Day 52 Percentage Quiz & Integers Introduction

6th Grade Math Standards: 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line 
diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea 

level, credits/debits, positive/negative electric charge); use positive and negative numbers to 

represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

The Learning Objective: Find the whole given a part. Find the percent of a number given a whole number percent from 1 to 100.Compare percentages, decimals, and fractions. Order percentages, decimals and fractions.Convert numbers between fractions and percentages. Convert between decimals and percentages.Convert numbers fluently from fractions to decimals and decimals to fractions.

Define an integer. Graph integers.

Quote of the Day: “People have more capacity for lifelong learning and brain development than they ever thought. People may start different...but experience, training, and personal effort take them the rest of the way. It’s not always people who start out the smartest who end up the smartest.” - Carol Dweck

Agenda:

1. Quiz on Percentages
2. Work on WQ #8 which was passed into me today and I gave back as students worked on the quiz
3. Flashcards/3 Column Notes
4. Integers Chant
5. Integers Notes
6. Integers Practice (homework, but it was mostly done in class)

The Assessment: The quiz was assessed. Here's a look back at some of the wrong answers that were common:

The mistakes made in numbers four and five were more common during the study guide than they were today. The student did know that turning a percent into a fraction requires them to use a denominator of 100. That part was basically drilled in. Obviously the directions of simplest form are missed here, but I'm actually more concerned with leaving the % symbol next to the number as part of the answer here. For students that did not simplify I only took off half because I think they demonstrate one of the skills required.

Here is another example of a student getting an answer wrong, but it's not as if the student has learned nothing. Should partial credit be given? In my opinion, the symbol for percent and differentiating between a percent and a fraction is part of mastery of this topic. There is no way of giving partial credit on these two questions. That said, I'm sure the student who answered these wrong will quickly make the note of what was wrong and I would like to retest the topic with them to confirm.

This answer came up a bunch of times. It's why it was my favorite no a few days back. Regardless of the number of times we practice it, it's still going to get a few students. I bet most students will classify this as a simple mistake as opposed to something they don't really understand.

You can't see number nine in the picture here, but it asked for 86% to be made into a decimal. I don't recall anyone getting it wrong. This one stumped them of course because of the decimal. I'm not sure I gave enough practice on this type of problem leading up to the quiz.

Again I see a mistake with place value. Similar to the 0.9 error. This problem is different in some regards though because I would have solved it simply by noting that 5/8 is greater than a half and the other two numbers are not. Of course not every student has this number sense handy, so most of them were dividing and determining what 5/8 was as a decimal or as this student did trying to figure out how to make 100 the denominator. 

Here the student demonstrates the process off to the left side but gets confused about the decimal. After seeing it doesn't make sense, the students proceeds to try division, but still can't make sense of it. I was happy with the perseverance. This problem and the one next to were the problems that were most challenging.

Solid attempt at a proportion here, but the student misses the concept that a percent is a ratio since the number is being compared to 100. 

Here the student can find the part given the whole, but uses the same method to find the whole given the part on number 13. 

I actually never showed the students division as a means to solving these problems. The method could have worked for the problem on the right if the student had made 15 a decimal and carried out the division problem by adding zeros to 75. Interestingly this student successfully converted percentages to decimals earlier in the quiz.

Homework: Integer practice

My Glass Half-Full Take: In one class, we visited another teacher to say the integer chant. "An integer is all whole numbers, their opposites, and zero." It was a great diversion for the kids and I always have fun doing something out of the ordinary. That other class came back later and visited us. I think that particular class will have a more solid understanding of that definition just from the originality of the idea than the other class, but time will tell. If I had thought of it earlier, I would have had the other classes go and pay a visit. Inspiration strikes at weird moments.

One Thing to Do Differently: The standard that we have to teach asks students to explain the meaning of zero. I wouldn't mind hearing what other math teachers have to say about that part of the standard. My interpretation is that zero is when money isn't lost or earned, the temperature doesn't rise or fall, etc. I think it's very basic, but perhaps I'm being too simplistic. I take pride in being rigorous, so hopefully I'm not underselling this concept.

Link of the Day: I really wish I had YouTube in high school. This video taught me something about force. I'm going to build a lever to lift the broken spirits of any students who feel like they can't find the percent of a number tomorrow.