractions and decimals !! Greater than 1 Less than 1 Concept 1 or 2 (write out) The dividend is greater than the divisor Dividend Divisor Dividend Divisor Greater than 1 Less than 1 Concept 1 or 2 (write out) The dividend is less than the divisor Agenda 7

  8. Explore – Rational Quotients Circle the larger number (Dividend or Divisor). Then, write greater than or less than, you may use inequality symbols ( < or > ). #1 is answered for you. < < Greater than > > > < > > > > < Agenda 8

  9. Summary & Key to Move On… An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8-inch piece of sausage if each piece is to be Problems 2 & 3 involve division to solve: Place a box around the dividend and circle the divisor. Write a numerical expression or equation. Then write whether the quotients will be greater than or less than 1. Name • Explain whether the quotient to the problem below is greater than or less than 1. Use the words “Dividend” and “Divisor” in your explanation. 2) How many halves, (1/2), are there in an eighth, (1/8)? 3) A hotdog is 7 ½ inches long. How many pieces can be cut from the hotdog if each piece is to be two-thirds of an inch? 9

  10. Part 2: Thinking about Modeling with Division…

  11. Warm Up How many halves, (1/2), are there in an eighth, (1/ • How many thirds, (1/3), are there in a fifth, (1/5)? • A) Equation_________________ • B) Quotient greater than or less than 1? ____________ • 2) A metal pole is 10 ½ feet long. How many pieces can be cut from the pole if each piece is to be seven eighths (7/8) of a foot? • A) Equation_________________ • B) Quotient greater than or less than 1? ____________ Less than 1 Greater than 1 11

  12. Launch 1 – Constructing Fractional Models Although other shapes, like circles, can be used in modeling, we are going to use horizontal rectangular visual models for our fractions. It takes 4 – fourths to make a whole. In this case you have 3 – fourths. Numerator represents how many of the spaces are “filled.” Denominator represents how many “spaces” you need in your rectangle, in this case 4 spaces make 1 whole rectangle 12

  13. Explore 1 – Make some models 1) Why are all the rectangles the same initial size? 2) Why might drawing the models be helpful? 3) What might make it difficult to draw a model? 13

  14. Launch 2A – Using models to divide 2 4 6 1 3 5 Food for Thought Why is the quotient greater than 1? Notice how cutting ¾ into eighths made this easier. holds/contains exactly 6… eighths 14

  15. Launch 2B – Using models to divide Won’t Fit Food for Thought Why is the quotient less than 1? Notice how cutting ½ into sixths made this easier. holds/contains exactly of 15

  16. Explore 2 - Draw it, Solve it, Share it Food for Thought Will the quotient be greater than or less than 1? Notice how cutting 2/3 into sixths made this easier. Greater holds/contains exactly 4… sixths 16

  17. Explore 3 - Draw it, Solve it, Share it A movie theater can only hold one fourth (1/4) of the school’s students. Three eighths (3/8) of the school went to the movies hoping to get tickets. What fraction of the students that went to the movies got tickets? Use visual models to solve. Movie Theater *Hint Box* Students Fit Part students that fit Want Tickets Whole that want tickets School’s Students 17

  18. Assessment • 1 of the following problems involves division of fractions. Circle and solve that problem only. Use visual fraction models. • Erika has (7/8) of a cake and Rob has (1/4). How much more cake does Erika have? • Joe wants to make pieces of string that are (1/4) inch and has a string that is (7/8) inches long. How many pieces can he make? • Stevie has (1/4) of the money and Renee wants (7/8) of his money. How much of the total money does Renee have? Name:__________ Key to Leave 18

  19. Try on your own with models…

  20. Try on your own with models…

  21. Part 3: Thinking more about the Division of Fractions

  22. Warm Up How many halves, (1/2), are there in an eighth, (1/ We know that 5 wholes cannot “fit into” (8/9) so our answer is less than 1. Attempt to solve for the quotient using the visual fraction models given. If you encounter trouble, record/explain what is giving you difficulty. 22

  23. Learning Objective for Today… Students Will Be Able To…divide fractions using the common denominator method. 23

  24. Launch 1A – Warm Up Revisited Common Denominators Remember all whole numbers can be placed over a denominator of 1. Why? Recall… A common denominator/multiple is a number that both of our denominators can “fit into.” It is helpful to find the least/lowest, but any common multiple can be used. In this problem, 9 and 1 “fit into” 9…which is the least common denominator. 18 is also a common multiple but not the least. 8 45 8 x 1 = = 9 x 5 9 x 1 = = 9 x 1 Why is (45/9) an equivalent fraction to (5/1)? Step 1: Rewrite problem with the LCD 24

  25. Launch 1B – Get to the Division!! Step 2: Divide from Left to Right * Since any number (including a fraction) divided by 1 is itself…our quotient is… And with practice you can move quickly… …the denominators “cancel” out (become 1) 25

  26. Explore 1 – The Division Process Fill in the missing numbers as indicated by the blank boxes. If the entire space is blank then you must supply all work necessary. “Fast Track” means that you may skip this step (optional). Common Denominators Equation Division Quotient Fast Track 26

  27. Explore 2 – Tying all Division Skills Together Rosie is running a track race with five teammates. The course is 4 and (1/8) miles long. If all 6 team members want to run equal distances, how many miles will each be running? Recognition Can you recognize the operation needed? (Add, Sub, Mult, or Div) 1 Division Translation 2 Can you translate this into a numerical equation? Can you hypothesize what a rational solution might look like before actually solving? (will it be greater or less than 1) Rationality 3 Less than 1 Can you determine a method of solving the equation? Determine 4 Common Den. more efficient than visual models Can you execute the accurate solution using skills learned? Execution 5 Take that! If you can, prove it ! 27

  28. Explore 3 – Fraction nitty gritty • Rohan is building a table and needs to purchase lumber. He has 8 and 2/3 feet of hard oak wood but determines that he needs 12 and 1/4 feet so he needs to buy the rest. Rohan will use 2/5 of the total 12 and 1/4 feet to make the legs of the table. This will be a tripod table so there will only be 3 legs. • How many feet of wood does Rohan purchase? • How many feet of wood is used to make the legs? (all together) • How long is each individual table leg? • How many feet of wood are used on the rest of the table? (if legs not included) Working with your partner, solve the above problems… 28

  29. Assessment Review your work from Explore 3 and compare your work to the solutions provided. At any point where your work is different or at any point that you don’t understand the solution process, explain either your confusion or what you did incorrectly. If your work matches exactly, write “I had that excatly.” (Be honest to help me understand where we stand). I should see much writing in the spaces on this page. How many feet of wood does Rohan purchase? How many feet of wood are used to make the legs? (all together) How long is each individual table leg? How many feet of wood are used on the rest of the table? (if legs not included) Name:__________ Key to Leave 29

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