Day 113: Functions Introduction

6th Grade Math Standards: 8.F.1 Understand that a function is a rule that assigns exactly one input to each output.

6.NS.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

The Learning Objective: Determine the input given a function rule and the output in a table. Determine the output given the function rule and the input in a table.

Agenda:

1. Self-Assessment from the Equations Quiz
2. Review the quiz as a whole class
3. Functions My Favorite No
4. Function Notes
5. Function Practice

The Assessment: The My Favorite No question gave students a chart where the rule was 2x, but most students filled in a number. Only four out of the 60 students in attendance wrote 2x, so for most students determining a function rule based on the input and output will be a new experience. For those students that already meet this concept, I will look to use quadratic, cubic, and multiple step rules to push their thinking.

Homework: Several students completed all work in class, but students were asked to finish the function worksheets for homework. The greatest difficulty for them was working backward when they had the output and had to derive the input based on the function rule and the output.

My Glass Half-Full Take: I think this is a relatively low-stress topic to teach as students level of confusion is dwarfed by the fact that we have already gone into great detail regarding variables over the past couple of weeks. This is where I happen to like the common core because it feels like we are able to dig deeper into a concept and the students can solidify holes in their learning on prior assessments as we continue to see variables.

One Thing I Wish I Did Differently: In my last class, I went ahead and did a little chant with motion stating that a function is a rule that assigns exactly one input to each output. I did not realize that this was an eighth grade standard until looking it up just now. I could have shared this information with the class and also done this chant with all classes. It's an opportunity to teach and have students up out of their seats in the action.

Day 112 Equations Quiz & Weekly Quiz Work

6th Grade Math Standards: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

The Learning Objective: Isolate a variable in order to solve an equation. Create an equation in a real-world context.

Agenda:

1. Pass back Weekly Quiz #18
2. Quiz on Equations
3. Pass out and start Weekly Quiz #19

The Assessment: The equations quiz

Homework: Finish Weekly Quiz #19

My Glass Half-Full Take: We intentionally left the Weekly Quiz off the internet over the weekend. I like the idea that the students did not have to worry about that over the weekend and could really get their work done in class. As I was reminded by one of the other math teachers earlier today, "These are 11 and 12 year olds after all." To some degree we are batting them over the heads with worksheets and quizzes and to a larger degree that's not who I want to be as a teacher.

One Thing to Do Differently: I don't think that students had a clear expectation of what the equations word problems expectations were as far as what I was assessing. I wish that I had told them up front that if the equation or the solution to the equation is wrong, the whole problem is wrong.

I also would have liked to put a timer on the board as students worked on the weekly quiz and told them that they should be completing at least two problems every five minutes. While this is obviously counter-productive in terms of putting time pressure on them and forcing errors upon them, I have a hard time keeping all students productive in a quiet room when I have to deal one on one with students' questions. One of the other math teachers told me that after students got done problems 1 and 2 they had to get checked by her. I liked this idea as long as I had a checklist to keep track of what students had not seen me. I often find that students can do nothing until a couple minutes left in class and by then it's too late to act in a way to help them.

Day 111 Equations Study Guide

6th Grade Math Standards: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

The Learning Objective: Isolate a variable by using the inverse operation. Compare an equation to an expression.

Agenda:

1. Equation balancing with pictures (MCAS Sample Problems Jumpstart)
2. Gave students a giant marker board to try the division word problems from the homework
3. Gave students the study guides to do in groups.
4. Reviewed study guides as a whole class.
5. Gave students challenge problems to work out as groups. One problem asked students to use the numbers 2, 0, 1, and 5 (for the year 2015) and come up with a solution using the four arithmetical operations ranging from 0 to 15 for all but two numbers. Another problem was a visual pattern from Fawn Ngyuen, and a third problem asked students to find a median (they haven't done this yet). 
6. Gave students a game of "Equation Wars." Basically I threw up a variable and two numbers. Each group had to put together four equations with the four major operations (group members picked the role of everyone in the group). For the first round, I gave 3 minutes for students to put the best effort into their problems. This included them checking the work and even explaining the work. 

The Assessment: Checking student marker boards, circumventing the classroom during the jumpstart, and in two classes circumventing the classroom for the study guide.

Homework: Study for the quiz which will be on Monday.

My Glass Half-Full Take: In one of my classes, I sat on my computer the entire time as students worked on the study guide. Why is this a good thing? Because I never do this. I always go on the computer to enter grades and homework assignments after school. This means I work later. That in turn means I have less time to read books, go for runs, watch sports, and have a life outside of school. I also should mention that I still listened to groups and was pleasantly surprised at the level of focus and teamwork in the groups of four. I went over the study guide with the entire class afterwards. Unfortunately I didn't try this in my other two classes, and I'm not sure if I could given the makeup of the classes.

One Thing to Do Differently: Equation Wars was so effective because I gave out munchkins to winning groups. I'm always listening to Freakonomics and the value of incentives. I hate having to bribe students to do work, but it did create a spike in student focus. I would like to try this game without giving students the physical reward (and if it fails try the physical reward again).

Link of the Day: Imprisonment can cause a vicious cycle for students. Only 1% of students with mothers in prison graduate college and 13% of students with fathers in college graduate. This study also said students with a parent in prison have a higher rate of attention deficit than students who miss a parent through divorce or death.

Day 110 Division Equations

6th Grade Math Standards: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

The Learning Objective: Isolate a variable in a division problem by isolating the variable.

