Day 61 Find the Whole Given the Part

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.

The Learning Objective: Find the part given the whole.

Quote of the Day: “So often we fail to acknowledge what we have because we’re so concerned about what we want. We fail to give real thanks for the many blessings for which we did nothing: our life itself, the flowers, the trees, our family and friends. This moment. All of our blessings we take for granted so much of the time.” - John Wooden

Question from Yesterday (as always from a student):

Assessment:

Agenda:

1. 99 Restaurant Jumpstart
2. Review the percent of a number material which the substitute covered
3. My favorite no. Mrs. H got 21 questions correct. She scored a 70%. How many questions were on the test?
4. Visual Proportions
5. Coupons

Glass-Half Full: I like making the real world connection right away to the lesson with the 99 Restaurant problem in which the tip is given, but the bill is not.

Regrets: The homework becomes too simplistic after the first four examples or so. There needs to be a variance in the difficulty. Students should need to divide by decimals or use scaling like the My Favorite No question. We could also bring in a percent of a number type of question to this homework which was straight from the book (Lesson 8).

Day 59: Ordering Percents, Fractions, Decimals

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.

The Learning Objective: Order fractions, decimals, and percentages

Question from Yesterday (as always from a student): What is 3/8 as a percent?

Assessment: Students did their choice of problem on the back of the notes and showed one of the teachers before getting a book and starting the homework.

Agenda:

1. Self Assessment of quiz
2. Review the quiz 
3. Pepper
4. Notes on ordering
5. Practice of ordering

Glass-Half Full: What went well today was the amount of time we had for pepper. It's amazing how these students vocabulary is relative to groups I have had in the past. The integration of pepper and spiraling back between different terms has been helpful in mastering these concepts and not storing them in the gutters of the brain.

Regrets: As one of the co-teachers told me, it's difficult to get a sense of the real-world connection for how this is all relevant. Not sure where to go with this as I believe it is just simply a skill that students need to have in their toolbox. Perhaps I can use the analogy of being able to speak different languages because these three math languages have very strict translations.

Day 58: Decimal, Fraction, Percent 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.

The Learning Objective: Convert between fractions, decimals and percents.

Quote of the Day: “People had been trying to achieve the four minute mile since the ancient Greeks. They decided it was impossible. Bone structure was all wrong. Inadequate lung power. There was a million reasons. Then one man, one single human being, proved that the doctors, the trainers, the athletes, and the millions who had tried and failed were all wrong. And miracle after miracles, the year after Roger Bannister broke the four-minute mile, thirty-seven other runners broke the four-minute mile, and the year after that three hundred runners broke the four minute mile. A few years ago, I stood at the finish line of the Fifth Avenue Mile and watched thirteen out of thirteen runners break the four-minute mile in a single race. In other word, the runner who had finished dead last would have been regarded as having accomplished the impossible a few decades ago. What happened? There were no great breakthroughs in training. Human bone structure didn’t suddenly improve. But human attitudes did.” – Harvey MacKay

Question from Yesterday (as always from a student): "What will 1.29 be as a percent?"

Assessment: The quiz

Agenda:

1. Four squares comparison
2. Review the homework and pepper
3. A couple review problems until the bell rang
4. Take the quiz
5. Work on the weekly quiz
6. What two factors will equal 1,000,000 without using any zeroes 

Glass-Half Full: The four squares jumpstart promotes vocabulary, teamwork, and engagement. I want more of this and it needs to happen weekly.

Regrets: Could there have been a study guide? It certainly would have helped with 3/8 into a percentage.

Day 57: Decimal & Percent Conversion

6th Grade Math Standards: 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.

The Learning Objective: Convert decimals to percentages

Quote of the Day: The odds of a perfect game being thrown in baseball (one in twenty thousand) are far smaller than the chance you will be struck by lightning in your lifetime. But a perfect game is precisely what Detroit Tigers pitcher Armando Galarraga had happening one early June evening in 2010. He’d recorded twenty-six consecutive outs and had gotten the twenty-seventh batter to tap a weak ground ball to the first baseman, tagged the bag ahead of the runner and got ready to celebrate. There was only one problem: the umpire, Jim Joyce, swung his arms wide and shouted “Safe!”

When he got back into the umpire’s locker room, Joyce immediately cued the game video and watched the play – only once. He saw how badly he’d blown the call. But instead of letting the dust settle in silence like so many of his colleagues, Joyce chose a different path. He walked straight to the Detroit Tigers locker room and requested an audience with Galarraga.

Face red as a tomato, and tears in his eyes, he hugged Galarraga and managed to get out two words before dissolving into tears: ‘Lo Siento.’

About 16 hours later, the Tigers and Indians played again, but the meeting that mattered came before the game when Galarraga was tabbed for the trip to home plate to turn in the lineup card. Joyce was waiting for him. The two exchanged handshakes and hugs in one of the most inspiring, emotional, and moving displays of sportsmanship any sport has ever seen.” – Dale Carnegie  
Question from Yesterday (as always from a student): "Is that a fraction or a ratio?"

Assessment: Weekly quiz was given back to students corrected with highlights to fix problems that were wrong; my favorite no; homework examples; pepper responses

Agenda:

1. Jumpstart with number lines 
2. Collect WQ 
3. Visual Patterns #14
4. Pepper as students put problems on the board
5. Review homework
6. My favorite no convert 2/9 to a percent and 0.7 to a percent
7. Notes on decimals to percentages 
8. Work on the homework

Glass-Half Full: This is the most I have ever seen students correctly determine what 0.7 is as a percentage. It was also nice to see how students came up with 22% on my favorite no. Some divided and some just found equivalent fractions (multiplying 9 by 11). The repeating decimal part of is what was new for the students.

Regrets: Not going over the 13th problem on the homework was a mistake because many students got it right. It just was one of those things I forgot within the flow of the class.

Day 56: Fraction & Percentage Conversion

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.

The Learning Objective: Convert between fractions and percents.

