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UMI Saturday

This lesson involves solving a problem where students need to determine the amount of wire needed to hang multiple model airplanes. It also includes a related problem about paying for the wire. The lesson aims to develop problem-solving skills and math comprehension.

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UMI Saturday

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  1. UMI Saturday October 11, 2014

  2. Hanging AirplanesA Problem Solving Lesson Overview Source of the problem: Exemplars Reference to Math Solutions books purchased for you: pages 51-56 in the book by Marilyn Burns, “About Teaching Mathematics”

  3. Steps for Student Success • Review concepts needed in the problem • Read for understanding, discuss vocabulary • Children work in groups AND individually. At the beginning give some time for each child to think about their own approach, then have the group work as a team. • Teacher facilitates, questions, questions, questions the darlings, looks for unique approaches, looks for different approaches • Teacher decides if a group or some students need an extension • Teacher decides if a group or some students need a “lite” version of the problem • Teacher is prepared with a meaningful extension for those who work quickly • Summarize the learning by sharing different approaches

  4. Hanging Airplanes (Original) • Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? • Wire sells for 97 cents a yard at the hardware store. Zack only wants to spend $4.00 for the wire. Will Zack be able to hang all his airplanes?

  5. Hanging Airplanes (C) • Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 9 inches of wire and the 4th model airplane needs 11 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? • Wire sells for 97 cents a yard at the hardware store. Pays for the wire with a $5 dollar bill. What are the possible ways he can get change back from his 5 dollars? Find all the ways.

  6. Hanging Airplanes (More accessible) • Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? How many inches of wire will Zack need to hang all 10 of his model airplanes?

  7. A Practice • Thanks so much for your patience! I know you can all work this problem very quickly. I am very appreciative that you allow me the time to demonstrate the teaching process.

  8. Doubling and Halving Overview Source of the work for your reference: Number Talks by Sherry Parrish, page 276 Purpose: To provide one more strategy for multiplication

  9. As you begin, • Choose numbers with lots of factors • Build arrays to demonstrate doubling and halving • Label the array with the appropriate multiplication problem

  10. Adding a visual for this strategy

  11. Doubling and Halving • We can simplify some multiplication problems using doubling and halving. • Use the strategy of doubling one factor and halving the other to help simplify and solve the following problems: Example: 5 x 16 10 x 8 20 x 4 40 x 2 80 x 1

  12. Doubling and Halving Practice Makes Perfect 5 x 68 10 x 34 20 x 17 Now, you might even use another strategy… 20 x (10 + 7)

  13. Practice at your table

  14. Doubling and Halving • Does this strategy always work? • Explain when the strategy of doubling and halving is most useful to simplify a multiplication problem.

  15. Small Group Discussion Questions for the Reading • 1. How does Marilyn Burns preference for teaching vocabulary differ, if at all, from the way you teach vocabulary in a reading class? Why do you think the approach should be different? (This is the idea of teaching for meaning before presenting the vocabulary word.) • 2. What are some math terms at the 5th grade level which have different meanings in other contexts? • 3. What are you doing in your room presently to support math vocabulary that is suggested in the article? Is there anything else that is successful for you? • 4. What changes will you need to make in your teaching if you adopt her suggestions?

  16. Reading Across The Curriculum Activities for “Can You Count to a Googol?” by Robert Wells • As you read the book write the numbers on the board and count the zeros. Tell the students there is a different way to write that number using math. Then, write 10 with an exponent. The exponent will equal the number of zeros in the number. See if the students can determine the pattern, write their own large numbers and then write them with an exponent. This is a good time to show context first and then to teach the vocabulary term, “exponent”. • Ask the students if they know anything else named a “Google”. Then talk about what Google does to help people. Is there anything you can’t ask Google? Why do you suppose the company named their search engine, “Google”?

  17. Reading Across The Curriculum • One thousand new dollar bills makes a stack about 4 inches (10 centimeters) high. Have students find the value of different items in the room that are approximately the size of a dollar bill by measuring their heightand making the comparison to the example. 4. A stack of bills ($1,000,000) has a volume of 62,400 cubic inches. (26 inches x 40 inches x 60 inches). Find the volume of items in the room and compare their size to the stack of one million dollars. Then, find the monetary value of each item. For example, find the volume of the file cabinet. Let’s say it is 48x24x60 inches= 69,129 cubic inches. Is it worth more, less or exactly a million dollars? How much more? Compare the two values and find the percent. 69/129 ÷ 62,400 = 1.107%. 1,107 percent of $1,000,000 =$1, 107,000.

  18. Game for Make and Take Purpose: To provide a game that can be used as either a center for two students or for the whole class working in pairs to reinforce their basic facts. Source: Math Games for Independent Practice, Game 26, page 141.

  19. Meeting with my Team Items to discuss • First, thanks for their kindness during my visit. • Please respond to my e-mail. I worry. • Add your teaching time to my chart. • Please don’t have a dog and pony show for me. Warts are fine. I understand that life is not perfect. • What questions do you have for me?

  20. That’s All Folks!

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