I thought this would be a great activity on a day that I wouldn’t be at school. I gave instructions for the substitute teacher to read to the students, along with all of the materials. Unfortunately, students seemed to glue pieces in random order. By just looking at the papers and not knowing what went on while I was away, I’m not sure if the students did not fully understand the directions or they just didn’t want to do the work. I do not fault the substitute teacher or the students. Rather it got me to thinking, what could I do better to keep all students accountable for actually doing the problems and for me to see the students thinking?

So, I re-ordered the cards on the handout so that the problems were in the first two rows, the middle steps were in the next two rows, and the final expressions were in the last two rows.

Instead of giving students all of the pieces at the start, they would only be given the initial problems to cut out and glue on their paper. Then they would have to work out the distributing and show me their work before getting the next set of cards. Students would be able to check their answers when they cut and glued these cards underneath their work. Finally, they would combine like terms and show me their final expressions before getting the last of the cards.

In the end, students still get to use the scissors and the glue. However, I can quickly glance at each student’s work to see who understands the concepts and if not, where they are making mistakes.

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The conversation went something like this:

Me: What did the donor pay for all of the tickets?

Student: $4200.

Me: How did you come up with that amount?

Student: The oranges tickets cost $2400, the yellow tickets cost $1200, and the green tickets cost $600.

Me: What do you mean?

Student: There are 6 orange tickets, 4 yellow tickets, and 6 green tickets. Orange tickets cost $400, so $400 times 6 is $2400. Yellow tickets cost $300, so $300 times 4 is $1200. Green tickets cost $100, so $100 times 6 is $600.

Me: Why didn’t you just add the total number of tickets and multiply that number by $400? or 300? or $100?

Student: Because the different colored tickets are worth different amounts.

Me: So, why can you only combine the yellow tickets with other yellow tickets?

Student: Because they are all worth the same amount.

Me: And why can you only combine the green tickets with other green tickets?

Student: Because they are all have the same value.

Me: And what about the orange tickets?

Student: You can add the orange tickets together because they have the same value.

At this point I introduced combining like terms with variables and constants. Each time a student tried to add something like 3x + 5 + 2x to get 10x, I reminded them of the different colored tickets. For instance, the 3x and the 2x are like the green tickets and the 5 is like the yellow ticket.

After we worked on a few problems in our interactive notebook, students worked with a partner to play a Combining Like Terms Dice Activity. I put stickers on a pair of wooden dice. On one die were different coefficients (positive and negative) with the variable x and on the other die were different coefficients (positive and negative) with the variable y. Students had to roll the pair of dice twice and write down the terms in the squares on the handout and then combine like terms. After completing four problems like this, they had to combine the answers of #1 and #2 together, and the answers for #3 and #4.

Partners would work on the problems independently and then check answers with each other. If they got different answers and could not agree, they could raise their hands to ask me for help.

After these two activities, I felt students were ready to tackle similar problems for homework. I wish I could incorporate visuals and games with every new concept!

I would love to hear about anyone else’s way to introduce combining like terms. Please share!

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Here is an example of a student’s work:

I was able to go around the room to see that students were showing their work with the distributive property and then circling and boxing in like terms to get the final answer.

After that, students worked in groups to figure out the errors in this free handout from Secondary Math Solutions.

Students had to locate the mistake, as well as explain how to correct the mistake using complete sentences.

In both activities, students needed to either show their steps or write out the process to complete the problems. Both activities allowed me to see who understood the problems and who needed more direction. Now for the test…

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In a previous blog, I mentioned that I was making changes to my 7th grade math curriculum. However, I noticed a spot in my 8th grade Pre-Algebra lesson plans where I could easily make a small inquiry-based task to get rid of direct instruction. This week my 8th grade Algebra students were reviewing how to multiply real numbers. In 7th grade we dealt mostly with multiplying only two numbers so my 8th graders were familiar with the rules that if two numbers had the same sign, their product was positive and if two numbers had different signs, their product was negative. However, in 8th grade Pre-Algebra, this concept is extended to multiplying more than two numbers. I wanted them to see that there is a pattern to multiplying with negative numbers. Rather than just tell them that the product of an even number of negative numbers is positive and the product of an odd number of negative numbers is negative, I wanted students to discover the pattern. I made this handout for the students to help them come to that conclusion on their own.

Students were given 5 minutes to work independently. Then they got in groups of 4 and discussed their answers for another 3 – 4 minutes. Finally, we met as a whole class, at which point we could write out the rules in our notebook.

It didn’t take a lot longer for students to work through the handout, but I know that the extra time was worth it because all students were working to find the answers, rather than just copying what I wrote down on the board.

Like I said, small steps, but with each step I hope my students will have greater understanding.