Quote of the Day: “The formula is 6-2-7; breathe in for 6 seconds, hold for 2 and breathe out for 7 seconds. Many times, the heart rate in training is far lower than it is in competition. This change in arousal between competition and training usually has adverse effects on performance. With this in mind, it is a priority for athletes to learn to control heart rate so that training and competition arousal states are similar.”

Question from Yesterday (as always from a student): If we divide 100 by the denominator and multiply the numerator will that get a decimal equivalent?

Assessment: Circumventing the room during homework, exit ticket

Agenda:

1. These 4 problems done in groups by class section. Whoever can point out the most "one of these things is not like the other" wins. 
2. Review the homework by having students go to the board and pepper
3. Fraction to decimal ticket to leave
4. Fraction to percent notes
5. Fraction to percent practice
6. Work on the weekly quiz

Glass-Half Full: The warm up problem was engaging, vocabulary enriching, and involved teamwork.

Regrets: There was a great deal of time to work on homework. I wish students had more focus so that they had more time to get the weekly quiz done.

Day 55: Fraction and Decimal Conversion

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.

The Learning Objective: Convert between fractions and decimals.

Quote of the Day: "Dr. Frankl had been imprisoned in a Nazi concentration camp with his wife, parents, and brother. His father died of pneumonia in Treblinka, his mother and brother were gassed at Auschwitz, and his wife, Tilly, died of malnutrition at the Bergen-Belsen concentration camp, two days after it was liberated by British troops. He alone survived. Frankl wrote afterward that everything can be taken from a man but one thing: the greatest of all human freedoms, the ability to choose how to respond to any given circumstance. Frankl said that we retain the freedom to choose our attitudes and actions in response to whatever life deals us.” – Joe Ehrmann

Question from Yesterday (as always from a student): What was the life expectancy for women at the time of Louisa May Alcott's death? What are factors that can alter life expectancy over time?

Assessment: During the my favorite no, I had 1 out of 27 students successfully convert 5/6 into a decimal. It was a little surprising because it is a skill we have been chipping away at slowly all year by putting their grades in fractions at the top of their pages in math class and social studies class. Most students wrote 1.2 (which is at least thinking about division), 0.56, 0.5, and 5.6.

Agenda:

1. Estimation 180 - Day 63 through 65
2. Pass out the weekly quiz
3. My Favorite No: Conver 5/6 to a decimal
4. Place value review using Turning Point Clickers
5. Fraction & Decimal packet 
6. Start weekly quiz (if time allows)

Glass-Half Full: Just seeing that only one out of twenty-seven in my first class could do the skill that we were working toward was valuable information. Now we can really focus on central issues such as what's too high and low for any proper fraction (it has to be between 0 and 1) and what the fraction bar means (division).

Regrets: More space to do the work on the packet.

Day 53: Zombie Bridge

6th Grade Math Standards: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

The Learning Objective: Persevere in problem solving

Quote of the Day: “When the USA Basketball team failed to win the gold medal at the 2004 Olympics in Athens, Greece, many asked, “How could this happen? How could the USA team - every player an NBA All-Star - lose to Argentina, Lithuania, and Puerto Rico? We sent great players. They sent great teams.” - John Wooden

Question from Yesterday (as always from a student): "How many numbers are between 11/5 and 12/5?"

Assessment: Circumventing the room during Zombie Bridge; self-assessment papers from the fractions test

Agenda:

1. Self Assessment
2. Review the test
3. Yummy Math & Mashed Potatoes 
4. Zombie Bridge

Glass-Half Full: Nobody out of 116 students solved Zombie Bridge. Yet all were engaged and involved in the process. The students were able to successfully get across the bridge in 19 minutes, but could not get under 18 minutes.

Regrets: The other team did the fractions test today and probably experienced better results. That being said, doing the test today meant not doing the Zombie Bridge problem. I want to have students not only get good grades, but enjoy math class. That's what Zombie Bridge helps us do, so it's hard to call this a regret, but I do wish that we did not have to give a test on a Monday. Then again, people are expected to perform in the real world on the first day of the week.

Link of the Day: The best 3 countries for working women: Finland, Sweeden, and Norway.

Day 52: Fractions with Like Denominators

6th Grade Math Standards: 6.NS.1 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?

The Learning Objective: Use all four operations with fractions in a mathematical and real-world context; identify the space between two rational numbers on a number line

Quote of the Day: “The idea that one evaluation can measure you forever is what creates the urgency for those with the fixed mindset. That’s why they must succeed perfectly and immediately. Who can afford the luxury of trying to grow when everything is on the line right now? Is there another way to judge potential? NASA thought so. When they were soliciting applications for astronauts, they rejected people with pure histories of success and instead selected people who had had significant failures and bounced back from them.” - Carol Dweck

Question from Yesterday (as always from a student): "What is 5/5 of 42,000?"

Assessment: Fractions Test

Agenda:

1. Pass back the weekly quiz
2. QSSQ 
3. Take the Test
4. Get to 10 using the Chrome books

Glass-Half Full: Students were very engaged by Get to 10 after the quiz. It's a challenge in the sense that there are some questions which ask students to get into negative numbers and that it's timed. It's something that can be reached on everyone's level though in that it only involves the 4 operations with single digits.

Regrets: As I said in an earlier lesson, there needs to be a whole day devoted to number line and finding common denominators. This concept was something which students did not seem to grasp on the test.

Link of the Day: Massachusetts is out on Parcc testing. A good move in my opinion.

Day 51: Fractions Review Game

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?

The Learning Objective: Use the four operations to solve fraction problems

Quote of the Day: Learn from the mistakes of others (from one of the student's fortune cookies).

Question from Yesterday (as always from a student): "Why is it that if it is a problem like 9 divided by 1/2 that the quotient comes out larger than the dividend?"

Assessment: Students used marker boards as we played Who Wants to Be a Millionaire using the questions that will be on the test (I didn't tell students that much).

