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Will the Pan Overflow?!

Will the Pan Overflow?!. http://vimeo.com/70264988 Guess how many meatballs it would take for the pan to overflow? Write down an estimate that is too big? Write down an estimate that is too small?. Meatballs. L.O: I understand how to calculate the volume of a sphere (Grade A).

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Will the Pan Overflow?!

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  1. Will the Pan Overflow?! • http://vimeo.com/70264988 • Guess how many meatballs it would take for the pan to overflow? • Write down an estimate that is too big? • Write down an estimate that is too small?

  2. Meatballs L.O: Iunderstand how to calculate the volume of a sphere (Grade A)

  3. Three Act Maths Page • http://www.101qs.com/2352-meatballs

  4. What do we need to know?

  5. Diameter

  6. Distance from Top of Pan

  7. Meatball Dimensions

  8. Number of Meatballs

  9. Calculating the Volume of a Sphere • http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=volume/volumeCones&taskID=1136

  10. The Answer! http://vimeo.com/70264989

  11. Teacher’s Notes • Ask them to write down a guess: will the sauce overflow? Ask them to guess how many meatballs it'll take. Guess guessguess. It's the cheapest, easiest thing I can do to get students interested in an answer and also bring them into the world of the task. • Ask them what information would be useful to know and how they would get it. Have them chat in groups about what's important. • If they come back at you telling you they want the radius of the pot and the radius of the meatballs, push on that. Ask them how they'd get the radius. That's tough. Is there an easier dimension to get? • Someone here may ask if the lip of the pot matters. It isn't a perfect cylinder. Give that kid a lot of status for checking those kinds of assumptions. Tell her, "It may matter. It isn't a perfect cylinder but modeling means asking, 'Is it good enough?'" • Give them the information you have. • Let them struggle with it enough to realize what kind of help they'll need. Then help them with the formula for cylinder and sphere volume. Do some worked examples. • Once they have their mathematical answer, have them recontextualize it. What are the units? If that lip matters, how many meatballs will it matter? Should you adjust your answer up or down? • Let's not assume students are now fluent with these volume operations. Give them a pile of practice tasks next. Your textbook probably has a large set of them already written.

  12. Scaffolding • Next I'll ask students to think for a minute about what information they have - both in my display of water and balls and in the sauce textbook problem, what information they wish they had, what step they think they would work to solve first. I'll ask students to pair up and discuss their plans. • Then I'll challenge teams of students (2 - 3 students working together) to determine how to prove their estimations. As they work I'll circulate to ask questions (in no particular order below ... ) • What is the volume of the pan? How do you know? • Why is knowing the sauce is 2 inches below the top of the pan significant? • What is the volume of a meatball? • How does the volume of one meatball affect the volume of the pot? • What is the formula for the volume of a cylinder? • What is the formula of a sphere? • How are radius and diameter related?

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