Nice to Meet You Area Model

This week my second grade students have been exploring multiplication strategies.  We started off early in the year looking at arrays and using doubling strategies.  Then we moved to helper facts.  These are still used to this day, but we introduced a new tool this week.  Enter the area model.  Hello!

Students transitioned from arrays to squares, but didn’t sit at that spot long.  Through the…

Hands-on

    My fourth grade group just finished up a unit on division.  They spent a great deal of time exploring division and what that means in the context of a variety of situations.  One of the more interesting parts of the unit delved into the use of the partial-quotients method.

You might be a fan of this method if you’ve ever wanted to know why the traditional division algorithm works.  I was in that boat.  During my K-12 math experience I never questioned what was introduced.  I was always encouraged to use the traditional division algorithm.  It didn’t make sense to me why I was dropping zeros or setting up the problem in a certain structure.  I just played school and figured that it wasn’t worth trying to find meaning, but instead just pass the class and move on.

For the past ten years I have been introducing the partial-quotients method to students.  This method brings more meaning to why the division process works.  Students also seems to grasp a better understanding of how partial-quotients can add up to a quotient with a remainder.

This year I introduced something different to the students.  Students were asked to use the partial-quotients method to divide numbers and then create an area model of the process.  I had quite a few confused looks as most students think of multiplication when using area models.  After modeling this a bit I noticed that students continued to have issues with appropriately spacing out their area models.  This was a great opportunity for students to use trial-and-error.

I noticed that students had to first use the partial-quotients method to find the quotient and remainder.  They then had to split up the area model into sections that matched the problem.  This spatial awareness piece is so important, yet I find students struggled with it to a point that they were asking for help.  Maybe it’s a lack of exposure, but estimating where to split up an area model to match the partial-quotients seemed to challenge students on another level.

This activity has me wondering how often students use spatial awareness strategies in the math classroom.  How often are they given these opportunities?  Reasoning and estimating strategies also play a role, but actually spacing out the partitions isn’t what students were expecting last week.

I’m looking forward to seeing how students progress in using area models moving forward.

Hello, everyone! This will be a place for me to post groups of concepts together, as well as answer questions that might require longer explanations. 

https://learnzillion.com/lessons/216-multiply-whole-numbers-by-mixed-numbers-using-area-models

Mrs. Wallaker's ShowMes to show you:)

https://drive.google.com/a/hollandpublicschools.org/file/d/0B9HBUfWoB37OY29XalNRdlZXZFU/view

Previously I talked to you about the AREA model (look at the previous post). Now, I'll apply it!

What sort of things prolong emotions?  These are just a few factors.

Uncertainty and Surprise--If something randomly and surprisingly happens to you, it's very confusing, and you spend more time attending and reacting to it.  So if you are a poor student and you randomly get an A+, it is really surprising, so you will be more happy.  I really like this study:  Experimenters randomly give students a card in the library w/ a dollar attached.  Half got a card that explains why they got it, half get a card that doesn't really explain it as well.  Test to see who is happier?  The people with the card that didn't explain it!

  Surprise!

Another study I like:  Have half of people write about how they met and started dating their significant other; have the other half write about how lucky they were to have their significant other and how they could have NOT met them or dated them.  So who was happier at the end?  The people who thought about NOT having their significant other and how lucky they were.

So you can get a happiness booster if you just take the time to think about how lucky you are and count your blessings!

Similarly, if you are unsure of what is going to happen, or in expectation of something, you attend and react to it more as well!  So if you just ordered something from the Something Store (google it!), you are so happy and excited because you are unsure of what you are going to get, and you are expecting it in the mail!  Also, this is why there are so many cliffhangers in TV shows.

  www.somethingstore.com

Rumination--This is especially for my friend Nuhad, who wanted to know how people who are depressed are unable to recover from negative events.  People who are depressed tend to fall into this cycle of rumination, where continually they spend time thinking of past failures and reliving them.  This refers to the ATTENTION part of the AREA model, where people are continuously attending to the event.  This leads to extended REACTion times, where they are just sad.  What would really help would be to make it to the next step, EXPLAIN, where they can explain the negative event in a positive way (this is also key, so if depressed people are explaining this negative event negatively, then it will affect how they feel about themselves and their identities negatively) to themselves, and manage to stop thinking about it so much and ADAPT it into the background. 

It is definitely hard, and there are ways to help with the EXPLAIN part of the process:  There is a writing exercise known as the Pennebaker writing exercise that is great (google it!), and there is a distancing thing people can do where they actually distance themselves away from the negative event.  Finally, just distracting yourself and preventing yourself from thinking about it helps. 

(This significantly improves your health, working memory, and helps you cope and find yourself)

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