Agenda:

1. Weekly Quiz collected
2. Check the homework
3. Get to 10
4. Review homework questions by having students come to the board and the rest of the class is doing Pepper while we wait
5. Who Wants to Be a Millionaire? If students finish problems early they will do get to 10

Glass-Half Full: Getting to 10 as we did Who Wants to Be a Millionaire was money. I always hated games because it created competition and classroom management problems as students would finish the same problem in different amounts of time, and some students would not know what to do while others did. By giving the students that finish early another task, it bought me time to work with students that were struggling. I also liked the marker boards because students were more inclined to show their answers

Regrets: The game part of this made it more interesting, but it was up to the students to keep track of their points. Somehow it would have been nice if I was using Kahoot or some other software to keep track of the numbers for the students. I was going to use PowerPoint, but for some reason it did not work.

Link of the Day: Only a quarter of the jobs in tech fields belong to women and according to this article it might be worse.

Day 50: Fraction Stations

6th Grade Math Standards: 6.NS.1 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?

The Learning Objective: Divide fractions to find a quotient; multiply fractions to find a product; find what fraction is between two other fractions

Quote of the Day: “What of the youth, the next generation of leaders? While many are forging tough paths and making a difference, others are engaged in passive entertainment-advocacy that requires little more than reposting or liking the website of a noble cause. The absence of hard work for young people can corrode their discipline, sense of responsibility, and self-worth. Meanwhile, in the developing world the extreme poverty rate has decreased from 52 percent in 1980, to 34 percent in 1999, to 21 percent in 2010 and it continues to fall. The people in this demographic have behaviors and mindsets that epitomize the rookie mode: unburdened by preconceived notions and eager to learn, whether from world-class experts via MOOCs (massive open online courses) or from improvising and innovating on shoestring budgets.” – Liz Wiseman

Question from Yesterday (as always from a student): "What is zero times zero?" "Why don't we take the reciprocal of the first fraction?" "Is there another way besides 'keep, change, reciprocal' to divide fractions?"

Assessment: Clickers

Agenda:

1. Quote, Star Student, Question
2. Clickers to determine what is between 2/4 and 3/4
3. Review the homework
4. Clickers to determine what is between 11/5 and 12/5
5. Stations: divide fractions, fractions and the number line, weekly quiz, marker boards, frayer model, and dividing fraction word problems 

Glass-Half Full: Stations gets students to move and is an excellent way to foster collaboration. One student was shocked when class was over. Time flew by and there was so much practice done. I also thought that by limiting the number of problems at each station it gave students a less overwhelming feeling than they would have had if a single worksheet with 18 problems was given.

Regrets: The issue of fractions and number lines needs to be its own lesson. A notes sheet should be designed with number lines to demonstrate and students need to recognize that there is a whole universe of numbers between any two fractions.

Link of the Day: A longer read (9 pages), but interesting take on how the minority of populations dictate decisions for the majority of populations.

Day 49: Dividing Fractions

6th Grade Math Standards: 6.NS.1 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?

The Learning Objective: Divide fractions to find a quotient

Quote of the Day: “Exercise improves mood. Recent studies have found that a regular workout regimen is an even more powerful mood elevator than prescription anti-depressants. What’s less well known, however, is the profound impact exercise has on learning, memory, and creativity…Neurological studies show that when we exert ourselves physically, we produce a protein called brain-derived neurotrophic factor (BDNF) that promotes the growth of neurons, especially in the memory regions of the brain…Learning and memory evolved in concert with motor functions that allowed our ancestors to track down food, so as far as our brain is concerned, if we’re not moving, there’s no real need to learn anything.” – Ron Friedman

Question from Yesterday (as always from a student): "Is zero considered a whole number?" "How can you tell if 3/4 or 7/9 is bigger?"

Assessment: Marker boards, circumventing the room

A couple things of note with these pictures. First of all, the objective is centered around the word division and this is of course multiplication. The reason for that is that in order for students to master division they should know not to take the reciprocal for multiplication problems. Students need to transfer between all four operations in order to truly master all of fraction operations. Not just do them in isolated situations.

Second of all, the pictures here show the value of cross reducing. Great to hear students using words like factor after we reviewed what was happening in these problems. 

Agenda:

1. Estimation 180 (one class only) and marker boards to review multiplying and adding fractions in other classes 
2. Homework review and weekly quiz feedback
3. QSSQ
4. Division of fractions activator. How do we split one full pizza [8 slices]among four people? How do we split 7/8 of a pizza among four people?
5. Division of fraction notes
6. Division of fractions practice (marker boards)
7. Division of fractions homework practice

Glass-Half Full: Marker boards have changed the way I teach. I can't believe I ever taught without them. It is wonderful for students to understand how to divide fractions and see evidence of it. That said, so many are memorizing a process. One student in my last class asked the magical question: "Why do we not take the reciprocal of the first fraction?" Another student in a different class asked, "Is there another way to solve these?" It's thinking. I am very pleased by it.

Regrets: I just need to make sure all classes hear these questions and have time to reflect on them. It's easy to memorize "keep, change, reciprocal" but understanding a little of the why it works is of much higher importance.

Link of the Day: Fawn Nguyen is the best teacher I've never met.

Day 48 Multiplying Fractions Day 2

6th Grade Math Standards: 6.NS.1 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?

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

The Learning Objective: Multiply fractions in a real-world context

Quote of the Day: “After seven experiments with hundreds of children, we had some of the clearest findings I’ve ever seen: Praising children’s intelligence harms their motivation and it harms their performance.” – Carol Dweck

Question from Yesterday (as always from a student): "You are saying 0 and 1 is between 3/8 shouldn't you say 3/8 is between 0 and 1?"

Assessment: Mad minutes, Marker boards, circumventing the room, checking last night's homework

Agenda:

1. Jumpstart - Visual Pattern #13
2. Question, Star Student, Quote of the Day
3. Review yesterday's exit ticket
4. Review the homework with the class on the board
5. 3-minute drill
6. Continue reviewing homework while simultaneously peppering students
7. Limits (from LTF)

Students were really challenged on the visual patterns for the first time this year. It was great to see them respond with persevering when they could not identify a quick pattern.

Glass-Half Full: The marker boards were a bit of a savior today. I just asked students to hold them up. I felt like the rat from Ratatouille when he was testing the work of the other rats who were cooking. "Good, simplify, nice, convert to a mixed number, multiply the fraction and the whole number, excellent use of cross reducing, you don't need a common denominator."

