The first week of school has been a blast. This is my first year at a middle school, and I am really enjoying these seventh and eighth graders. They are an impressive bunch, and I am very excited for what is sure to be a great year.

Starting off the year, I got the idea from a friend of mine to present a really nice counting problem. We started looking at a soda can pyramid picture that I found. The bottom row of the pyramid has 11 cans with each successive row having one less can until the single can at the top.

The goal was to count the number of cans, and after students went through and added them all together, we tried to come up with a better way of counting that would be more efficient. A few students picked up on the trick commonly credited to Gauss, which was fun because I was able to show them a nice numberphile video about the counting problem after they worked it out.

The fun began when they were faced with a pyramid that has 50 cans at the bottom. They thought about it independently for a couple of minutes, then they were split into six groups to work out the problem on big white boards. Below are some of the great ideas they came up with and presented to the class.

This idea was about turning the pyramid into a square and subtracting off the area. The coolest part about this idea was that the group accounted for the single can at the top of the pyramid.

This idea was about adding up groups of tens, nines, eights, and so on. The group noticed that each successive group of numbers was reduced by five, which was very cool, and they were able to use that to quickly get to multiplying their sums.

This idea was very impressive to me. This group was trying to find a formula to use to find the number of cans. They went through a few different ideas, tried them out to see if they worked, and they finally landed on this beauty for any pyramid with base B.

The other three groups came up with similar solutions, and this served as a great problem for the start of the year. They loved working in groups, they really enjoyed using the white boards, and I enjoyed being able to go to each group and help them make sure that each member of the group was on board and asking good questions.

I look forward to posting more of these fun activities throughout the year. I am very excited about the start of the new year.

## Saturday, August 31, 2013

## Sunday, August 18, 2013

### Count Down to the First Day of School: 2 days and 9 hours

Students arrive this Wednesday, and I am starting to get more and more excited about starting a new year with a new set of students. Tomorrow will serve as my day to finish getting my classroom ready, and Tuesday will be the day I get to meet students and parents for the first time. The summer has flown by, and I find myself reflecting on all that I have learned from last year and from this summer.

My goals for this year include making better use of technology to help reduce the time it takes for me to give feedback to the students, being effective in challenging students to figure things out with tough questions while providing just enough supports to keep them from feeling discouraged, and I want to execute effective problem based learning this year.

Some challenges I'm anticipating include the space limitations in my classroom, the time it will take me to plan and set up the technology, and my ability to manage my classes when they work with each other.

Another goal is to journal at least every week on my progress, so we will see how that goes.

Wish me luck, and tell me what your goals are?

My goals for this year include making better use of technology to help reduce the time it takes for me to give feedback to the students, being effective in challenging students to figure things out with tough questions while providing just enough supports to keep them from feeling discouraged, and I want to execute effective problem based learning this year.

Some challenges I'm anticipating include the space limitations in my classroom, the time it will take me to plan and set up the technology, and my ability to manage my classes when they work with each other.

Another goal is to journal at least every week on my progress, so we will see how that goes.

Wish me luck, and tell me what your goals are?

## Friday, August 16, 2013

### Bottle Holder Problem Idea

Last weekend I had the privilege of having dinner with my grandparents. While I was there, my grandma showed me a gift she received on the form of this wine bottle holder. Upon seeing it, I instantly thought of a number of questions.

1) What is the angle of the base of the holder?

2) At what angle is the bottle in relation to the holder?

3) Are those angles the same?

4) Is there a way to prove the angle congruence?

5) If the bottle angle is equal to the angle of the base is that a requirement for the holder to work?

6) At what level of liquid will the bottle fail to stay up?

7) Would it be possible to dispense liquid from the bottle while it is in the holder? If so, for how long?

These are all questions that my family and I brought up during dinner, and I think it would be interesting for students to think about these questions and formulate a way to answer them.

What questions would you ask, and do you know the answers to any of the ones above?

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