![]() This hand on lesson is something any teacher could easily put together. Students had to take turns shaping and slicing the figures. Most groups preferred to use the plastic knife for slicing, but I did have a couple groups use the dental floss. Each group had a container of play doh, a plastic knife, and dental floss. I used the itty bitty containers that people give out for TOT sometimes. Play doh worked very well and was easy to clean up and keep track of (each group got a different color play doh so there was no confusion). The lessons involved students making 3-d figures out of clay (although I used play doh). My accelerated students really enjoyed these lessons and did a fabulous job working in their collaborative groups. They devoted three lessons to this standard: slicing through a cube, slicing through right rectangular prisms, slicing through right rectangular pyramids. I was really pleased with how the Carnegie Curriculum addressed this standard in the collaborative classroom text. There are 6 dots in B, and there are 2 dots in A and B.CCSS 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane section of right rectangular prisms and right rectangular pyramids. Here, each dot represents a possible outcome. Doing the math,įinally, visualizing this idea for the students with a Venn diagram may help them understand more clearly. Meanwhile, P( B) is the number of outcomes in each of you all having at least 2 slices, which we already know is 6 out of 21 outcomes. From our original list, we narrow it down to 2 out of 21 outcomes. ![]() ![]() Using our formula for conditional probability, we know P( A and B) occurring is the probability you've each had at least 2 slices and you have had 3. We want to connect this to what we already know. Students should recognize that we've counted the fraction of outcomes of event B (you've all had at least 2 slices) that also belong to A (you've had exactly 3 slices). Your chances have gone up! P( A| B) = 2⁄ 6 ≈ 0.33. This time, there are only 6 possible outcomes, and 2 of them result in you getting exactly 3 slices. We can count all the possible outcomes where each of you have had at least 2 slices. The probability changes when you are all staring each other down after having two slices apiece. The probability of this occurring, call it event A, is 4⁄ 21 ≈ 0.19. We see there are 4 out of 21 situations where you'll get exactly 3 slices. We can count all of the possible outcomes, and from them count the number that result in 3 slices for you. This is the fraction of outcomes of B that also belongs to A. They should also understand that P( A| B) represents the outcomes remaining for A to occur once B has already occurred. Students should be able to identify why these two probabilities are not always equal. ![]() They know how to calculate P( A| B) using the formula Students should already recognize that these probabilities, P( A) and P( A| B) are different, but they may not necessarily understand why. Always the resourceful one.īut what if you hadn't been so resourceful? Before you started eating, what is the probability you would have exactly three slices of pizza, P( A)? Once you've each had two slices, what is the probability you'd have exactly three slices, P( A| B)? (Here, event B is you each have had 2 slices, and there are only two left.) As the pacifist of the group, you grabbed a plastic knife and cut the 2 slices into three equal portions, narrowly averting the mozzarella melee. Only two slices remained for the three of you. Realizing what was going on, Bob stuffed the his remaining second slice into his mouth. At the same time, Billy finished his second slice. You finished up your second slice and grabbed a sip of soda. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.ĭo you remember the last time you went out for pizza with a couple of friends? The three of you sat there laughing and eating away at the 8-slice, New York style, pepperoni pizza in front of you.
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