Regrets: Assigning too many problems on the homework yesterday. I never assessed many of the questions and did not review them in class either.

Link of the Day: Puzzlor is fun and a little challenging at times.

Day 47 Multiplying Fractions

6th Grade Math Standards: 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.NS.1 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?

The Learning Objective: Multiply fractions to get a product.

Quote of the Day: "Nine Reasons I swear: It please my mom so much. It is a display of my manliness. It proves I have great self-control. It indicates how clearly my mind functions. It makes conversation so pleasant. It leaves no doubt in anyone’s mind as to my upbringing. It impresses people. It makes me a very desirable personality to children. It is an unmistakable sign of my culture and refinement.” – Joe Ehrmann

Question from Yesterday (as always from a student): “How many times does Friday the 13th occur in a decade?” 

Assessment: My favorite no, the clickers, circumventing the room

Agenda:

1. Self-Assessment
2. Question, Star Student, Quote of the Day
3. Review the quiz with the class
4. Do a clicker question based on paying attention to quiz review 
5. My favorite no 1/2 times 3/5 
6. Multiplying fraction notes
7. Exit Ticket
8. Start homework

Glass-Half Full: My favorite no was very useful in terms of getting students to see that multiplying was much easier than adding fractions.

Regrets: I have to get students to understand that 3/4 is not between 3 and 4. And that 7/9 is not between 7 and 9. This needs to be a concept that is mastered before even the notes go out in order for them to get any value out of estimating fraction products.

Day 46: Fractions Quiz

6th Grade Math Standards: 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc) /bd.)

The Learning Objective: Add and subtract fractions with like and unlike denominators

Quote of the Day: "One marker of a challenging personality is the tendency to describe oneself as a victim. The more people view themselves as victims, the easier it is for them to shirk personal responsibility for their circumstances.” – Ron Friedman

Question from Yesterday (as always from a student): "If the mistake of 2/7 + 2/7 = 4/14 is made it simplifies to 2/7. Will that always be the case if we fall for the wolf?"

Assessment: Checking the homework; circumventing the room; the weekly quiz; the quiz on fractions

Agenda:

1. Collect weekly quizzes
2. Check homework as students do various problems on their marker boards
3. Use decks of cards to play a game. The first card drawn is the numerator of the first fraction, the second card drawn is the denominator, the third is the next numerator, and the fourth card is the next denominator. Whether to add or subtract the fractions is determined by the color of the first card. If it is black, the students add and if it is red the students subtract. We used the marker boards to play this game. 
4. Pass out weekly quiz #8 

Glass-Half Full: There was a little debate about whether to push this quiz another day off or not. I am usually the one screaming to move forward and move faster. I felt with this particular quiz, that it was a fifth grade standard, and although some students still lacked consistency, all students to at least a small degree were demonstrating necessary skills and many students were at mastery. Sometimes we hit an iceberg. I feel as though that did not really happen today.

The two mistakes in the above picture to me are virtually correct. They were taken from two different quizzes and happened on several occasions. The students completed the wrong operation, but knew to keep the denominator the same, how to find a common denominator, and how to change the numerator. There is a red x, but I'm not concerned. On a side note, I wonder if I should be calling these problems correct. If these two problems were graded on a 4 point scale in stead of a black and white scale, they certainly would not earn 1's. To what degree in the real world are students being prepared better by having them go back and forth with addition and subtraction like this?

That said, there were still some mistakes that I have more concern over. This problem was something we spent considerable time on. Still some students came up with this answer, which is wrong on several levels. I'm going to continue to give feedback on this answer.

Regrets: The 8th question of the quiz (linked above) could have been worded better. The 7th question of the quiz was not covered well enough leading up to the quiz. We did work on finding a common denominator twice within a problem, but it was in a real-world context - this was just a mathematical context and students were forced to use order of operations which we have not covered to date.

The card game got a little confusing as I tried to implement mixed numbers with face cards. The trouble came when students got face cards twice or three times in a turn. They didn't know what fraction to use with what face card. They also were seeing face cards with improper fractions. Not that that was a problem for students that required a challenge, but for students that were struggling to reach the objective and not ready for such a challenge, it only dug them deeper into the hole. I think differentiating this game can be done if I were to use it again.

Link of the Day: I think this is interesting in terms of looking to spice up an exit ticket. I really like the idea of create a multiple choice question that will cause people to get the wrong answer (makes students think about potential mistakes in addition to finding the correct answer).

Day 45: Unlike Fractions

6th Grade Math Standards: 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc) /bd.)

The Learning Objective: Add and subtract fractions

Quote of the Day: "If you can't explain it simply, you don't know it well enough." - Albert Einstein

Question from Yesterday (as always from a student): "Is 4/4 a proper or improper fraction?"

Assessment: Individual marker boards to try problems with unlike denominators

Agenda:

1. Visual Pattern #10
2. My favorite no: 11 and 3/5 minus 6 and 4/5
3. My favorite no: 11 and 3/5 minus 6 and 3/4
4. Took down notes of how to do one problem in the spiral notebook
5. Chanted how to add and subtract fractions we needed a common denominator first
6. Used the marker boards to see if students could do it on their own (did two to three problems per class - including one that required borrowing or improper fractions)
7. Passed out the homework and started the homework in class

Glass-Half Full: In one class, I was checking off students in my head throughout my walks up and down rows. Eventually I narrowed it down to three students that could not do the skill independently. As the students worked on the homework, I continued to oversee everyone, but focused my time on these three students until they were able to demonstrate the skill independently. In my opinion these students have not mastered the skill, but I could give them a quiz tomorrow and they could do well on it.

Regrets: I wish more students had worked on the Weekly Quiz #7 on their day off. I let them know about my disappointment in my sense of high expectations tone.

Link of the Day: This article got me to think that rubrics aren't always good. The more general, the better because it does not restrict student thinking.

Day 44: Adding and Subtracting Like Fractions

6th Grade Math Standards: 3.NF. 3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

The Learning Objective: Add and subtract like fractions

Quote of the Day: "The only must win was World War II." - Marv Levy

Question from Yesterday (as always from a student): Upon being asked to make 52/4 a mixed number. "Is 12 and 4/4 ok?"

