Day 72: Coordinate Plane Quiz and Battleship

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Objective: Locate a point in the coordinate plane; identify the four quadrants in the coordinate plane; reflect a point in the coordinate plane; create polygons in the coordinate plane; find the distance between two points in the coordinate plane

Agenda:

1. QSSQ 
2. Quiz on coordinate plane
3. Battleship brackets 

Assessment: Coordinate plane quiz

Glass Half-Full: Students in two of my three classes have been bothering me since the start of the unit to play Battleship. Today we did it. In a unique way compared to what I have done in the past, I set up brackets and had winning students play against other winning students and losing students play against other losing students. I explained the format before the quiz and they were all fired up. As a result of the students playing Battleship and not needing my direction or cueing them to task, I was able to grade the quizzes and call up individual students to clarify errors on this quiz or past assessments.

Regrets: There was a question that I had students find the distance between two points on a coordinate plane in which there was a trapezoid. We had gotten practice with finding the distance between two points, but always with peg boards or at least by looking at those points on a coordinate plane. I never left the students to find the answer with just giving them the coordinates as was the case on this quiz. Consequently, I passed out graph paper and told students to plot the trapezoid first to make finding the distance easier. I would like to remove this scaffold in the future though and will have to teach it in order to do so.

Day 71: Coordinate Plane Review

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Objective: Locate a point in the coordinate plane; identify the four quadrants in the coordinate plane; reflect a point in the coordinate plane; create polygons in the coordinate plane; find the distance between two points in the coordinate plane

Agenda:

1. Which one doesn't belong? Number 5
2. QSSQ 
3. Review the coordinate plane reflections homework and exit ticket
4. Pepper
5. Try a couple more reflection problems (back of exit ticket was not done the previous day)
6. Study guide 
7. Peg boards to show what reflections are 

Assessment: The peg boards; back of exit tickets; pepper

Glass Half-Full: I lit a fire in the students regarding their lack of effort in the reflection problems. I was fine with them struggling on some of the theory questions on the homework, but the fact that they did not highlight demonstrated a weakness in their effort. Our quote of the day dealt with Elizabeth Spiegel who is known as the toughest and best chess coach in the country for students in the middle school grades. In the book How Children Succeed, she was extremely critical of a person on her team who took only two seconds to make a move. The quote and the process for learning reflections were well correlated and students got the message with my own coach like tone regarding their low efforts.

Regrets: The exit tickets demonstrated that students would struggle with the homework. Some of the homework questions would have been better utilized as classwork. For instance students were asked if points are reflected across both axes if the new points are (-x, -y) if they started out as (x, y). This was something completely over the heads of all but about three of my students. Yet in explaining it, students were interested in knowing more about this topic. It got to the point where one students asked me about reflecting across the line y = x to take a point and move to quadrants with one reflection (she of course did not use those exact words, but still...).

Day 70: Reflections in the Coordinate Plane

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Objective: Reflect a point in the coordinate plane; determine the distance between two points that share one axis in a coordinate plane

Agenda:

1. Visual Pattern 
2. QSSQ 
3. Review homework
4. Use peg boards to see if students could create a rectangle and also count the distance between two points.
5. Reflections notes 
6. Use highlighters to find reflections of points in coordinate plane (exit ticket)
7. Pass out homework on reflections

Assessment: The peg boards was something I circumvented the room to ensure that students were recognizing where points went and how many spaces should be between points. I also circumvented the room to ensure students were highlighting as I asked on the exit ticket (many needed a reminder).

Glass Half-Full: Experience creates anticipation. I knew students would reflect points across the wrong axis and was able to jump on them when they did this for not highlighting which axis (or fence as I use in an analogy). Hopefully that will show up in their homework.

Regrets: This lesson was slightly rushed. I need to do a better job of bringing up reflections in the real world such as how the word ambulance is written or how a zit on one side of your face shows up on the other side of your face in the mirror. With a real world connection, there will be a higher interest level and investment from the students.

Day 69: Intro to Coordinate Plane

6th Grade Math Standards: 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Objective: Locate a point in the coordinate plane; identify the quadrant of a point in the coordinate plane

Agenda:

1. Self-Assessment
2. QSSQ
3. Review Quiz
4. Provide students coordinate plane notes and graphic organizer
5. Practice
6. Homework

Assessment: I circumvented the room as students tried the last practice problems and homework problems on their own.

Glass Half-Full: The graphic organizer allows for me to do other things as students get the notes in partners. I put grades into the grade book in one class and made the initial plans to a weekly quiz two weeks down the line as a result of this in class. Students barely needed any instruction from me and if they did it was a four second answer.