Agenda:

1. Weight balance jumpstart challenge
2. Review the homework
3. Division equations my favorite no 
4. Division equation notes
5. Multiplication and division combined homework worksheet (word problems included) 

The Assessment: If I was teaching this for the first time, I'd assume all the students knew to cancel out whatever number is with the operation by doing the inverse operation. By year six of teaching equations, I know though that despite practicing with the other three operations there is still a lot of this:

It's what makes My Favorite No so useful as a pre-assessment. Kids see their own mistakes and can actually learn before taking notes.

Homework: Instead of focusing on giving just division, we combined the division and subtraction equations. It could have been harder if we completely mixed the problems but instead just division was on one side and just multiplication equations on the other. That said, word problems with division are still a great struggle. It's like in baseball when you tell a hitter a fastball is coming, that doesn't mean they can hit it.

My Glass Half-Full Take: I enjoy my classes enthusiasm and competitive edge in my favorite no. I always set out a random number such as "10 students in this class will make an error on this problem." It captivates them and gets them to think. When I display the wrong answer students are so quick to want to tell me what is wrong, but I always ask what is right first and it leads to great conversation.

One Thing to Do Differently: In terms of the more basic problems, I'd like to get the two operations mixed up. I also think that doing division word problems as a whole class is a good idea because the division word problems are a headache for many. So often students ask why they can't just multiply to solve. It's a fair question. I always say that they need to learn how to set up and solve one step equations because bigger things await.

Link of the Day: For math teachers who want to know more about teachers who blog and tweet.

Day 109 Multiplication Equations

6th Grade Math Standards: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

The Learning Objective: Isolate a variable in a multiplication equation by isolating the variable.

Quote of the Day: “Failing doesn’t make you a failure. Failing makes you a competitor. Every competitor fails. If you lay it on the line, you will come up short at times. Failure is a part of competing, and embracing that fact is an important component of toughness. Tough people fail, but tough people are not failures. The only failures are those who give up, or give in.” - Jay Bilas

Agenda:

1. Jumpstart
2. Subtraction Equations reviewed
3. Addition and subtraction equations combined practice
4. Multiplication equations notes
5. Multiplication equations practice
6. Equations Challenge problem (if time)

The Assessment: The addition and subtraction combined practice was done with a partner and the teacher circumventing the classroom. The multiplication equation practice was also checked by myself.

Homework: Page 555 #1-7, 556 # 11, 13-15, 557 #17-28 & The weekly quiz

My Glass Half-Full Take: When the equations challenge problem was done I had much more success when I read the quote of the day right before. I only used this problem in two classes, but the students really enjoyed it. I have gotten away from the quote of the day of late, but it does add value as I saw today. I also think it was key that the students got a challenge problem because the week has been dry in general.

One Thing to Do Differently: The combined addition and subtraction practice should focus one hundred percent on word problems instead of drill and kill types of problems (the sheet as it is constructed now has both word problems and drill and kill types). At most students should be asked to do three of these types of problems. The rest are a waste of time.

Day 108 Subtraction Equations

6th Grade Math Standards: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

The Learning Objective: Isolate a variable in an addition or subtraction problem by isolating the variable.

Agenda:

1. Self-Assessment 
2. Review Quizzes on distributive property and combining like terms
3. Addition Equation homework review
4. Subtraction Equation Notes
5. Subtraction Equation Practice 
6. Start homework

The Assessment: After the notes were done, students were asked to try a couple problems from the book that were not part of the homework and were checked before going onto the homework. The self-assessment as always was kept in the classroom and served as a way for students to verify what they need more exposure to in the future.

Homework: Page 539 #1-9 and #15-17

My Glass Half-Full Take: It was apparent in looking at homework from addition equations that students were not properly isolating the variable in one class particularly more than the others. In doing the same drill as the previous day, students were able to take a step in the right direction and begin showing how to cancel the work.

One Thing to Do Differently: Overall this was a very boring lesson. I say that not only for the kids, but for myself. I have no voice to begin with today, but I also wasn't helped by the lack of flare this lesson had. I need a song, a dance, a challenge - something to get enthusiastic about it myself.

Day 107: Equivalent Expressions Quiz & Introducing Equations

6th Grade Math Standards: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, x, and q are all rational nonnegative numbers.

The Learning Objective: Combine like terms to find equivalent expressions. Use the distributive property to find equivalent expressions. Solve an addition equation using the inverse operation to both sides of the equation.

Agenda:

1. Pass back last week's weekly quiz and hand out this week's weekly quiz
2. Take the quiz
3. Work on the weekly quiz
4. Basketball team - I had students pick teams and then said that one player got injured. If a player is taken off one team, what should the other team do to be fair? 
5. Addition equation notes
6. Addition equation practice and homework

The Assessment: The quiz and problems #20 and 21 out of the textbook as well as the homework problems.

Homework: Page 529 out of the Glencoe book problems #1-19 and 22 as well as the weekly quiz being due tomorrow

My Glass Half-Full Take: I think that thanks to having more time and longer classes these students understand the distributive property and combining like terms much better than the classes the past two years have.

One Thing to Do Differently: I need to give much more examples of the formatting for adding equations in the notes. Students should do about 8 until they have the process down. I also liked showing the last class the problem 5n + 8 = n - 12 to show them why the process is so important (even though that problem was completely over their heads).