Assessment: After a meeting with the other sixth grade math teachers, we decided to mad minutes. Students were timed for three minutes to see what they know on multiplication facts and to see equally as importantly how fast they could answer sixty questions. It was also great to circumvent the room as students worked with their partner to add and subtract different like fractions using the tiles.

This group was missing the fourths.

Agenda:

1. Estimation 180 tape measures
2. My favorite no (borrowing with fractions)
3. Fraction notes done simultaneously while playing with the fraction tiles
4. Pepper
5. Mad minutes
6. Unlike Fractions practice
7. Work on WQ #6

Glass-Half Full: I got a lot of great questions today from students that could be used as the next question of the day. Students asked about the decimal numbers that were on the fraction tiles (as well as the percent numbers). There was also a question as to whether 4/4 is an improper fraction or a proper fraction. During estimation 180 we were asking what was a bigger a foot or a meter. We also discussed how many yards were in 25 feet. All questions that I did not anticipate going into today.

Regrets: In one of my classes, I did not cover the idea of 11 and 3/5 minus 6 and 4/5 well enough. It appears that most students wish to borrow instead of making the fractions improper. As teachers last year, we decided to show the improper fractions as the preferred method. This year, based on the pre-assessment it is helpful to know I should teach borrowing.

Link of the Day: Get your labels right. Get your decimals right. Verizon doesn't have them right and that sort of thing isn't good for a brand.

Day 43: Ratios Test Review & Fractions Intro

6th Grade Math Standards: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

6.NS.1 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?

The Learning Objective: Transfer numbers between improper and mixed fractions

Quote of the Day: “Research shows most communication is nonverbal; only a small percentage is based on spoken words. We communicate with facial expressions, gestures, eye contact, posture, and especially the tone of our voice.” – Joe Ehrmann

Question from Yesterday (as always from a student): What should we simplify to get simplest form? 10 cm to 40 cm? 12 cm to 48 cm? 15 cm to 60 cm? The sum of all the lengths to the sum of all the perimeters?

Assessment: Circumventing the classroom during the notes portion of class

Agenda:

1. Fill out the checklist for the self-assessment
2. Review the test 
3. Weekly Quiz collected
4. Fraction Notes
5. Hershey Bar Activity

Glass-Half Full: As the standards indicate, we took the class back in time today. There were some third grade standards mixed in. I think out of guilt, we threw in the definition for reciprocal (6th grade concept). That said, certain students did struggle. In circumventing the room, I was able to work with students until they could complete one of each type of problem (converting improper to mixed and mixed to improper) on their own.

Regrets: The Hershey Bar activity is not going to be used by me next year. I like hands on, but the questions here don't get students to think (not to mention the word column needs to get changed to row).

Day 42 Ratios Test

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 29
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.

The Learning Objective: Write a ratio; find a unit rate; use a tape diagram to solve ratio problems; use a double number line to solve ratio problems; simplify ratios; determine if two ratios are equivalent; compare ratios to see what a better deal is

Quote of the Day: “We go to a higher level when we treat others better than they treat us. When it comes to dealing with others, there are really only three routes we can take:

The low road - Where we treat others worse than they treat us.

The middle road - Where we treat others the same as they treat us.

The high road - Where we treat others better than they treat us.

The low road damages relationships and alienates others from us. The middle road may not drive people away, but it doesn’t attract them either. But the high road creates positive relationships with others and attracts people to us - even in the midst of conflict.” - John Maxwell

Assessment: The ratios test and the weekly quiz were due today, so I was busy grading. The results were mixed and there was not any one question that stood out more than the rest as being a question that students answered incorrectly.

Here a student simplified and then tried to do a unit rate (incorrectly). What's important for me is that they did order the numbers correctly. Obviously the term simplest form and knowing that the smaller number should be on top here are issues that will need to get reviewed when I pass the tests back. 

It was nice to see students write 6.4 packs instead of $6.4. 

Students were choosing to use double number lines (they also used charts, unit rates, and equivalent rates, and divide then multiply). It was great to see a variety of methods.

I had students try this type of problem the day I introduced tape diagrams. Literally nobody could do it in the 3 to 5 minutes that I gave students. This concept was brand new and it was nice to see so many students conquer it like this.

Agenda:

1. Take the test
2. Work on the next weekly quiz

Glass-Half Full: Students are learning. The evidence is there. It's not everyone and it's not every question, but I give them credit for working hard.

Regrets: These are the concepts that are not mastered yet and I think deserve continual attention: simplest form and order of ratios. There is also the issue of comparing prices, but I will leave that to weekly quizzes versus spending class time on it because they can be the type of questions that take a long time.

Day 41: Ratios Test 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.

The Learning Objective: Describe the relationship between two numbers with a double number line; use a tape diagram to find equivalent ratios; use scaling to find two equivalent ratios; find a unit rate; determine if ratios are equivalent

Quote of the Day: “I wonder what a team would look like if they only focused on growth? What if the coach only spoke to their players about getting better that day in practice or during a game? Is that doable? Is that sustainable? Is that even an option? Well the majority of information in our society flies in the face of this idea, but it’s exactly what happened to the Butler Men’s Basketball program when Brad Stevens took over as the head coach. He and his staff took a group of players most top program’s didn’t even recruit, to back-to-back national championship games. In his current position holding the most historic job in NBA history, Stevens had this to say about goals: ‘I know it sounds strange, but I don’t really have goals. I focus on getting better every single day.’” – Joshua Medcalf

Question from Yesterday (as always from a student): "Why are the dots connected on some graphs but not on others?"

Assessment: Circumventing the classroom; checking homework and weekly quizzes

Agenda:

1. Visual Pattern #9
2. Review the homework
3. Quote, Star Student, Question of the Day
4. Study guide done in partners. I went to the board once every ten minutes to review material. 

