Day 106 Equivalent Expressions Study Guide

6th Grade Math Standards: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for
The Learning Objective: Find equivalent expressions; simplify expressions

Quote of the Day: "Any organization whose leader seeks stardom at the expense of the team is not one I would want to join regardless of the paycheck." - John Wooden

Agenda:

1. Journal Write
2. Review the homework
3. Dunkin Donuts practice problem
4. Study guide read aloud. I told students to write down that they should circle and underline on word problems and to circle all like terms before attempting those types of problems
5. Study guide done out in partners 
6. Review the study guide with the class

Interesting to note I thought I would run out of time and had two other things ready (more like terms practice and pepper again), but did not have time after reviewing the study guide.

The Assessment: I circumvented the room during the study guide to see how students were doing. One thing I emphasized was remembering to multiply by all the terms in parenthesis in doing the distributive property.

The Dunkin Donuts problem was assessed by me as well. About 33% of students answered this correctly. The issue that threw them for a loop was the idea of four twenty-five count munchkins. Many students wanted to use twenty-five in the expression, but this was superfluous information as the next sentence said, "each box costs $x." It did not matter how many came in a box.

The homework was a big issue too. Students continue to struggle with vocabulary although there was significant improvement versus where they were just 24 hours before.

Homework: With today's class falling on a Friday, it's always a risk, but students are going to study for the quiz over the weekend. The weekly quiz is also available online.

My Glass Half-Full Take: Students worked with a partner but they did not need much help from me. Occasionally I would give them one piece of information such as how to set up a word problem with the distributive property, but I was really encouraged with how their like terms word problems came out. I am confident that they will be successful on the quiz on Monday.

One Thing to Do Differently: Not that I would do this differently, but I actually gave away a box of munchkins to the class that did the best job on the Dunkin Donuts practice problem. I told the classes before I gave away the munchkins that I would pay attention as I reviewed the homework that way they would be successful on the subsequent problem. Despite my forewarning only a third of the students answered this question right. Perhaps next year as students review their homework I will give them a different color utensil to put in the work that I put in as we review the homework in anticipation of their confusion and lack of familiarity with combining like terms in a real-world context.

Link of the Day: This is a good resource for helping students understand the cost of living courtesy of FreeTech4Teachers.

Day 105 Combining Like Terms Word Problems

6th Grade Math Standards: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for

The Learning Objective: Combine like terms to find equivalent expressions in a real-world context

Quote of the Day: “If I were asked to give what I consider the single most useful bit of advice for all humanity, it would be this: Expect trouble as an inevitable part of life and when it comes, hold your head high, look it squarely in the eye and say, ‘I will be bigger than you. You cannot defeat me.’” - Anne Landers

Agenda:

1. Journal write
2. Review the homework
3. Pepper with the vocabulary and examples
4. Notes on like terms
5. Like terms practice from the textbook

The Assessment: Pepper was a great way to assess vocabulary. I timed it in one class and it took us just over 5 minutes for everyone in the class to answer one question.

The journal write was also assessed. Students did not know the vocabulary and that's another reason why pepper was effective. In one class I had less than 25% of students answer a single question correctly. The feedback I gave to students was that at home they really need to review their notes a second time after writing them. Not that I don't feel somewhat accountable for students not knowing the vocabulary, but it was delivered to them the day prior to this lesson.

In the second of two problems on the notes I broke down the word problem into smaller steps. I had the students first circle and underline what they knew and what they were trying to find. Next I reviewed that process on the board. The second step was to draw what was happening. Students did this individually first, and then I did it at the board. The third step was to write an expression. Again students tried and I showed how to do it after they had thought about it. The fourth step was to simplify that expression. It was a good way to give feedback and include students in the thinking process.

The homework time varied from class to class. Throughout the day I was giving more and more time for homework. Students were struggling for the most part with it - which was exactly what I expected.

Homework: Page 499 #9, 11, 12 Page 501 #29-33, Page 502 #18 and 19. The weekly quiz #17 is due tomorrow in class

My Glass Half-Full Take: I really enjoyed the pace of the notes and the focus I got from my students. It was a great balance between lecture and seeing what the students knew.

One Thing to Do Differently: Two practice problems was not enough. They needed a third and they needed to do it completely independently (without me emphasizing which step to do next). I would add one more problem to the notes and take one off the homework in the future.

Link of the Day: The wind chill formula explained. Very relative to what we've been learning lately (variable expression, exponents, integers) and the weather lately.

Day 104 Combining Like Terms

6th Grade Math Standards: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for

The Learning Objective: Identify like terms as terms having the same variable

Agenda:

1. Jumpstart
2. HW review 
3. Big Spender
4. It's not complicated
5. Like term notes
6. Like terms practice

The Assessment: The homework was checked with emphasis on the word problems. Many students had issues because a question asked about the number of seats on a 777 aircraft. Most students did not recognize that 777 was the type of aircraft and had nothing to do with seats. It was not a math error but a reading comprehension error.

