Another new unit and another Which one Doesn’t Belong? to start out.

Then we did notice/wonder with tree diagrams.

After doing some practice with tree diagrams, I encourage students to start looking for a pattern to figure out the total possible outcomes each time. Most often students are able to notice the counting principle. Sometimes students will notice the pattern before I even mention it. They’ll ask, “Can’t you just…” I usually nearly scream at them, “Wait! Not yet! Don’t ruin it for those that haven’t noticed the pattern yet!”

Tree diagrams are good opportunities for students to make up the problems as they go.

One problem I like to give students is “A tree diagram has 16 possible outcomes. What could the tree diagram be?”

Then we start talking more about probability. After spending a day on theoretical probability we start talking about experimental probability. I know there have to be some awesome probability activities for 6th grade, but I haven’t found them yet. (If you’ve got some, please send them my way!) What I’ve done the past several years is set up 5 different stations for students to work through: coin toss, dice, deck of cards, box with different colored cubes in it, and a wheel with different colors on it. Then students compare their experimental probabilities with the theoretical probability.

Here’s an example of one of the stations for experimental probability.

I also use this as an opportunity to review converting between fractions, decimals, and percents. Another way that I like to spiral concepts in this unit is to give a problem like the following:

The following numbers are written on cards and put into a box: 1, 1, 3, 4, 5, and 8. What is the probability of randomly picking a prime number? a factor of 20? A multiple of 4?

To review we play mathketball. Students LOVE this simple game. Students make a circle around the room with their desks, and I put a trash can in the middle of the room. Students answer a question I put up on the board, and if they get it correct, they get to crumple up their 1/4 sheet of paper and try to make a basket.

Here’s an example problem from that.

Here’s a different class playing mathketball, but you get the idea of what it is. I do try to pick topics for mathketball where the problems shouldn’t take students too long to solve and/or have fewer steps. I don’t want students to feel rushed, but I also don’t want students who complete problems quickly to be waiting a long time.

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