6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
The Learning Objective: Discover how your test average is calculated. Rationalize what will make your test average grow and fall.
Quote of the Day: “Two young women told us that they have just returned from Iraq after having their HET truck disabled when an insurgent’s bullet went through the engine block. ‘It was a lucky shot,’ one of them said. Even if the insurgent had been aiming there, it would be highly unlikely to get that result.’ When asked what they did when the truck was disabled they said ‘We were taking fire and just hunkered down, protected the vehicle, and waited for reinforcements to arrive. We’re not just going to leave it there.’ As we parted, they thanked us for being there. I told them we should be profusely thanking them, and we did. Then one of them said, ‘you don’t have to be here. We do.’I could not believe how committed and courageous those two soldiers were. In our time at Camp Arifjan we found that was the rule rather than the exception.” - Jay Bilas
- MCAS Math March Madness
- Vocabulary pepper: The four terms were central tendency, mean, median, and mode. With some students I asked questions such as "What data value will increase a mean of 36?" Or "When will we have to average two numbers to find a median?"
- Review the homework
- Calculate your own grade.
- Pass out the next night's homework and work on that in class
The Assessment: The MCAS Madness results were 68% on the question regarding the number line, 68% on the question regarding how many questions were on the quiz, 100% on the question regarding what the algebraic expression was worth, and 95% on the question that gave the diameter and asked for the radius.
I told students we needed to get 5 correct consecutively in order to quit playing pepper. It took ten minutes in one class when I measured it.
Students were able to calculate their own grade with differing levels of cuing and scaffolding. Some students met greater challenges when I told them to find what score on their next quiz (which was printed on the sheet) if they wanted to raise their average by two points. A couple students met this challenge successfully. I put together yet another problem from here for students that involved finding a median.
Glass Half-Full: I liked the idea of having students calculate their test grades. It gave a practical and motivating reason for why finding a mean is a pertinent skill in their lives. It also notified them of their current performance in class. Students who owed me a quiz became worried that their grade was so low. Students that had done poorly begged to retake the next quiz. Students asked why the April 2nd quiz was missing (today's date of course is March 31st). The connections to our objective were great but curiosity only grew as a result of the customization of the question.
One Regret: On the homework I want to try to change the second question so that the axes are already labeled and the graph has a title. There are enough challenges for most of the class on this worksheet that this little "spoon feed" would serve me better to get students to remain focused with their questions as they pertain to central tendency.
Link of the Day: More engaging mean questions. Would you rather carry 80 bars of soap or 30 bath towels?
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