Mini Beach Ball Toss:
The weather is snowy and bitterly cold. We are antsy! We needed some energy because we couldn't go outside today to play. I found my little beach ball, turned on Beach Boys music on iTunes through the SB and I tossed a blow up mini beach ball at one of my more rambunctious students and surprise him, starting a little fun.
I asked him: What's 1/3 of 18? After he answered, I instructed him to make up a comparison problem using 1/4 1/2, 1/3 etc. of another whole number. He chose 1/4 of 16 and tossed the ball to a girl who easily solved it as 4. The ball continued to be tossed around as students solved problems. I like this game because it: One; forces them to divide mentally and supports fluency standards. Two; forces them to think about division equations and comparisons using fractions and their reciprocal. When we stopped, we discussed how mental math and that having to figure out division by using the reciprocal was helpful in understanding comparison to the whole. They had a lot of fun with this and were really amazed at how quickly they could think about dividing using the reciprocal.
Get Going! I used page 1 of SB file, Powers of 10; Extending Their Thinking (please download) and Google Docs to do the job. This helped students collaborate, share, see and edit work as we learned how to write concisely and accurately about what they already know about the inverse. We used iPads and their Google Doc accounts. If you do not have the technology or just your computer and SB, have students write in their notebooks and then have them dictate what they wrote.
The Google Doc allows them to see each other's writing as they write and I hoped they would build upon their own writing by looking at the examples of other students.
The progression of this lesson works like this:
1. I opened up my SB file on Board to start a discussion about the inverse. I did this because the Google Doc will create distraction that I didn't want to start just yet and I wanted to set them up for tomorrow's lesson. (They will recognize the page when we begin tomorrow as this SB file is used again.)
I spent about 5 minutes getting clear explanations of what the inverse is. "Understands the inverse" shows a great explanation of his understanding of the inverse. The next clip shows a student who is confusing Commutative Property with the Inverse. Confusion between inverse and Commutative Property. (My reflection addresses this in a little more depth.)
2. Then, I opened up my created Google Doc on the SB and showed them how it works. I assigned each of them a number to type in so that they didn't type over each others work.
3. I gave them about 10 minutes to type and explain what the inverse meant, encouraging the use of the word bank they have been collecting through the unit that contains content vocabulary like, divisor, dividend, quotient, product, factor, etc.
After everyone was finished writing I held a writer's collaboration. Writing Collaboration Sample from Class . We discussed which answers were well written by looking at sentence structure and clarity as well as use of math content words. Students were able to collectively look at the writing and have examples written by their classmates in front of them to compare their work. As we went through each one, I wrote my suggestions and support right there in front of them where they could see in another color. They enjoyed this because I made sure I said something positive for each one. I use this strategy after I establish a feeling of safety within the class dynamics, to get kids to become more proficient in writing about math and an interesting way of assessing what is missing from their thinking. Students have a chance to support one another and take responsibility through this technique.
Students added their thoughts as I talked, and I encouraged their input about sentences, whether they thought there was enough vocabulary or clarity. Mostly, they were intrigued with seeing their writing up on the Smart Board. It also establishes understanding of the value of writing for others and that we have a responsibility to use good writing skills so we create solid and clear messages.
This is Common Core! This is what it is about! Mastering understanding of the relationship between inverse operations through writing hold them accountable for thinking and not just for doing problems.