**This blog is about starting, finishing, and the thinking involved in each. It contains two lessons plans utilizing MTV strategies. One is an introductory lesson for an Algebra 3 class, while the other is a review session for an Algebra 2 class. They can be adapted to many other Algebra topics. The two strategies I chose are Chalk Talk for the start and Generate-Sort-Convert-Elaborate: Concept Mapping for the finish.**

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**Lesson 1: Chalk Talk: Review of Functions (Algebra 3)**

**Overview: **Units 2 and 3 will include operations and extensions of functions that were originally introduced in Algebra 2. This lesson is designed to take 2 days to give the students the opportunity to tap into prior knowledge about what they remember and understand from Algebra 2 before tackling new processes with the functions. It will also serve as a pre-assessment to allow the teacher to adjust and adapt the subsequent review lessons to ensure that all students have the same base of knowledge before tackling the new concepts. Getting the students up and sharing is a bonus. This could possibly be done in one class period, depending on the length of the periods. I chose to do it in two periods to allow for more conversation and discussion. Day 1 will be done whole class, which is a slight adaptation, while Day 2 will be done as a station exercise, which is how Chalk Talk is normally presented.

**Goal:** To help the students recall the different functions studied in Algebra 2, as well as what their graphs look like, how to graph them, some of the specific properties of the different functions, and how they are related. *Note to teacher**: deficiencies or confusion in any of these areas will inform my next few “review” lessons.*

**Standards:** While there are multiple standards addressed in the original instruction of the various functions, no specific standards fit the review process.

**Materials:** Day 1 – A white board or chalk board and lots of dry erase markers or chalk Day 2 – Chart paper (4-6 pieces) and markers

**Day 1: **(*This is a slight adaptation: While conventional strategy has Chalk Talk as a silent, stations activity, this will be whole class and involve a lot of discussion…hopefully.*) In the middle of the white board will be the prompt: “FUNCTIONS IN ALGEBRA”. Direct their attention to the white board and ask them “*What comes to mind when you think about FUNCTIONS as it relates to Algebra?*” Remind them that they are to think back to the things they were taught in Algebra 1 and 2.

- Give them a few minutes to think about it, then have the students go to the board and write down a word, idea, phrase, or picture that comes to mind. All students will go to the board. Have them go up in groups of 5 or 6 so no one feels put on the spot being the only person up there. They can put their input anywhere on the board.
- After everyone has put something up, then start a discussion about what each one means.
- Some sample questions include: Do any tie together? If they do, how are they related? Are all the different functions you learned in Algebra 2 up there? Which ones are missing? What do the functions look like? Hopefully this will generate more ideas. As they come up, you can have the students go up and add them to the board, or the teacher can do it.
- Ideas I am hoping show up, and will prompt myself if not, include: families of functions, graphs and making them, domain and range, and solving functions.
- Wrap up the day by picking 5-6 topics or ideas. Ask the students to write those chosen on a blank sheet of paper. For homework, think of two or three things about each topic. It can be something they know that relates or maybe a question they may have about it.
- Tell them that a picture of their creation will be posted on their Google Classroom site for them to look at if they choose.

Hopefully, the white board will look something like this, with a lot less empty spaces by the time your discussion is completed.

**Day 2:** The room will be set up with 5-6 tables spread out with chart paper on each one that represents the topics chosen on Day 1.

- This time the Chalk Talk will be silent. Put them in groups, just to facilitate moving around the room.
- They are to visit each station and write down an idea or question relating to the topic. It will remain anonymous, so hopefully no one will be uncomfortable participating.
- There will be multiple markers at each station. This should be completed in 15-20 minutes.

Once everyone has circulated through the room, place each chart paper on the white board and discuss each one individually. If the class was thorough on Day 1, some ideas will not be new. That is okay, as long as the connection is there. *Note to teacher**: Make sure you have some questions for each topic to move the discussion along should it bog down. Remember this is a pre-assessment. Students will formally review these topics over the next few days, so specific processes can/will be discussed then. You are looking for connections and understanding so you can gauge the level of review needed. *

**Assessment: **Since this is a review/introductory lesson, there will be no summative assessment. The homework between Day 1 and Day 2 will be used as a formative assessment, as well as a participation component. *Note to teacher**: if a summative assessment is desired, one possibility is to have the student pick a topic and write a paragraph or two detailing what they learned about the topic from the 2 day process.*

Social Media:

Below are a couple YouTube videos showing Chalk Talk in action (in different subjects):

https://www.youtube.com/watch?v=3Q2eeaYKCmY

https://www.youtube.com/watch?v=xpxAaT3h70M&t=8s

https://www.youtube.com/watch?v=knhen8U6h68

Below are a couple links to blogs or articles on Chalk Talk through the Pinterest web site:

http://visiblethinkingroutines.blogspot.com.au/2013/05/chalk-talk.html

http://langwitches.org/blog/2014/05/11/visible-thinking-routine-in-action-chalk-talk/

https://literacylove.com/2013/10/10/making-thinking-visible-1-chalk-talks/

**Lesson 2: Generate-Sort-Convert-Elaborate; Concept Maps – Solving Quadratic Functions Review (Algebra 2 B)**

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**Overview: **The chapter on Quadratic Equations and Functions is one of our longer and more difficult chapters. There is a lot of material. Modeling, properties, graphing, translations, factoring (multiple types), completing the square, the discriminant, and the quadratic formula all come in to play, and it can get a bit overwhelming for the students. There is one part of the unit where we discuss solving quadratics by various means, and this lesson is meant as a review/wrap-up of that section, prior to a short assessment on it. I plan on it taking two days.