Regrets: The students are really struggling with what is negative and positive. It's as if the integers unit did not happen. I wish that we had done the kinesthetic version of this lesson where the desks become grouped into different quadrants and students can get used to what negative is within the context of our "homemade coordinate plane."

Day 68: Integers Quiz

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative positions of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3o C > –7o C to express the fact that –3o C is warmer than –7o C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Objective: Order integers; Justify why an integer is bigger than another integer; define absolute value; evaluate an expression with absolute value; define integer

Agenda:

1. Jumpstart
2. QSSQ 
3. Review absolute value and comparing integers homework
4. Pepper
5. Integers study guide
6. Integers quiz 
7. Weekly Quiz 
8. Challenge problem 

Assessment:

Glass Half-Full: During pepper we were emphasizing how to find 10 percent of a number. This was a gap in student learning two days previous to this point in the year as evidenced by the quizzes we took on percentages. When students faced a question that interleaved the percentages standards on the integer quiz, they handled it with much more success than they had previously.

Regrets: I do not think I was explicit enough with students about a number further to the right on a number line being greater than a number to the left on the number line. Many students cited that they would rather owe three dollars than seven dollars when justifying that -3 is greater than -7 (which I allowed), but I think the number line understanding is more mathematically pleasing (for lack of a better term because I'm typing all of these recaps weeks after I actually taught them).

I also do not like students saying that -3 is greater because it is closer to zero. This rule only applies to negative numbers being compared to other negative numbers and students are failing to mention this within their explanation.

Day 67: Absolute Value and Ordering Integers

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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. 7.

6.NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative positions of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3o C > –7o C to express the fact that –3o C is warmer than –7o C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Objective: Evaluate expressions with absolute value brackets; define what zero means in the context of a real world problem; order integers; analyze why one integer is greater than another integer

Agenda:

1. Self-Assessment
2. QSSQ 
3. Review the quiz 
4. Review the integers homework practice 
5. Introduce absolute value (Dunkin Donuts)
6. Students do absolute value practice independently
7. Skit with ordering integers
8. Comparing and ordering integer notes
9. Comparing and ordering integer practice

Assessment: At the end of each class, students were able to start homework assignments as I circumvented the room; as part of the self-assessments students stated whether they made simple mistakes or did not understand concepts from the quiz

Glass Half-Full: Despite the high number of items on the agenda, today's lessons had a good flow to them. Each concept can keep be explained and even analyzed quickly. When I told students they would have another quiz tomorrow, they were a little shocked since that would mean only two days between quizzes, but this was truly all that was necessary.

Regrets: The only problem with these lessons is that I do not cover ordering of rational numbers and really do not touch the term rational numbers in these lessons. Students had some difficulty when ordering all negative numbers, but once I pointed it out to them, they were quick to see this in future problems. Numbers such as -5.75 on a number line are a little more troublesome for many students though and I failed to really hit that today.

Day 66: Percentages Quiz & Integers Intro

6th Grade Math Standards: 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. 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.7. Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative positions of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3o C > –7o C to express the fact that –3o C is warmer than –7o C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Objective: Convert between percentages, decimals, and fractions; order percentages, decimals and fractions; find the part given whole; find the whole given part; use percentages to solve real world problems

Agenda:

1. QSSQ 
2. Percentages Quiz 
3. Work on WQ 
4. After Quiz Challenge
5. Pepper
6. An integer is all whole numbers, their opposites, and zero
7. Intro to Integers
8. Integers homework practice

Assessment: Integers notes were done with independent practice and the teacher circumventing the classroom; the quiz was assessed for a grade

Glass Half-Full: I think this is the right time of the year to teach one of the simpler concepts we have. Students do not have to make as many calculations with integers, absolute value, etc. in sixth grade. And at this time of the year (right before Christmas and New Year's), there are plenty of distractions so this is a good time to take it easier.

Regrets: There are still obvious fundamentals lacking in student's abilities to solve percent problems. Not that I'm not accountable for that, but I did send a note off to all parents and guardians about having their child be responsible for calculating the tip at a restaurant because these kids are at the point where they go to restaurants without supervision. Is the tip supposed to be random? Are they just going to Google it? Calculating a tip was something I learned very young, and it's a little disappointing to see the lack of experience my students have with this skill.

