Day 7: Repeating Decimals & Equations

Quote of the Day: “You have to think about how you come across to others. Being polite and having good manners are the most important keys. You would think that the first thing people notice about you is your appearance. But generally this is not the case. What others notice more than looks are the positive things that you possess - your smile, your self-confidence, your sincerity, and your attitude.” - Napoleon Hill

Question of the Day (as always from a student): What is the difference between finding the square root and a sign with a 2 in it, a 3 in it, etc.?

Math Objective: Discover patterns for fractions with denominators of 2, 3, 4, 5, 6, 7, 8, and 9.

Lesson Sequence:

1. Number Talk 71 - 29
2. QSSQ
3. Review HW/Pepper
4. Finish the fraction to decimal conversions using a calculator
5. Discuss the various patterns

Regrets: None of the classes have discovered why the denominators of 3, 6, 7, and 9 repeat when the other denominators do not. They have at least brought up the fact that several of these repeat though.

I also think that we need to get more voices to speak up with the number talks. Students are failing to connect ideas from the previous lessons (which also centered on subtraction problems) to this lesson. We are going to do a number talk reflection to being classes next week to see if students can set goals around building off the ideas of others and also getting their voice to be part of the conversation.

Glass Half-Full: It was powerful to see students verbalize their patterns and also stop doing the standard algorithm when they recognized certain patterns - the ninths in particular.

Honors Math Objective: Find a value for a variable in a two step equation

Lesson Sequence:

1. Number Talk 71 - 29
2. QSSQ
3. In each group of 4, students were in charge of one problem. The solution from that one problem was then applied to the second problem. All students worked this out on marker boards.

Regrets: I completely messed up the directions and did not realize it for about eight minutes. I thought that all four students could work on their problems simultaneously. As a result, students were stranded because they had two variables in their problems and had no idea how to find the value of both variables (it would have been impossible as a matter of fact). I finally clarified for them that the solution from Problem 1 must be applied to Problem 2, and that gets applied to problem 3. Indirectly, this was not that big of a deal since the students could in fact begin distributing and move numbers from one side of the equals sign to the other before they knew the values of either variable. If I had explained the directions the way I was supposed to, we would have never recognized this (myself included).

Glass Half-Full: After my blunder, the students had blunders of their own. They had trouble combining a "+30 and -1" to become a 29 (many students wrote 31). They also were not bringing the sign with them when distributing. At the end of class I asked students to raise a fist of five. Five being very frustrated and one being very calm. The entire class had 4s and 5s in the air. I then asked them how fast time went by. Five being fast and 1 being slow. Again there were mostly 4s and 5s in the air. My point: we embraced the struggle.