Activities+Outline

The math activities and instructional strategies of the unit must meet the following criteria
1) Develops your students’ mathematical understandings (conceptual, procedural, and problem-solving) of a particular mathematics topic 2) ** Includes mathematical tasks that are high cognitive demand (i.e. rich & rigorous) ** 3) Links to Washington State math content standards & Common Core standards 4) ** Utilizes research on the student learning and teaching of this specific topic ** 5) Uses standards-based assessment that is systematically analyzed and includes multiple formative, summative, and self-assessment strategies to monitor and improve instruction 6) ** Promotes equitable student participation and engagement (special attention power/status issues, culture, language, disability, gender, individual interests) ** 7) ** Engages family/community ** 8) Develops academic language and mathematical discourse

I bolded the bullets that deserve our most needed attention at this point.

Time to tune up our lessons' ideas
 * 1) intro activity by having students determine what is impossible..........certain and tying them to decimal, fraction and percentage.
 * 2) Main activity at this point seem leaning toward the spinner. If you guys have a chance to read "Put the right spin" article, they have students design the spinner and have them experiment their design afterward. Thus we can have students transitional from idea to representation. A spinner is a nice concept because it relatively involve fraction (part/whole) which can be use to translate to decimal/percentage smoothly. One of the learning outcome as a result of this activity is that for students to recognize "smaller area--->heading toward the impossible direction and vice versa
 * 3) I LIKE THIS IDEA. I'LL TAKE A LOOK AT THE ARTICLE. **-Ok, I just skimmed over the article, and my concern is that acitivity has to accomplish a lot in order for the kids to get the picture. Is there anway we can trim it and still reach the goal of the acitivty? Or should we look for a simpler alternative ?**
 * 4) **Sue here - I was wondering if this would work with dice. It's a theorectical 1/6 probability but we could have the students collect data and compile it for all classes to work with later. It would be easy - a simple tally sheet, maybe taking turns with a partner, then pairs could share until we had a class set of data (which could be compiled for a days worth of data). What do you think? We would have experimental data to compare with the theoretical. Spinner is ok too, but I think we would need to have premade simple spinners to not run out of time.**

What I observe so far is that we are trying to "grasp" the big ideas of basic (but fundamental) concepts of probability while shying away from a typical approach to probability such as we specify the theorictal probability, perform the experiment and finally make meaningful connections between the two. For example, rolling a single dice. each numeral has 1/6 chance of landing....and we conduct the experiment.

Another way to approach to the main activity is to have a "preset" spinner--which can be something on "probability of getting the birthday month" correct. But does it match criteria #2? I THINK IT COULD MEET CRITERIA 2, IT JUST DEPENDS ON THE QUESTIONS OR TASKS WE HAVE THEM ANSWER OR DO. I don't know for sure. But the approach mentioned above as adapted from "Put the right spin" does seem to fit that requirement (reading between the lines from that research piece).

criteria #7 is a bit tricky, shoutouts on this will be great (HOW ABOUT USING ONE OF THE GAMES WE WILL CHOOSE, AND HAVE THE KIDS BRING IT HOME TO PLAY WITH A FAMILY MEMBER, OR FRIEND NOT IN CLASS AND RECORD THE RESULTS. THIS INCORPORATES IMPORTANT PEOPLE TO THE STUDENTS INTO THE ENJOYMENT OF THEIR MATH LEARNING...) I like that. Maybe we could play one of the multicultural games, and then have the students discuss it with their families, and find out if they like a different game of chance (which they could play at home with their families and then share back with the class?)

Learning goals of the mini-unit: What do you want the students to know and be able to do?
I am copying and pasting from the Draft Page. What I copied is a general reflection upon the propose "lesson activities" on this page. Again these are the long and general version:

2. The Probability characterized along the continuum from impossible to certain (Impossible, least likely, likely, certain) (probability of an event expressed in number: decimal 0 to 1; percent 0%-100%)

//(students may ask "why not negative, 1.5...or 110%) I think this is really important - maybe even worthy of a lesson!// I AGREE.

3. As number of trials increase, better estimate of probability increase...approaching close to theoretical probability.


 * I had an idea of compiling data from an event and recording it for each of my 5 classes and show the students how data changes from just looking at the results from one class to looking at the compiled data of all 5 and how this shows the way larger numbers more closely reflect the //theoretical probability//. I like this too - could we compile data from a game and use in our thrid lesson? I THINK WE COULD DO THAT...
 * develop simulation approach to solve real-world problems -Yes in VDW (p.468) they discuss using //simulation// "as a technique used for answering real-world questions or making decisions in complex situations... many times simulations are conducted because it is too dangerous, complex, or expensive to manipulate the real situation". Immediately that show "Mythbusters" comes to mind that has been on the //Discovery// channel for the past few years -also using dummies in cars for safety tests in new cars. They also use the example on this page of when designing a rocket and testing systems for possible failure, using a model, even a computer model, helps give a more accurate estimate of possible failure because using a computer model for the event allows the possibility of conducting 1000's of trials which ties back in the higher the amount of trials brings the result closer and closer to //theoretical probability//.
 * More Intuitive
 * Educated guesses versus wild guesses