Day 5: Repeating Decimals

Quote of the Day: “Do rewards motivate people? Absolutely. They motivate people to get rewards.” - Daniel Pink

Question of the Day: Why is 9/9 equal to 1 instead of .9 repeating?

Regular Math Objective: Place a fraction that is converted as a repeated decimal on a number line. 8.NS.1

Lesson Sequence:

1. Number talk 43 - 8. It was astonishing how many students used the standard algorithm in their heads instead of other methods. I cannot picture borrowing in my own head. Myself and the other teachers in the room contributed our own strategies after the students had shared theirs to let them know that even the adults think about the problem differently. 
2. Quote, Star Students, Question of the Day
3. Reviewed the homework and did pepper for the vocabulary terms from yesterday
4. Had students locate points on a number line. I kept telling the students to do the problems on the right of the page first since they were all terminating decimals and were much easier to locate on the number line. The students would then stop instinctively before doing the left side of the sheet. All that being said, I need to edit the sheet so that students can put these points on the number line in the order of terminating decimals first and then repeating decimals. Students struggled to find the right place to put the repeating decimals on the number line. The exit ticket also confirmed this. 
5. Exit Ticket. Many students did not finish this since I gave it out with about three or four minutes left in class. 
6. 2-4-2 Homework

Regrets: The exit ticket was revealing. Many students had issues converting fractions into decimals. For the fraction 4/15 students were putting 3.75 meaning that they were dividing 15 by 4. That being said, by the time they looked at number two on the exit ticket and saw the number line they should have recognized their mistake. I think as a result of the lack of time they had to complete the exit ticket they were not able to process all of this.

Glass Half-Full: I spent more time than I usually would giving feedback directly on the exit ticket for students to see in class the next day. My goal in doing this is to let students know that I value their effort on exit tickets and also that they start to find their mistakes on these exit tickets.

Honors Math Objective: Convert repeating decimals to fractions

Lesson Sequence:

1. Number Talk 43 - 8. 
2. Quote, Star Student, Question of the Day
3. Reviewed what the numbers inside a square root symbol mean from the previous night's homework 
4. Repeated decimals worksheet from the Mathematics Assessment Project. 

Glass Half-Full: The lesson really took off when students had to convert .54 repeating to a decimal. I made the mistake initially of helping a student through that problem, but went around to other groups shortly thereafter who were struggling and did not give it away. I focused instead on what was happening when students tried to subtract .45 repeating from .54 repeating if they were trying to do 100x - 10x. We ran out of time just as students were starting to get some clarity. 

Regrets: As a result of running out of time on that one issue, I could not give an exit ticket. The students were working collaboratively and productively in groups, but I would have liked to see what they retained individually at the end of the class.