Day 4: Rational Numbers

Quote of the Day: “Katie Ledeckey’s coach, Bruce Gemmell, says she’s always relished a challenge. ‘There’s a little video clip that Katie’s parents have of one of her first swim meets,’ Bruce told me. ‘It’s just one lap. She’s six years old. She swims a few strokes and then grabs on to the lane line. She swims a few more strokes and grabs on to the lane line again. Finally, she gets to the end of the pool and gets out of the water. Dad’s filming it, and he asks, ‘Tell me about your first race. How was it?’ She goes, ‘Great!’ A few seconds later, she adds, ‘That was hard!’ And she’s beaming - a smile from ear to ear. That says it all right there. She has that attitude with everything we do.’” -Angela Duckworth

Question of the Day: How do we know if a number is an outlier?

Lesson Sequence in Regular Math:

Objective: Convert fractions to decimals and decimals to fractions

1. Number Talk using this dot configuration. In case the link does not work, it is a 3x3 configuration with the dot in the middle missing. All of the students in my classes were getting 8 dots except for one. That class took the way I asked the question a little too literal because they said the color of the dots was different than how I asked in the question. Despite the lack of variety in student answers, it was interesting for the first time to conduct a number talk as students went through the various ways that they chose to count. For more on number talks just Google Jo Boaler Stanford.
2. Quote of the Day, Star Student, Question of the Day
3. My Favorite No: What is bigger 2.375 or the fraction 2 and 3/8? All students were given an index card to show the math out and then we went over it on the board. Typically, I collect the index cards, but for some reason today I did not do it. The picture above was an interesting way of doing this task that I think demonstrates stronger mastery of the standard than someone doing the standard division algorithm.
4. Vocabulary. I am teaching four classes of regular math this year in eighth grade which is a relatively big change from what I have been doing the past two years in sixth grade. I only have the eighth graders for 50 minutes where as in sixth grade the students had 100 minutes of math per day. In my first class, I was having the students write the definitions and the examples as I essentially stood and delivered. Luckily my colleague and I had a break after this class and decided to ditch this. It was boring and put little emphasis on student learning. Instead we just passed out sheets with the definitions and examples already done out. Then we gave students five minutes to practice the words with a partner. I went around the room and saw that the students were not using this time to fool around which made me think this is what we will do moving forward with new vocabulary.
5. Assigned that night's homework.

Lesson Sequence in Honors:

Objective: Analyze patterns between repeating decimals and terminating decimals

1. I did the same number talk to ensure that students got this routine. This particular class took about fifteen minutes to complete the many ways they came up with for counting the 8 dots.
2. Quote of the Day, Star Student, Question of the Day
3. Converting the fractions with denominators of 2, 3, 4, 5, 6, 7, 8, and 9 to Decimals. This worksheet was taken from a longer assignment from the Mathematics Assessment Project teaching the 8.NS.1 standard of getting students to take repeating decimals and turn them into fractions. We will get to the rest of that part of that resource this week. 
4. Discussing the patterns in groups and then as a whole class to what the fractions were. It was really interesting to see the pattern with the 7ths myself. I had never known that all of the digits were the same for 1/7, 2/7, etc. Some students recognized this on their own, but the one thing I did stop and show students was the hexagon that was formed between the numbers 142857 and how the numbers across from each other had a sum of nine. 
5. Assigned that night's homework. 

Regrets: I had way more things written on the agenda than I taught today. I am still adjusting to only having half the time that I'm used to having with the students. 

Glass Half-Full: In all classes I thought the Number Talk routine was kicked off to a successful start. Students were respectful of the time that I was giving them to wait and determine different ways to arrive at the same solution. 

In the honors class, I was really pleased that the students were left with a cliff hanger. They noticed the pattern for ninths was that the numerator was repeated, but they also questioned that 9/9 should be .9 repeated instead of 1.