Day 65: Percentages Study Guide

6th Grade Math Standards: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Objective: Convert between percentages, decimals, and fractions; order percentages, decimals and fractions; find the part given whole; find the whole given part; use percentages to solve real world problems

Agenda:

1. Visual Pattern #27
2. QSSQ 
3. Skipped reviewing homework and opted instead for my own couple of problems I made up on the spot. 
4. Study Guide 
5. Stations: 99 Restaurant Tip, other practice material 

Assessment: Students worked in groups on the stations and I sat in on two specific stations. The 99 restaurant station (which challenged them) and then a percent problem that forced students to consider the thousandths place as it was converted to a decimal were the places I put myself. The study guide was done individually or in partners and then reviewed for all students.

Glass Half-Full: I think that problems escalated in difficulty as the days progressed in this unit. Each day logically built on the preceding day and at the same time all students were challenged without being pushed past the point of giving up. Kind of the goal of teaching, right?

Regrets: Some of the station stuff was impossible to review because of the pace of the group activities and my availability and necessary instruction at the two stations that I needed to visit.

Day 64: Part Given Whole

6th Grade Math Standards: 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Objective: Find the part given the whole amount; find the whole given the part; find the percent given the part and the whole

Agenda:

1. Open Middle
2. QSSQ 
3. Review of percent of a number homework 
4. Proportion frayer model
5. Part Given whole notes
6. Part given whole practice 

Assessment: Students did some problems from the notes on their own as I circumvented and other students helped.

Glass Half-Full: The Open Middle problem was something students struggled with despite the fact that Robert Kaplinsky calls it a fourth grade problem. I decided not to go over the answer in any classes and hang onto the problem as a bonus for the quiz.

Regrets: I got lazy and did not interleave well at all on these notes. Students got used to setting up proportions, but never had to think about what number was a part and what number was a whole because the part was always the number that was given. If I could have even added one problem in which the whole was given (percent of a number) it would have forced students to think more about how the problem was written. These problems are an issue of literacy as much as math once the basic understanding of what a percent is met.

Day 63: 20 Percent Off or 20 Dollars Off?

6th Grade Math Standards: 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems, including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. 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. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Objective: Determine if 20% off or $20 off is a better deal

Agenda:

1. Self Assessment
2. QSSQ
3. Review the Quiz
4. My Favorite No (20% of 64)
5. 20% off or $20 off from Dan Meyer 
6. Homework Practice

Assessment: I circumvented the room as students worked on the homework and the notes. There was also the self-assessment sheet that students got after the quiz. One of the sixty students could find the answer to the my favorite no question. That student used multiplication, so I worked with that student on the ten percent rule.

Glass Half-Full: This was probably the fourth time I've used Dan Meyer's Dualing Discount activity to teach how to find the percent of a number. It was probably the best that I have done because I let the students know ahead of time not to shout out ideas to enhance the likelihood that many students would be discovering that sometimes 20% was better and sometimes $20 off was better.

Regrets: This lesson does take more than one would think just looking at the agenda and especially the dueling discount problems. I did not use all of Meyer's problems, and did not need to either. My frustration was that we could not have a discussion or a a calculation surrounding at what point does the price of the item not matter regardless of the coupon. Perhaps I could speed this up by giving students four more examples (not have them do the calculation) and then give them more time to analyze what was happening.

Day 62: Fraction, Percentages, and Decimals Quiz

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.

Objective: Convert between fractions, percentages, and decimals; compare and order fractions, decimals ,and percentages

Agenda:

1. Quick study guide review (especially interleaving problem)
2. QSSQ 
3. Take the quiz
4. Fix the weekly quiz 
5. Find two factors that have a product of 1,000,000
6. At the start of the next class pass out notes on comparing and ordering fractions, percentages, and decimals but I had students work in groups rather than do it as a lecture. The format worked well in the disciplined classes, but as much in the classes that were hyperactive. 
7. Did page 135 #25-27 for homework. 

Assessment: Circumvented the room during number six. The quiz and weekly quiz were corrected by me.

Glass Half-Full: I'm happy that I only gave three homework problems. No need for more as I can tell who is doing well and who needs remediation from there.

Regrets: On the quiz most students struggled with making 3/8 a percentage. It could have been better highlighted as an area of concern coming into today. Not to say that the concept was not reviewed, but we should have been a star next to the concept of percentages with decimals.

Day 61: Final Quiz Prep

6th Grade Math Standards: 6.RP.3c c. 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.

Objective: Convert fractions, percentages, and decimals

Question of the Day: Is there any difference between 0.42 and .42?