Glass-Half Full: I was much more relaxed today than I had been in the previous two classes. There were 18 questions on the study guide. On about 6 of them, I could differentiate with students to the point where we were challenging even the students that had the greatest grasp of ratios. Instead of getting torn up about the fact that students were not doing enough work, I focused on having students get the couple of questions that they did.

Regrets: On the study guide, we can go down to about 14 questions. There were three questions on unit rate and only one is truly needed. I think that there needs to be more time spent on equivalent ratios questions and questions that compare to see what a better deal is.

Link of the Day: Krispy Kreme picture on NDD (National Doughnut Day).

Day 40: Graphing Ratios

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

The Learning Objective: Graph ratios on the coordinate plane

Quote of the Day: “The sun and wind debated about which was the stronger, and the wind said, ‘I’ll prove I am. See the old man down there with a coat? I bet I can get his coat off him quicker than you can.’ So the sun went behind a cloud, and the wind blew until it was almost a tornado, but the harder it blew, the tighter the old man clutched his coat to him.
Finally the wind calmed down and gave up, and then the sun came out from behind the clouds and smiled kindly on the old man. Presently, the man mopped his brow and pulled off his coat. The sun then reminded the wind that gentleness and friendliness were always stronger than fury and force.” – Dale Carnegie
Question from Yesterday (as always from a student): How do we find equivalent ratios?

Assessment: There was a guided practice built into the book, which was used as a ticket to start the homework.

Agenda:

1. Jumpstart with tape diagrams and check weekly quizzes
2. Review the equivalent ratios homework
3. Graphing ratios notes
4. Graphing ratios practice
5. Graphing ratios homework

Glass-Half Full: I enjoyed the kinesthetic motions of the x-axis, y-axis origin (making a cross with the arms and hitting my head), and making parenthesis with the arms for ordered pair.

Regrets: I hate the math book for not connecting the dots on certain problems to demonstrate that there are decimal relationships between variables such as time and money. It is a higher order concept for some students that need to be challenged.

Link of the Day: Growth mindset in 9 statements that turn into larger things to read.

Day 39: Equivalent Ratios

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.

The Learning Objective: Determine if two rates are equivalent or not.

Quote of the Day: "“Joanne came up with a big idea in 1990, but within six months her mother suddenly passed away. She was living in England at the time, and decided to accept a teaching job in Portugal to try and escape the grief.

Shortly after moving to Portugal she falls in love and gets married. Less than three years after being married her husband abandons her with their three year-old daughter. She moved to Scotland to be closer to her sister. Joanne was living on welfare and had hit rock bottom.

She started writing the story that was birthed back in 1990. Eventually she gets a publishing deal and is given a three thousand dollar writing advance. The publisher didn’t think much of the work and only published a limited number of books. They also asked Joanne to create a pseudonym to write under to disguise her identity as a female writer, and hopefully attract male readers. Joanne doesn’t have a middle name, but her mother’s name was Katherine, so she wrote under the name J.K. Rowling. You are probably familiar with her work. That first book she wrote was Harry Potter. ‘I was set free because my greatest fear had been realized and I still had a daughter that I adored, and I had an old typewriter and a big idea. And so rock bottom became a solid foundation on which I rebuilt my life,’ she said.” – Joshua Medcalf
Question from Yesterday (as always from a student): How many mini bears would fit inside a super bear?

Assessment: Circumventing the room during the notes

Agenda:

1. Jumpstart with double number lines
2. Return Weekly Quizzes
3. Notes on equivalent ratios
4. Using ratio table practice
5. Equivalent ratio practice out of the textbook

Glass-Half Full: I wrote an email to parents regarding how solid attendance has been this year, the effort of students to retake quizzes and tests, and homework. I had students at lunch and after school today. It's very rewarding to see students want to work hard and to play a small part in giving them that motivation.

Regrets: I'm just going to type and make no deleting as I go. It's frustrating to be on a treadmill like it felt today. There was so much to cover and not enough time to cover it. Ratio tables, double number lines, and equivalent ratios are all cousins, but they also could be done on three separate days (double number lines was given the Friday class). There were too many note problems. Too many homework problems. There should have been less questions and more thinking. I should have been more enthusiastic about the challenges. A problem in the book changed units on students without any big flashing lights and I should have had students work on that problem for fifteen minutes and discuss the intricacies of it. We are getting away from the weekly pepper, visual patterns, and estimation that helped students enjoy my class for the first 30 days. I want to slow things down and do math that let's them think.

Link of the Day: Visual math focuses on a different part of the brain than simply making numerical calculations and research indicates that when visual math and the numerical side of math are in sync, the strongest connections and learning is taking place.

Day 38: Double Number Line

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. MA.3.e. Solve problems that relate the mass of an object to its volume.

The Learning Objective: Use a double number line diagram to describe a relationship between units

Quote of the Day: "If everyone has the attitude that someone else will do it, then nobody will do it." - Camfel Productions

Question from Yesterday (as always from a student): "Is 3.2 a different number then 3.20?"

Assessment: Circumventing the room to see that students were putting the correct numbers on the double number line; checking the homework

Agenda:

1. Jumpstart
2. Review the homework
3. Ask a question upon seeing this video
4. Create a double number line between mini bears and grams 
5. Create a double number line between regular bears and grams 
6. Answer the question how many mini bears are inside the super bear?
7. How many regular bears are inside the super bear?

Glass-Half Full: This concept is on the easier side of tape diagrams which we did yesterday. The hardest part about this topic for me is finding resources for it. I have created my own stuff for it, but enjoy the Dan Meyer Gummy Bear activity much more for engaging the students. I'll show them my stuff on Monday as a review.

Regrets: Today was a shortened day because of an assembly we had in the morning. We rushed the answer to how many mini and regular bears would equal a super bear and about half of the class was probably clueless as to how we discovered the answers here because of time pressure.

Link of the Day: Freakonomics always informs in interesting ways, but my ears perk up when I know that it's about education. Listen to the piece on gaming in schools.

Day 37: Tape Diagrams

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.
MA.3.e. Solve problems that relate the mass of an object to its volume.

