This week, my Algebra 1 classes started the outcome that includes GCF and LCM. Before I said anything about the next topic, I told my classes that I had this problem that I needed help solving.

*The principal asked me to take the other teachers through an activity during our next in-service day. He wants the other teachers to work in groups to create lesson plans for our new anti-bullying campaign. For this training I will have access to 48 iPads and 60 copies of the anti-bullying book (I am not allowed to make more copies because of copyright laws). I've decided to have the teachers work in teams and compete against each other. In order to have the teachers create the most lesson plans, I want to have as many groups as possible. Also, since they are competing against each other I want each groups to have the same amount of resources (iPads and books). Lastly, since I have these resources I want them to all be used. No iPad (or book) left behind.*

Next I put the students into groups of 3 or 4 and gave them 48 pennies to represent the iPads and 60 paperclips to represent the books. Below are some photos of the students' work.

If a group was stuck I would ask them if I could have two groups. Yes, because each group would have 24 iPads and 30 books. Next, I would ask if I could get more groups, since that is one of my objectives. Could I have 5 groups? No, you can't split 48 into 5 groups evenly. Great! Now work from there.

Every time a group claimed to have an answer, my response was "Can I get more groups?"

Eventually each group discovered that I could have 12 groups of teachers working with 4 iPads and 5 books.

We had a class discussion on this that eventually lead to GCF.

Next I displayed this website on shipping routes. I would put in what seemed to be random numbers for each boat and asked the class when the two boats would be at dock again at the same time.

I started with 2 and 4 minutes, then 4 and 5, then 4 and 6, and finally, 3.2 and 2.4 minutes. You can have so much fun with this one.

I found shipping routes originally on 101.qs.

Thank you! I just tried this with my class and it was a hit!! It's so simple but they had a great time trying to figure out all of the combinations before we went into the method.

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