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This summer I read Making Thinking Visible and I am in the process of reading Creating Cultures of Thinking, both written by Ron Ritchhart. In the first chapter of Creating a Culture of Thinking, Ritchhart compares schools in the past (emphasis on rote learning and tests/grades) with what schools could become (emphasis on a culture of thinking). As I was reading about schools in the past, I could totally relate with it because that was how I was taught. And, I was okay with that. I didn’t know any better and I loved school! When I began teaching, I taught the only way I knew and felt that I was doing a good job. Well…thank goodness for great research, books, conferences, Twitter, and the MTBoS!

“Learning is a consequence of thinking.” In his book, Making Thinking Visible, Ritchhart gives an extensive list of ways to visualize student learning. Not all of the ways will fit in my math class, but it made me more aware of the fact that I have to make student thinking visible. Even though there are many great ideas, Ritchhart cautions about making too many changes all at once. It is better to start with a few new ideas and have students get familiar with those routines so that they improve their responses, rather than not understanding what you are trying to accomplish and giving shallow responses.

I know that I need more writing and conversations to take place in my classroom. So, I set out to look at my 7^{th} grade curriculum and evaluate what I am already doing and where I can make changes, even small ones, to get students engaged, not just passive participants in their learning.

To start, I needed a visual of what my units looked like. To make it easy, I printed off a blank monthly calendar and wrote in activities, assignments, quizzes, etc. for the first four units. Then, I color-coded each activity to see the common elements.

As I started this evaluation, I knew right away that I needed to make changes. On a sticky note, I started to write items that I wanted to incorporate into my lesson planning. This post-it sat next to me as I reviewed each lesson. Rather than scrapping everything I’ve used in the past, I revised pieces of lessons. Sometimes it only required a tweaking of my line of questioning; other times I made an activity to get the students to answer the questions instead of using direct instruction. In this way all students would be engaged in the inquiry rather than only a few.

In a few days I get to put these changes up for the test. Bring it on! I will blog about the changes and the outcomes. More tweaking might be needed, but it is a start. Here’s to a great year!

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I’m jumping on the band wagon and writing about 20 facts you may not know about me:

- My favorite food is pizza. I love to read about and try different doughs and toppings. For my 50th birthday, I received a Weber grill and a KettlePizza insert.
- I have been married for 29 years to a Canadian.
- I have four children: Rebecca (28 yrs. old), Rachel (26 yrs. old), Michael (24 yrs. old), and Hannah (20 yrs. old).
- I teach at the same school that my mother, my children, and I attended.
- Math is my second degree and career. I have a B.A. in Criminal Justice and I worked as a litigation paralegal.
- Several years ago I went skydiving and it was a blast!
- My favorite color is red.
- My husband and I love to camp. Last year we downsized to a smaller pop-up camper but upgraded to one with a refrigerator. No more coolers with everything floating in the melting ice!
- My husband and I are getting into wine tasting. Whenever we go on vacation, we check out at least one local winery. Last summer, we camped (see # 7) in the Finger Lakes area and visited some wineries on the Cayuga and Seneca wine trails.
- Currently, my daughter, Hannah, and I are hooked on Covert Affairs. We have watched three seasons already this summer and we hope to finish season four before she goes back to college next week.
- Another show that I like to watch is Fixer Upper. Can Chip and Joanna Gaines come and renovate my house?!
- My favorite season is Fall. I love the colors of the leaves and the cooler weather.
- Most of my school wardrobe is black, gray, and maroon. In that way I can mix and match the pants, capris, shirts, cardigans, and scarves to make my wardrobe look bigger than it really is.
- I began playing the violin in first grade. I don’t play it as much as I would like, but occasionally I will play for church.
- I love to cook (and eat)! When I am feeling stressed or overwhelmed, you can usually find me in the kitchen making more food than we can possibly eat.
- I try to get to the gym three or four times each week (see #15). I think I read that if you do something for 30 days it becomes a habit. Well, after four years of going to the gym, I still have to push myself to go.
- I was born on Friday the 13th. No, I am not superstitious!
- My favorite number is 13.
- If I had the choice between doing a Suduko or a crossword puzzle I would choose the crossword puzzle. Is that weird for a math teacher?
- I’ve lived in four different states: New Jersey, Michigan, Pennsylvania, and Montana.

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I teach at a private school that uses MAP (Measures of Academic Progress) testing as an assessment tool to measure student growth. Our students test in the Fall and then again the Spring. I am not one to teach to the test, but I still get nervous in the Spring because I want the scores to indicate that my students are growing and meeting their growth target. Since the Spring test is given in late May, there are a few topics that we do not cover until after the test, but students might be asked questions on these concepts. I want to find a way that would help students get some review and practice for such concepts but not take up too much time since we will be covering them later on in the year.