The Learning Objective: Solve ratio problems using a tape diagram

Quote of the Day: “Curt Carlson was founder of multibillion-dollar Carlson Companies. That today includes Radisson Hotels and the restaurant T.G.I. Friday’s. He said the first five days of the week, Monday through Friday, are when you work to keep up with the competition. It’s on Saturdays and Sundays that you get ahead of them. To a lot of people, Carlson was a workaholic. Of course, he didn’t think so; to him, work wasn’t work.” – Harvey MacKay

Question from Yesterday (as always from a student): Several students were asking about this question from the weekly quiz:

We raised $10,000 simply by selling sweaters. Sweaters were $40 apiece. How many sweaters were sold?

Assessment: Students stood up when they were done the third problem; also used a fist of five

Agenda:

1. Self-Assess on the ratios quiz
2. Review ratio quiz
3. Quote, Star Student, revisit the question of the day
4. Tape Diagram Notes
5. Tape Diagram Practice 

Glass-Half Full: I like hearing students say "Can I retake it?" I like the laughs I get when I tell the story about a student that said that he hated me because I make him learn.

Regrets: The activator was absent. I have students simply try the problem without any instruction first, so it helps explain how useful the process is. That said, I'd like to connect the problem to real life somehow or make this into a 3-act problem somehow.

Link of the Day: Robot grading isn't far off it would seem.

Day 35: Ratios Study Guide

6th Grade Math Standards: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

The Learning Objective: Find a unit rate

Quote of the Day: “A person’s happiness is related to the happiness of their friends, their friends’ friends, and their friends’ friends’ friends. We found that each additional happy friend increases a person’s probability of being happy by about 9%. By comparison, an extra $5000 in income increased happiness by about 2%.” – Dale Carnegie

Question from Yesterday (as always from a student): "Why would anyone ever want 0.8 of a pencil?" In response to finding a unit rate of 4.8 pencils per $1.

Assessment: Circumventing the room.

Agenda:

1. Entering the class students worked on the study guide
2. I passed back and collected weekly quiz materials as students worked on numbers 1 and 2.
3. We worked on each problem part by part until the ten questions were completed
4. Either Get to 10 or pepper to close out the class 

Glass-Half Full: The pace of the study guide was slow, but effective. I think it kept the students that were struggling involved better than simply giving the students the opportunity to do ten at a time.

Regrets: I wish there was something for the higher students to work on as they finished in some ways, but also believe that them helping students who were struggling was valuable as well.

Day 36: Ratios Quiz

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

The Learning Objective: Write a ratio three ways; find a ratio and put it in simplest form; find a unit rate in a real-world context

Quote of the Day: “Cooperative behavior requires individuals to understand that by working together they will be able to accomplish something that no one can accomplish on his or her own. Jim Vesterman considered himself a reasonably good team player, yet he learned an indelible lesson in the power of group effort when he joined the Marine Corps. It started on his first day of boot camp at Parris Island as he and his fellow recruits learned to make their beds. His experience went something like this: the men are told that their objective is to have every bed in the platoon made; the drill instructor begins counting, and everyone has three minutes to make his bed (‘hospital corners and the proverbial quarter bounce’); they step back in line when done. So, Jim explains, he made his bed, stepped back in line, and felt ‘pretty proud, because when three minutes were up, there weren’t more than ten men who had finished.’ However, the drill instructor wasn’t handing out any congratulations; rather, he was shouting out that they had all day to get this right, looking at all the beds that were unfinished. Jim ripped off the sheets again… and again, and again. Finally the drill instructor looked him in the eye and pointed out, ‘Your bunkmate isn’t done. What are you doing?’ Apparently Jim had been thinking that he was done while his bunkmate struggled. Finally the light dawned on Jim, and working together with his bunkmate, they made both beds, and much faster than they had each done on his own.” – Barry Posner

Question from Yesterday (as always from a student):   In 2018, Mrs. Buxton expects to sign up for Instagram. Assuming she gets 45 likes 2 minutes after her photo has been posted and that Mr. Brazille has 98 likes after 12 minutes, which photo is getting more likes per minute? 

On this question, students were asking what to round to. We went over the fact that it's fairly obvious who has more likes and once the work has demonstrated who has more, there's no need to even get into the decimals.

Assessment: The quiz; the weekly quiz

Agenda:

1. Quote/Star Student/Question of the Day
2. Take the quiz
3. Work on the WQ #5

Glass-Half Full: I was really happy with the success we had in highlighting ratio words to solve the last two problems on the quiz. In general students were putting the units in the order that was given in the problem, so reading comprehension was strong.

Regrets: It was a hard quiz and the hardest question was problem five. Overall though I was elated with their effort on this quiz and I thought that the time we had to prepare for it and the way in which we prepared to it is something that I would repeat in the future.

Link of the Day: This is from 2006 and was I found it through Dan Meyer's blog. Everything written is still true.

Day 34: Unit Rates Let's Go Shopping!

6th Grade Math Standards: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

The Learning Objective: Find a unit rate in a real-world context

Quote of the Day: “There are plenty of teams in every sport that have great players and never win titles. Most of the time, those players aren’t willing to sacrifice for the greater good of the team. The funny thing is, in the end, their unwillingness to sacrifice only makes individual goals more difficult to achieve. One thing I believe to the fullest is that if you think and achieve as a team, the individual accolades will take care of themselves. Talent wins games, but teamwork and intelligence win championships.” - Michael Jordan

Question from Yesterday (as always from a student): "Why not divide the top part of the ratio by itself and the bottom part of the ratio by itself?"

Assessment: I collected the unit rate work that students had made on the trip to Stop & Shop, but as I was circumventing the room I made a new assessment on the fly. In the last 5 minutes of class, I asked the students if we had 31 pounds to $22, would there be more than 1 or less than 1 pound per $1 and why? The reason I asked this was because students were simply guessing on where to put their dividend and divisor. The exit ticket really helped clarify that this was the main struggle students were having putting together a unit rate. I also asked where the dividend and divisor would go. The thinking is clear, so tomorrow part of the agenda will be to review these types of comments from students. I actually posted one of these on Instagram already.