I also collected the jump start from students after I had reviewed it. I gave students forewarning that the jump start would be collected in order to increase the likelihood that students would pay attention to details as we corrected. 

In one class I had students work in partners in the book and then gave them the homework after they had shown the skill I wanted to see for combining like terms. It was the best class in terms of demonstrating the skill on paper. 

I also had students try two problems from the notes on their own.

Homework: Combining like terms practice worksheet (only one word problem).

My Glass Half-Full Take: The big spender word problem was something I created yesterday as an off shoot to the It's not complicated video which I had shown last year and did not like the results that I had gotten. I needed to draw out the idea further, and I did it with the big spender problem. It was perfect. It was very concrete relative to what kids got from me last year in combining like terms. Saying something like "don't add the coefficients if the variables aren't the same" is mere memorizing. Telling students that purchasing five convertibles and four bags of popcorn is not the same as multiplying the popcorn cost and the convertible cost by nine is using common sense.

One Thing to Do Differently: When we did the story about popcorn and cars, perhaps I could have given students a number for how much the popcorn was and how much the car was to prove 4p + 5c did not equal 9pc.

Link of the Day: The distributive property at its finest.

Day 103: Distributive Property Day 2

6th Grade Math Standards: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

The Learning Objective: Find equivalent expressions by using the distributive property in a real-world context

Agenda:

1. Jumpstart: Place value, algebraic expressions vocabulary, writing algebraic expressions
2. Homework review from the distributive property last night
3. My favorite no challenge 3 (2 + x -3c + 4 + 2x)
4. Word problem practice 
5. Homework practice 

The Assessment:

Homework: Tonight's homework included more practice with basic distributive property (we are really solid overall as a sixth grade at the moment) and also word problem practice.

My Glass Half-Full Take: Solving word problems was actually easier than the seemingly more basic 3(2 + c) types of problems. The reason being is that the word problems are actually more concrete. It's not to say that the students were screaming give me more, but it was nice to see them respond as if to say, "that's all you got?".

I really like the way they handled the My Favorite No challenge. As I told the students I think it exaggerates what the distributive property is all about.

One Thing to Do Differently: Looking at the picture above I wonder if symbols and algebra tiles did more harm than good. Every student does learn differently, but to me this process is so easy. Multiply what's in the parenthesis by what's out. Then again, we use place value bars, paper coins and other manipulatives that eventually seem out of touch with where we are, but initially they are good training wheels.

Day 102 Distributive Property

6th Grade Math Standards: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

The Learning Objective: Use the distributive property to find equivalent expressions

Quote of the Day: "Step. Step back. And leap!"

Agenda:

1. Self-Assessment
2. Review variable quiz
3. My favorite no
4. Algebra tiles and notes
5. Exit ticket
6. Start the homework

The Assessment: The question in my favorite no asked student to find an equivalent expression using the distributive property for the expression 3(c-2).

No a single student could do this task, so there was at least the satisfaction in knowing that students would go home with a new skill at the end of the day if it was taught well. That being said, looking at the tickets to leave, some students did not go home with a new skill. This can be a very abstract concept with variables included, and I knew going in that I was going to spend at least two classes on this topic.

Homework: The students were given a worksheet with problems similar to the my favorite no problem and also three word problems. Interestingly the word problems did not all directly connect to the distributive property, so hopefully the students will read them carefully. I will see tomorrow. Students also need to do the weekly quiz by Wednesday this week.

My Glass Half-Full Take: The exit ticket did indicate that some learning certainly took place with some students. I would say around 65 to 70% of the students seemed to get through the exit ticket with everything correct. In two out of the three classes, the other teacher and I were able to review mistakes with students on their exit ticket, so in most cases the homework was a reinforcement activity rather than a pull your hair out activity.

One Thing to Do Differently: The idea of 3 (2x + 1) blew their minds even after a couple other examples. The reason for that was the coefficient of 2. I tried to break it down as x + x. I used a more concrete example of 2 x 7 being the same as 7 + 7. I liked my analogy, but I teach math for a living. Still I liked sliding this into their minds as I think the concept also is helpful in combining like terms.

My overall stance on the distributive property and combining like terms for sixth graders is that the kids have to start somewhere. This is where they start, and it's a painful beginning, but hopefully the exposure they receive in sixth grade helps them down the road.

Link of the Day: I got a good deal of reading Nix the Tricks yesterday. One thing that I've always done is use the term cancel. I take for granted that students will understand that a +7 and a -7 cancels. I like the recommendation of telling students it is 0 rather than saying the term cancel which can lead to confusion.