Day 59 – Cookie Sharing

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Math 8 – Today’s class was working on sharing a cookie problem. It turned out to be a fantastic class, perhaps the best we’ve had this year. The problem had a low entry with lots of ways to solve it. We were able to walk around the room and see the different solutions.

The above solution is one of the most intuitive.  Students realize that 1/2 the people get 1/2 the cookies (21) and since they each share this equally, they each get 10.5.  This continues for the next two people.

Below is the most common solution.  Students would turn this into a rate question as students naturally understand rates with little to no instruction. They find that 3.5 cookies cost $1 and then calculate how many cookies each person can have.

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The rate thing is pretty interesting. Why are students so comfortable with rates? I think it’s because rates are usually very concrete. They explain the relationship between tangible things. Cookies per unit dollar. Kilometers per unit hour. Miles per unit gallon.

Next we had the fraction solution. This one is really neat because in our discussion the students realize that they are once again dealing with percents. 7/12 is 7 parts of the whole.

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Finally I would end our tour with the primary goal for the lesson: equivalent ratios.  This wasn’t the most common solution, but every class did have it.

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Once you get to the equivalent ratio solution, you can see that it is perhaps the cleanest to exhibit and explain. I didn’t see this at the time, and I may come back to it and highlight this property.

The class was full of Flow, engaged students and learning.  So awesome.

Now here is my dirty secret about the day. Many of my students were on field trips so the class size was in the range of 18 kids.  While I can totally manage a class of 30, wow does the party change when the numbers drop.  Behaviour problems were almost non-existent, and the level of dialogue was amazing.

If someone tells you that class size doesn’t matter, maybe they’re right… Unless they’re referring to a class where students are engaged in collaborative work that needs to be discussed and shared, in which case they will be dead wrong.

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Day 51 – Discounts

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Math 8 – Today the class worked on the above problem. Lots of groups had problems with it, and couldn’t move off the idea that 30% + 45% + 25% = 100%. They couldn’t think of any other thing to do with the numbers.

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There was also some nasty misconceptions with adding fractions! Lots of kids did 45/100 + 25/100 + 30/100 = 100/300.

By the third class of math 8 I finally found out what I had to do as a teacher to get the students on the right track. First, I had to make sure that the problem doesn’t turn into a money issue. If students equate the discount to saving money, there will be trouble. Keep the problem centered on saving gas, because everyone agrees that you can’t have a car drive without using fuel. Secondly, I had to really listen carefully to what the students say and really jump in when they say something like “45% of 70”. A ha! What operation is associated with the word “of”? That’s right, multiplication, not addition…

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The neat thing about this problem, after I’ve done the good things needed to pull it off, is how engaged the students get. They can taste how close they are to a solution and want to solve it.  It was Friday afternoon, the dismissal bell had gone, and I had several kids sticking around to finish their work.