To get their brains warmed up today for fun, I drew four squares on the board. I asked my students to divide each square into fourths, four different ways. I asked them to try it in their notebooks for a few minutes before we volunteered to try on the board. It told them that there could not be repeat divisions. All the ways had to be completely different.
They all took a few minutes at drawing the divisions in their squares in their notebooks and suddenly their hands shot up to volunteer with the enthusiastic "OOhh, Oohh! I got it !" sounds that drive the level of excitement about problem solving in math class.
The first student came up and drew what I expected. I have made an Educreations video that shows what was going on and the solution so you can try this with your students in the classroom. Practice drawing that last box a little bit before you teach it.
By the time we were done, they were pretty mad at me, but I explained that I wanted them to understand that often math has abstract ideas. That it produces things that fit patterns that we don't expect. I wanted them to understand that division can mean more than just one way of thinking, just like the box method and different entry points we all use to solve. I explained that the last design fit the rules, but not what we were used to thinking about, much like learning box method division.
I asked students to join me in front of the whiteboard on the floor.
Before I began the lesson, I shared with them their pretest scores from several weeks ago. The highest score on that pretest was 1 out of 33 points. I talk with my students about growth and progress continually on different levels because it helps students see how they are mastering CCSS. I have chosen to review the pretest now because I want them to start appreciating how far they have come in this division unit and also think about what goals they need to set !
The day before, I passed out Division Test Review 1 & Division Test Review 2 according to student mastery levels. I had them partnered up with a person who had the opposite worksheet than they did. They had worked on these in class from the day before and used this opportunity to use this completed review assignment as a final discussion. It was time to acknowledge our learning, ask more questions and review standards learned. They compared their sheets to help support each other in their learning and coach each other. This collaboration is helpful in building confidence, affirming their understanding and developing trust.
I wrote each problem sample first from Test Review 1 and then Test Review 2 so that students could share answers and ask questions no matter which sheet they had completed. They collaborated in their work to find out where they made a mistake. It was often subtraction. Once and awhile it was multiplication facts like 8 x 60 listed as 240. (Whoops! ) Dialogue about strategies went back and forth between partners when the word problems were the topic.
Each student shared their equations and we debated where they were written correctly. I explained that sometimes problems can be solved with different equations. But that the ones on this assignment were pretty straight forward. Two step problems are difficult and we debated the problem about the power outage. In this problem, the last step is subtraction. Most missed it.
We discussed the meaning behind each number in the equation and then it made sense to most students. They could see they had only solved for the people whose power was restored on Wednesday and not Thursday. So we discussed how we can tell it is a multliple step problem.
I asked if students had any more questions about their work.
I asked students to get out their notebooks and list the goals that are on our whiteboard. I list "kid friendly" goals paraphrased directly from the CCSS. I know that if they write them down, their brains will further understand what they need to know. Through writing, reading is forced, and then through the discussion of each one, the synthesis completely takes place. It gives them direction and completes the review assignment. The next task was to discuss what we needed to do to prove we mastered our goals and standards. The question posed was: What are you going to do to show you have mastered these standards?
Finally, we listed the most important things that would help us master the formal test. Our Notes contains blue writing that are what my class found that was important for them to remember.
I wanted to close this lesson today by having my students write to me about the things they appreciated learning, how they were going to show me how they mastered standards, and/or areas in which they needed more support. Using the notes from the board that we had compiled, I wanted them to list the specific things they would be using to show mastery. I reminded them how far they had come in mastering standards in comparison to the pre-test scores, but that division is complicated and they need to think about how they would succeed. I took a look at each student's list as they finished them. Afterward, I had students log onto Read, Write, Think.org onto the Letter Generator and choose Friendly Letter.
From this generator, they could write a properly written letter to me, reflecting, acknowledging their responsibility to learn the standards, explaining their thoughts and writing what they needed to do to practice. I will use this to also help assess their test readiness and look at what questions they may still have. With individualized learning, I will assess only those who I think are ready.
In this Educreations Video, you can see some of the samples of the letters we generated and printed. Language arts standards are being mastered through this writing lesson too. These letters were written as rough drafts. They will be edited later.