Day 23: Study Guide & Sieve of Erastothenes

6th Grade Math Standards: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). MA.4.a. Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

Objective: Find the prime factorization of a composite number; identify a number as prime or composite; determine if two numbers are relatively prime

Quote of the Day: “Colonel Stas Preczewski, coach of the army crew team at West Point a few years ago, faced a baffling problem. Through extensive testing he had determined the strengths and abilities of every rower on his team. He had measured each man’s power on ergometers and had composed crews in every possible combination in order to calculate each member’s contribution. He was able to rank his rowers objectively and precisely from best to worst. He then put the eight best in his varsity boat and the eight others, the weakest, in the junior varsity boat. The problem: The JV boat beat the varsity boat two-thirds of the time...The varsity boat was full of resentment over who was contributing the most, while the JV rowers, feeling they had nothing to lose, supported one another happily.
One day he [Coach Preczewski] lined up the varsity crew in four pairs. He told them they were to wrestle for ninety seconds. Only rule: no punching. ‘It was like WWF,’ he recalls. When he stopped them, he noticed that no one was winning. Each man was discovering that his opponent was just as strong and determined as he was. Preczewski then had them change opponents and wrestle again. By the third round they were choosing their own opponents - ‘One guy would point at another and say, ‘You!’ Peczewski says. On the fourth or fifth round, one of the rowers started laughing, and they all piled into a general brawl. Eventually someone said, ‘Coach, can we go row now?’ From then on the varsity boat flew, and made it to the semifinals in the national tournament.” - Geoff Colvin
Question of the Day: "Is there any case where two numbers don't have a common factor including one?"

Agenda:

1. Visual Pattern #12
2. QSSQ
3. Review Homework
4. Study guide on prime factorization
5. Coloring the 100s grid (Sieve of Erastothenes)

Assessment: The study guides were done in pairs, so I went around the room to check in with students. Given the dearth of problems on the study guide, if I saw an issue I would create another problem on the spot and have a student do that or get a partner who had the right information to teach the other partner in front of me.

Glass Half-Full: I had two students who really have struggled to this point in the year write everything they know based on the drawing of the visual pattern. One made a chart, wrote how many green and how many black diamonds there were, and from there we were able to have a very good conversation. All of it started though with what we know and it only took two minutes (I timed it).

Regrets: The Sieve of Erastothenes was not done as well as I would like to see. I could have given the students written directions that told them to circle the prime and then color its multiples instead of doing it orally.

Link of the Day: Dan Meyer has done it again. In a lesson that teaches the math and the morals. Pokemon Go.