Agenda:

1. Jumpstart with munchkins from Dunkin Donuts. A 25-count costs $4.99. A 50-count costs $7.49. What is the unit rate of each?
2. Quote, Star Student, Question
3. Weekly Quiz recap
4. Review the homework (students went to the board to do problems)
5. Pictures from my trip to Stop & Shop

Glass-Half Full: Students associate the number one with a unit rate without much difficulty. I thought it was also critical that I integrated the exit ticket into each class because this is historically such a large issue.

Regrets: In reviewing the question from yesterday, there was too much of me speaking and not enough of them speaking. I need to ask less questions and get them to think deeper on the few questions that I'm asking. In reviewing the question of the day, I also hit on the ticket to leave question, but I think my commanding the stage as opposed to the students thwarted students from understanding the lesson sooner.

Link of the Day: Four strikes and your out is a great way to bring people who are finished with work together to continue to be productive while others finish up.

Day 33: Unit Rates

6th Grade Math Standards: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 29

The Learning Objective: Find a unit rate; analyze a unit cost to see what the best deal is

Quote of the Day: "When we attempt to use criticism to win an argument, to make a point, or to incite change, we are taking two steps backward. People can be led to change as horses can be led to water, but deprecation will rarely inspire the results you are aiming for.” – Dale Carnegie

Observation from Yesterday (as always from a student): "The price of cans will also change when there's only 5 cans because there is a recycling refund."
"If there is one missing, it should be cheaper than normal because the customer could argue the goods are damaged."

Assessment: Letting students try problems on their own from the notes; circumventing the room during the visual pattern

Agenda:

1. Visual Pattern #7. Write one thing you know. Write another thing you know. Draw the 4th step. Make a chart. How many trees are in Step 43? 
2. Unit Rate Notes
3. Unit Rate Homework

Glass-Half Full: In the first class, the co-teacher I was working with looked like she was going to jump out from the back of the classroom and attack me like a tiger. We were finding a unit rate and dividing 5 by 74. This was the students first experience dividing 5 by 74 I think (the occasion is rare unfortunately because they are two beautiful numbers). So why was it made into a glass half-full situation? It allowed us to use calculators. Students were literally asking how to clear their answers, were asking questions about how many decimals to write, etc.

Regrets: As far as time went, depending on the class I could have left out visual patterns. The notes took a while and in one class, I did not bother to assign homework because I did not fairly assess those students and it would have been an assignment that they potentially did wrong. I also think that it might have been better to start with a much more basic example in the notes (I did verbally give them two birds to one stone and four wheels to one car).

Link of the Day: We have Chromebooks in my school, so if this is you as well this link could be of use. What to do with Chromebooks.

Day 32: Partial Products

6th Grade Math Standards: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

The Learning Objective: Find the price of a single item in a product with multiple items

Quote of the Day: Born into poverty, Lincoln was faced with defeat throughout his life. He lost eight elections, twice failed in business and suffered a nervous breakdown. He could have quit many times - but he didn't and because he didn't quit, he became one of the greatest presidents in the history of our country.

Here is a sketch of Lincoln's road to the White House:

1816 His family was forced out of their home. He had to work to support them.

1818 His mother died.

1831 Failed in business.

1832 Ran for state legislature - lost.      

l832 Also lost his job - wanted to go to law school but couldn't get in.         

1833 Borrowed some money from a friend to begin a business and by the

end of the year he was bankrupt. He spent the next 17 years of his life

paying off this debt.

1834 Ran for state legislature again - won.         

1835 Was engaged to be married, sweetheart died and his heart was broken.

1836 Had a total nervous breakdown and was in bed for six months.         

1838 Sought to become speaker of the state legislature - defeated.

1840 Sought to become elector - defeated.        

1843 Ran for Congress - lost.  

1846 Ran for Congress again - this time he won - went to Washington and

did a good job.   

1848 Ran for re-election to Congress - lost.       

1849 Sought the job of land officer in his home state - rejected.   

1854 Ran for Senate of the United States - lost.

1856 Sought the Vice-Presidential nomination at his party's national

convention - got less than 100 votes.    

1858 Ran for U.S. Senate again - again he lost.  

1860 Elected president of the United States.

Question from Yesterday (as always from a student): Does the order matter in a ratio? Is 3 Kittens to 5 puppies the same as 5 puppies to 3 kittens?

What would happen to a ratio that was already put in simplest form if we added one more part to either ingredient? So if we had 20 chickens to 10 wolves and that ratio was simplified to 2:1 could it be 2:2 or even 1:1 if we added one more wolf?

Assessment: The homework from the night before was assessed with emphasis on number 18. In one class, I never had time to distribute homework, so I had them do it in class and worked with them on the highlighting aspect of breaking down the ratio problems.

Agenda:

1. Partial Product (from Dan Meyer)
2. Review homework and exit ticket
3. Nana's Paint Mix Up (from Dan Meyer)
4. Journal four questions. What is a ratio? What are three ways to write a ratio? What are the four steps to write a ratio? What is a wolf in ratios?

Glass Half-Full: I really enjoyed walking around the room and seeing students too high and too low responses to the Partial Product problem. I'm happy to see so many students giving logical numbers and following it up with logical reasoning. I'm sure the estimation will result in improvement in test scores, but if I had only a day or week to prepare for the test I wouldn't do estimation based activities. The time it takes to make it work is so much longer, but by taking the long view these students are really building a real world type of number sense. And the best part of all is that it is so much deeper than simply preparing the students for a standardized test. These problems are everyday things that can change the way that they perceive their decision making today.

Regrets: For the class that did the homework in class, I could not get to Nana's Paint Mix Up in class. I will obviously try to fit it in the future, but if we end up not getting to it, it will be unfortunate. In one class, I just sat with one group of two and worked it through with them in an unassuming manner. The rest of the class worked in partners and from what I could hear genuinely put effort toward finding a solution. The group I worked with ended up using 45 red and 9 white scoops of paint. The other students that correctly answered the problem used 25 red and 5 white scoops. It was great to listen to the answers that I got when I called on a couple students at random after giving ten minutes to try and solve.

Link of the Day: A list of the most innovative countries in the world. Finland is number one, the U.S. is number five.