Agenda:

1. Visual Pattern #34
2. QSSQ 
3. Review HW (#13-15 and the back) & Pepper
4. My Favorite No. Convert 0.3 into a percent. Convert 7% into a decimal.
5. Practice of decimal and percentage conversion
6. Study guide of converting between fractions, percentages, and fractions

Assessment: Circumventing the room during items three, five, and six of the agenda. During item two students simply brought their sticky notes up to me.

Glass Half-Full: The pace of this allowed for a good deal of feedback. I had students in work in partners on item number five in the agenda and I just circumvented the classroom. It was very apparent that the only difficulty involved one digit numbers or mixed numbers. Anything two digits the students had down. This was interesting because I resisted the temptation of telling students to slide the decimal two places. Instead I wildly praised students for writing each as a fraction out of 100 before converting.

I had students do the study guide as if it were the actual quiz. Inevitably I did give away answers and help them along, but it had a similar feel and the study guide was very much on par with the quiz.

Regrets: The homework from the night before should have had all the whole numbers changed from 2 to 1 in the four multiple choice options. I was the one that created that particular question, so score one for the math students.

Day 60: Percent Defined

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.

Objective: Convert fractions to percentages; convert percentages and decimals

Agenda:

1. Open Middle (third grade problem) 
2. QSSQ 
3. Pepper
4. Practice with fraction and decimal conversion
5. Percentage definition 
6. Converting between fractions, decimals and percentages notes
7. Fractions, decimals and percentages practice

Assessment: I circumvented the room as students worked out solutions to the problems. I really tried to sell students to write out the fraction before finding the decimal equivalent of a fraction. Single digit numbers are frequently a misunderstood concept because of a lack of place value knowledge and the ignorance of what the term percentage really means.

Glass Half-Full: Despite the third grade label of the warm up problem, the students were challenged and required to persevere. It was a problem that brought out students that do not normally shine and brought down those that normally do.

Regrets: I did not really do a good job of connecting the importance of this lesson to the real world. In past years, I take a box score from a sporting game, but I forgot today and also part of me said that the kids that hate sports probably hate me.

Day 59: Decimal & Fraction Conversion

6th Grade Math Standards: 6.RP.3c c. 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.

Objective: Convert from fractions to decimals

Agenda:

1. Self-Assessment
2. QSSQ 
3. Review Test
4. My Favorite No. Convert 5/6 to a decimal. Find your grade.
5. Notes on conversion from decimal to fraction and then fraction to decimal
6. Exit Tickets. 

Assessment: The my favorite no was telling. In one class nobody could convert five-sixths to a decimal. One student said 0.83, but without the repitin bar. All year myself and the social studies teacher have been putting the grades in fraction form. It turns out the students would have practically no clue to know what they actually got for a grade (see picture). They did much better with the grade after the feedback of five-sixths was given.



There was also the exit ticket.

Glass Half-Full: We had a curriculum day earlier in the week. The focus for the whole year has been on writing. The cry from the math department is that we did not need writing as much. Now I'm typically of an open mind, so I went into today's meeting willing to learn, think, and be persuaded.

Ultimately the conclusion I reached was (as the common core sort of states) that I am a writing teacher. With that thought in mind, I really tried to focus on the exit ticket from a writing perspective. I wanted students to nail the math by telling a fifth grade student how to convert (see objective), but also to use solid transition words in describing the process. What I got was a mixed bag. That was not the important part. The important part was incorporating professional development into my lesson immediately after receiving professional development.

Regrets: The writing prompt should state that the directions on conversions are for a fifth grader and that I'm focused on the transition words, but I explained this orally. Like I said, focusing beyond the math in their writing is a new thing for me.

Day 58: Fraction Test

6th Grade Math Standards: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Objective: Divide fractions to find a quotient; locate a fraction between two numerators of a like denominator that are next to each other on the number line (find what's between 10/3 and 11/3); multiply fractions to find a product; add fractions to find a sum; subtract fractions to find a difference

Agenda:

1. QSSQ
2. Fractions Test
3. Work on WQ 
4. Challenge Problems

Assessment: The test.

Glass Half-Full: The operations were done on problems one through eight and if that was the entire test grades would have been much higher. Kids can carry out the algorithm. Not surprisingly it's the higher order stuff such as application in the real world and finding holes between 10/3 and 11/3 where we struggled.

Regrets: The assessment included an interleaving question of 46 divided by 5. Students were instructed to find it using decimals, but I never reviewed this as part of the study guide the day prior, so I was not as stringent as the other math teachers probably were when students gave an answer of 9 and 1/5.

I also feel like this test is not as high up Bloom's Taxonomy as it could be.