Day 14: Greatest Common Factor Hands On

6th Grade Math Standards: 6.NS.4 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 solutions of problems.
The Learning Objective: Find the greatest common factor of two or more numbers.

Quote of the Day: "Walt Disney's request for a bank loan was denied 301 times before he finally got a yes." - John Maxwell

Agenda:

1. Jumpstart with three Greatest Common Factor problems
2. Review the jumpstart and homework
3. Find the greatest common factor in my group of tickets and cards.
4. Begin the homework
5. Visual Patterns 3 and 4 (if the homework is completed). 

The Assessment: I partnered students up and gave them either a stack of tickets or trading cards that could be sorted into two groups. Once the cards and tickets were sorted, I asked students to divide them into as many groups as possible so that each type of card or ticket was included the same amount of times in each group. It sounds confusing because it is. Here's a better look at what the students did once the task of counting how many of each card was taken care of.

Looking at the top picture of Michael Jordan and Shaquille O'neal you can see that there are 10 Shaq cards and 5 MJ cards, so the cards were broken up into groups of 2 Shaq cards and 1 MJ card. The kids really enjoyed the activity and also were fascinated with the collection that I have acquired (nobody took the free opportunity to make a crack about how old I must be - very polite crew). All that being said, they could do this in a hands on activity but struggled more in the word problem version of this same problem. Here's the problem that they got in the homework:

Barbara is making candy bags for her birthday party. She has 24 lollipops, 12 candy bars, and 42 pieces of gum. She wants each bag to have the same number of each kind of candy. What is the greatest number of bags she can make if all the candy is used? How many pieces of each kind of candy will be in each bag? 

I'm thinking that the problem from the homework is very boring and wordy. Whereas my example students got to play and didn't have to read. It was more engaging and less intimidating. It's tricky though because our friend Barbara is precisely how the students will be assessed while I feel like the basketball cards is a closer representation to a real world problem.

Homework: The students were given almost a full class period to do the homework which was nine greatest common factor questions (with varying levels of Bloom Taxonomy).

My Glass Half-Full Take: I had students stay with me during lunch for the first time this year to work on divisibility rules and I felt like a lot got accomplished. I also had a few students stay after school, and again I believe a good deal was accomplished. This time is crucial for students to get extra help and for me as their teacher to reach them when they are struggling in the bigger fish tank of the classroom.

One Thing to Do Differently: In my third class of the day, I did a problem similar to the Barbara problem with the class after we used the trading cards and tickets. I drew pictures to help the class see it better. I would do that with all three classes if I need to teach this lesson again next school year. It's a good way to connect the hands on and the hands off.

Link of the Day: If we want innovation, we need diversity. Of course diversity also leads to a decrease in trust, lower communication and other downsides according to this same article.