More STAAR practice. Starting with old material and will soon get to the most recent material…
We continued our discussion of OUTLIERS and how they affect different measures of central tendency.
Today students worked through several different graphs, interpreting the data and answering questions related to the graph. They worked in their small group, helping each other and figuring it out on their own.
We collected more data today so that we would have random numbers to explore mean, median, mode, and range — the measures of central tendency.
I chose a random sampling of students from the class to give us this data. They each had to tell how many first cousins they have.
I gave them time to think and then randomly selected 9 students. Luckily, in two of the 3 classes we had an obvious OUTLIER (a new term, for some), but it was just what I was hoping for. While most students had anywhere from 4 to 15 cousins, two students in separate classes had 55 and 53 cousins, respectively. WOW!
We then discussed the outlier and what it does to these measures of central tendency. Students worked in small groups to compare the mean, median, and mode with the outlier to the mean, median, and mode without the outlier.
In the end, they discovered the median number is least affected by the outlier. We had a rushed ending to class so we will discuss this some more tomorrow!
Students came in and read this on the board:
Some thought this was somehow an April Fool’s joke… but instead, I wanted them to unknowingly create their own data. They stretched their arms, their legs, spread around the room, 3..2..1 GO! They jumped for 50 seconds, counting their jumps in their head. After time was up, each student came up to the board to write down their total. At their seats, the rest of the class filled in the data onto their notes.
We used this data to create a frequency table, stem-and-leaf plot, and then a line plot. We discussed how these displays all differ and how one may be a better display than another, depending on what we want to learn from the data.
7th graders took a STAAR writing test today so I did not meet with them.
We finished up probability and continued some STAAR review.
We started STAAR review today–just a review on beginning of the year items. We will continue this at least once a week up until STAAR.
In the warm up, I knew students had a grasp on the Fundamental Counting Principle when it involved events such as choosing 4 tops and 5 pants….how many possible outfits? They knew you just multiply each events’ outcome to find the total possible outcomes. We did an example involving Amy’s ice cream (9 ice cream flavors, 31 “crush’ns” options…how many possible combos of 1 topping ice cream flavors can we make?) (9 x 31 = 279 outcomes). They got it!
However, we spent lots of time going over the sample space problems that involve more than 2 events: flipping 3 coins, or problems like, “How many outcomes are there on a three-question true or false test?”
Students inevitably want to multiply the 3 questions x 2 choices each to get 6 possible outcomes. We had to review that the Fundamental Counting Principle states that you multiply the outcomes of each event. In this case, that would mean 2 outcomes for question 1 (true/false), 2 outcomes for question 2 (true/false), and 2 outcomes for question 3(true/false). That means, we multiply 2 x 2 x 2 to get 8. This review seemed to help clarify the misconceptions.
How many of you have trouble putting together an outfit each morning?
Lots of hands went up. In this example, students had to create “outfits” given 3 tops and 2 skirts. Many quickly realized the “Fundamental Counting Principle” what states if you take the number of outcomes of one event and multiply it by the number of outcomes of another event, you will get the number of all possible outcomes.
In this case 3 outcomes of shirts x 2 outcomes of skirts = 6 possible outcomes.
After some brief notes, we did a spinner experiment on the Smartboard. Smartboard has some great interactive components, one of which is a spinner that actually spins! Before actually doing the experiment, we talked about the theoretical probability of landing on a certain color. If we spin the spinner 5 times, it should land on each individual color 1 time each. Students understood that if we spun the spinner 20 times, it would then land on each color 4 times (ah, proportional thinking!) In experimental probability, we realized these chances are not always true.
I gave several students a chance to come up to the board and spin the spinner (which just involves “tapping” the spinner one time). They had a lot of fun trying to guess where it would land and would cheer when it landed on the color of their “bet”. (Watch out Las Vegas!)
20 spins with the tallies recorded, and students were ready to answer some questions on experimental probability. They worked in groups and then answers were put up onto the board.