I've been finding ways to sneak in lessons about the Nature and Processes of Science to my students in context of the curriculum we are exploring, but sometimes, these lessons are fun to have on their own. For their final assessment in chemistry, my ninth grade students will be designing and conducting an investigation to find the identity of two mystery powders. As a part of this assessment, they have to be able to demonstrate that they can write a clear, accurate, and reproducible procedure. I did some digging found an excellent resource published by the Muskegon Area Intermediate School District that I used to scaffold the procedure writing portion of this assignment. Materials:
Engage I started the lesson by asking students two questions:
Explore PART 1: Designing the Structure and Writing the Procedure Notes: Although I gave students the option of either writing the procedure as they built the structure or after, all of them chose the latter option which I found interesting. I gave my students a time limit of 25 minutes to complete this part of the activity, which turned out to be a little rushed because it took them some time to settle on a design. In the future, I need to reemphasize the main point of the activity, which is to write a clear, accurate, and reproducible procedure that someone else can follow. I ended up giving students closer to 30 minutes. Groups that did not finish within the time limit handed in an incomplete procedure. PART 2: Following and Evaluating a Procedure Notes: This was probably the most fun part of the lesson as students were very excited about putting their procedures to the test! At this point, I was busy at the front of the room comparing the structures groups built to the originals, although I wish I spent more time walking around asking probing questions such as, "What makes this procedure easy/difficult to follow? How can you tell which way the pieces are oriented? What would make this step clearer?" Explain After students had a chance to follow another group's procedure, they completed question #5 in Part II of the student handout (above). Once the students have had time to write down their thoughts I had them share their feedback with the other groups. Notes: Some students began to get overly critical and picky about each other's procedure. At this point, I reminded them of what constructive feedback looks like, and reminded them that mistakes are OKAY  they are part of the learning process. Extend An extension might be to have students followup this activity with a procedure about making a peanut butter and jelly sandwich, brushing their teeth, or some other common, everyday task. Note: This would also be a good time to discuss how scientific procedures differ from everyday ones, and how the formatting may change depending on the class. For example, in my class, students will be expected to write their procedures in past tense and include labeled diagrams with figure captions written below the diagram. Evaluate I will evaluate my students on their ability to write clear, accurate, and reproducible procedures as a part of their Mystery Solids Investigation performance task.
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Lesson Theme: Introduction to Probability and Counting Prerequisite Knowledge: Permutations and Combinations Here's an activity that I introduced to four groups of tenth graders in a recent unit on probability:
Provide minimal guidance as the groups decide on the number of combinations for each scenario. I made an exception for students who asked clarifying questions, such as:  Are there any repeating digits?  How many digits repeat? The hints are open to interpretation on purpose in order to get students thinking about the sorts of constraints they would need to consider when calculating the total number of outcomes. The discussion phase of the activity provided a rich opportunity to address student misconceptions about permutations and combinations, as well as the importance of reasoning, i.e. Does this number make sense? Is this estimate too high or too low? How does this number compare with my initial guess (intuition)? What if there were no constraints, what would the answer be? The Solutions: TEAM GARRY  3 digit code, repetitions allowed. This hint is not much of a hint at all. "Repetitions allowed" could mean that there may be or may not be any repetitions in the code. So, one possible answer is simply 10 x 10 x 10 = 1000. There are ten ways of picking the first, second, and third digits. TEAM ORVILLE  3 digit code, no repetitions. This narrows the playing field a bit. 10 x 9 x 8 = 720. Ten ways to pick the first digit, only 9 choices left for the second, then 8 for the third. TEAM APRIL  4 digit code, numbers 2 and 3 appear in the code. (a) This would be significantly easier if the ONLY numbers in the code were 2 and 3. There are only 4 possible combinations, which are easy to figure out by hand: {2323, 3232, 2233, 3322} or 4!/ (2! x 2!) = 4. (b) With repetition. There are 4 ways of positioning the "2" in a four digit combination. For each way that the "2" has been positioned, there are 3 ways to position the "3." In total, we can arrange the digits "2" and "3" in 4 x 3 or 12 ways. If repetition is allowed, the total number of combinations would be 12 x 10 x 10 = 1200. (c) Without repetition. Similar to above, except that once we have found a placement for the "2" and "3", there are only 8 and 7 digits left to choose from respectively. The final answer would be 2 x 8 x 7 = 672 My notes and observations:

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