## Wednesday, March 2, 2016

### Day 112: Estimation, Exponents & FAL Quadratic Gallery Walk

Today's estimation was how tall a bus was that Mr. Stadel was standing in front of. Most students thought it was double his height or a little less than double. Many students remembered his height. Students had to convert the answer to inches, so I asked students if they knew a trick for multiplying 11 by a 2 digit number. Only about 3 kids knew it. Basically if you want 11 times 14, you split the 14, add the digits, and that sum is the middle digit. So, 11 times 14 is 153.

We discussed the ranking of some numbers in scientific notation on the Size it Up worksheet from the FAL, and student volunteers told me which number multiplied by 4000 got another number. We discussed strategies for multiplying decimals by whole numbers, whole numbers by whole numbers, and numbers in scientific notation by each other. Then they started on 8.2.2. It reviewed multiplying power numbers thankfully which they needed. Then they worked on power of a power problems, and discovered that when raising a power to a power you multiply the exponents.

They didn't get much further than that, and we will pick up tomorrow with the difference between (2x)^3 and 2x^3 as well as dividing power numbers.
 Discussing the multiplying by 11's trick here for 11 times 13.
 Here a student said they "just guessed" as their reasoning. We went back to her reasoning after Kyle thought it was a little more than 2 Mr. Stadel's. I asked if anyone could state Tatyana's reasoning based on her estimate, and Emma said that Tatyana must think it's a little less than 2 Mr. Stadel's, based on her estimate.
In accelerated we practiced having a quiet and fast start, when I wrote that message on my personal whiteboard as they came in. They proved to me that they could do it, and I will continue to do this until we don't need that reminder.

I got students started right away on matching the equations to the graphs for this awesome Representation Quadratic Functions Graphically FAL. Some thought they were done once they had matched them. I told them that they had to fill in the blanks for the missing representations of the equations. Some got to writing justifications on their posters. I think they need to work on being OK with more than 1 person working on the poster at the same time. I saw a lot of great conversations, reasoning, and collaboration.

I was very impressed that a student remembered to substitute the a value if -1/2 from the standard form into the quadratic form. I will try to remember to point that out tomorrow.
 Here one team member is working on equations, another is working on gluing the matches onto the poster.
 In this group one student was working out going from one form of a quadratic to another algebraically.
In the 15 minutes I gave them 5 minutes to walk around (gallery walk) and pick a poster to give constructive feedback to. Since we have 32 students and 8 tables, I said only 4 people per table maximum. Since students had struggled with giving productive constructive feedback in the past, I put up this image I found on twitter that Norma posted to help them:

 I think I want to make a poster of this for the classroom, and make the font much bigger.
Students wrote their feedback on blue post it notes, and stuck them on the poster and went back to their own poster to read the feedback given to them. Then in the last 5 minutes I let them revise and finish their pre-test for this activity, and told them that they should be much more knowledgeable about quadratics after this activity.

 Giving feedback on posters during the gallery walk.

 Not skimping on the feedback! Woohoo.