In the front of our 7th grade textbook is a Countdown to Testing consisting of five problems to be completed each week for 24 weeks. Each of the five problems covers a different aspect of the common core standards. In the past, I have tried doing one problem each day, however, with only 42 minute periods three days a week and one 72 minute block each week, adding one more transition into the schedule didn’t always work. For this reason I am going to try giving the students an extra homework assignment that I assign on Monday and collect the following Monday. Since I do not assign homework each night, I am hoping that this will not be a problem.

I created a template similar to the setup in the textbook for students to complete the problems on. Students will have a week to complete this assignment at their convenience. We will then go over the answers during our block day, which is on Tuesday.

I do not want this assignment to just be about getting the right answers. Rather, I am hoping to encourage students to discuss the different ways that they used to answer the questions, thereby reinforcing the fact that there is more than one way to get to an answer. Additionally, since all of the problems are word problems similar in form to many of the MAP testing questions, I am hoping that this will strengthen their test taking skills.

In my previous blog I mentioned that I was reading Making Thinking Visible. I feel that this discussion time could be a great place to incorporate some of the practices mentioned in the book. However, I haven’t quite thought that out yet. I will leave that for another blog. Until then…

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For the past two years, I have had great intentions of blogging more, but then life gets in the way and anything that is not part of my” regular” routine gets pushed to the back burner. So, before school starts making life busier, I want to try to get blogging set into my routine.

I have been reading Making Thinking Visible this summer and I hope to reflect on the many additions and changes I have already made in my 7th grade curriculum and the the changes that are yet to come. In the process I hope to make new connections, get new ideas, and give back to the many wonderful people who have helped and inspired me.

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For the past few weeks, my 7th grade Algebra students have been learning how to factor polynomials. Every day we list the methods we have previously learned before going on to the next method. I gave nicknames to each of the factoring methods to help students remember the methods:

- GCF
- Difference of 2 Squares
- PST – Perfect Square Trinomial
- Trinomial to 2 Binomials
- c is (+)
- c is (-)
- a > 1

- Grouping

After learning every method, I wanted to see how well the students understood the factoring process. Students had to choose one of the methods and make up one problem and explain how to factor it. They used Google presentation to show each step of the process. Then, they uploaded their slides to Movenote.com and recorded themselves explaining their slides.

Before we began working on the project, we talked a lot about what makes a good slide: the entire script is not written on the slides, each slide should contain only one step of the factoring process, and the graphics should enhance, not detract, from the presentation. Then we talked about the what makes a good video presentation: look into the camera, speak slowly, and explain the method one step at a time.

I gave them this movenote-video-rubric.

Students shared the first draft their Movenote video with me. We watched each video as a class and talked first about the strengths and then how the video could be improved. Students took notes when their video was being critiqued. Then students were given a chance to edit their video with the suggestions made by the class before handing in the final draft.

I have to admit I was very pleased with my students’ creativity and level of understanding. It was a great way to allow students to have choices in a topic that is fairly abstract. However, I would greatly appreciate any suggestions on how to improve this project.

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Two of my favorite questions to use in class are: what do you notice? and what patterns do you see? It is amazing to see the range of perception, from the most trivial matters – you used all even numbers in your examples – to very deep understanding. I have had a lot of success in adding these two questions to teaching students how exponents work when multiplying monomials, dividing monomials, and with finding the power of a power.

Since my students love to work on whiteboards, I have the students use the individual whiteboards to expand the following problems and then put the answer in exponential form. As they are doing this, I ask students to look for any patterns.

I then start with, what do you notice? followed by what patterns do you see? Most students can see that the base stays the same and the exponents are added together. At this point, students can write the generalized algorithm and do several problems without having to expand each number out.

I start the next lesson on dividing monomials the same way. Students use individual whiteboards to expand the problems out, divide out the common factors, and put the answer in exponential form.

Again, I ask students what do you notice? and what patterns do you see? before we write the general algorithm and do some examples.

By the time we get to finding a power of a power, students understand how exponents are working and this lesson is a bit easier for them to comprehend. I still ask them what do you notice? and what patterns do you see? because I want them to verbalize their thinking and understanding.

These two questions made me realize the need to allow students to start the process of understanding, rather than me giving them the needed information. They need to work out the problems on their own so they can each see what is happening. Otherwise, there is usually the same few students who see it faster than the rest and they say the answer before everyone else can process the information at their own speed. Additionally, It allows me to gauge where each student is at, rather than starting them too far ahead in the concept. Their answers can tell me if I need to back up a bit before proceeding with the lesson I have for the day. I might need to slow down and ask more (better) questions.

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