**Goal:** To have students prepare a Concept Map to help them organize their thinking when it comes to solving quadratic equations. Over the past several days we discussed several methods they can use to solve them, and the goals is to help them organize their thinking about the different methods and when to use them. **Teacher note:** While we may know what we would hope is on each map, what each student thinks important or helpful will vary, so expect a wide variety of detail.

**Standards:** While they are not being taught a single specific standard in this lesson, there are several that they have been exposed to over the past several days that are part of this review:

A-CED.A.2: I can graph quadratic functions written in standard form.

A-SSE.A.2: I can find common and binomial factors of quadratic expressions. I can factor special quadratic expressions.

A-CED.A.1: I can solve quadratic equations by factoring. I can solve quadratic equations by graphing.

A-REI.B.4b: I can solve quadratic equations by completing the square. I can solve quadratic equations by the quadratic formula.

**Materials:** Small and medium sized post-it notes, large sheet of paper (preferably at least 11 x 14), writing utensil.

**General Information: **

- I will allow them to work in groups of three or four, but each student will be responsible for producing his own concept map. The exercise will conclude with a homework assignment after day 2 that is their quiz review, and they will be encouraged to use their completed concept map to assist them where needed.
- The Post-It notes are so they can write things down, decide on the size used by the importance of the idea, and move things around as they decide on the linkage to other items and processes.
- The finished product may include the post it notes (taped or glued in place) or they may transfer the ideas and links to the paper directly once their final decisions are made.

**Day 1: **I will have introduced concept maps to them earlier, but once all the material distributed and groups formed, I will review the idea of a concept map with them. Ideally, we will have done them earlier in the year and they will be able to refer to their own product as reference. Then we will begin:

__Generate__**:**They will take a piece of paper and list all the major and minor ideas they can think of as it relates to the unit on solving quadratics. Since this is a review, I will give them about 10 minutes to work together. They will have access to their notes should they wish to use them. After 10 minutes, we will have a 5-minute discussion where they will share what they have listed.*Teacher note**: this discussion is optional, but since this is a B class and not college prep I feel it’s important that the discussion happen so anyone who might have missed a day or two, or does not have good notes is not left out.*__Sort__They will then transfer the ideas on their lists to post-it notes so they can do the sort process. Discussion in the group should be about the relative importance of each idea, which are the main topics and which are support ideas. This will allow them to use respective sizes of post-it notes to reflect that. They should also be deciding which ideas go together, placing them on their paper with the important, or main ideas in the middle and lesser or connected ones on the outside. Again, while the decisions and process are as a group, each individual is responsible for his own product. They DO NOT have to do it all the same.*:*

*I believe the first two steps will consume all of the period, so cut them off with enough time to clean up and store their work. If any are not done with the sorting phase, they finish that up as homework.*

** Day 2:** Get the students back into their groups of four, remind them what they did during first two steps, and then move into step 3.

This is the point where the students will solidify where each Post-it should go, and then connect them by drawing lines to connect ideas and process that should go together. Any ideas that need branching out should be so indicated by lines also.__Connect:__Have the students pick one or two of the ideas, ideally one that has given them problems, and write a few notes on the paper to help them solve that problem or issue. Make sure the elaboration is along the connecting line to the problem area. If they need to access their notes to do so, that is fine.__Elaborate:__*Teacher note**: remember that these are supposed to be somewhat personal to each student’s needs, so this is one area where they may deviate from others in the group. Encourage some initiative here for personalizing it to their needs.*__Share__**:**(while not a segment listed in the title, a vital part of the process) Once they are finished with their concept map, I will have them pair up with someone who was not in their group and exchange maps. Encourage them to talk to their new partner to find out what they may have done different, and why. Suggest they take notes on the differences in case they may want to alter their own later. I will them have them switch one more time and compare notes again.

As wrap-up, they may make any adjustments to their concept maps, based on their discussion during the Share portion, during the remainder of class. If needed, they may finish up as homework and turn in at the start of class the next day.

**Assessment: **Since each student is responsible for producing their own Concept Map, this will serve as the assessment piece. I plan to allow them to use their Concept Map as a resource on the next days quiz. They will submit it with their completed quiz at the end of the next class period.

**Social media:**

Below are several links to the GSCE:CM routine and Concept Maps on YouTube:

https://www.youtube.com/watch?v=DCnuRtdTGWM

https://www.youtube.com/watch?v=IwqxAJpxrnk&t=22s

https://www.youtube.com/watch?v=vuBLI6ijHHg

https://www.youtube.com/watch?v=bQlgx5biqCQ

Below are several links to the GSCE:CM routine and Concept maps from Pinterest:

http://making-teaching-visible.blogspot.com/2014/05/generate-sort-connect-elaborate.html

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Chris, FABULOUS! This blog post is the entire package….. well laid out, executed and the content is captivating. I love how you used these two MTV strategies to help students think and connect with what they are experiencing in your class. Won’t it be exciting to see how the students respond? At first, students are not used to doing MTV strategies but if you start out with “baby steps”, then they quickly catch up and look forward to them.

Your youtube links are powerful as are your graphics. I am incredibly grateful that you stuck with it in posting this important blog post… thank you!

Natasha, thanks for your kind words and the questions. I believe that making the webs as we go is a very good idea, particularly for some of my IEP and 504 students. I actually tried it last year, having them do a graphic organizer as we went through the entire unit on quadratics. The problem was not all did it with an intention to be a resource for themselves, so their finished product was just a regurgitation of the algorithms and methods and in most cases, incomplete. I feel that doing it as a specific post-unit review exercise will force them to think about what they learned and how it connects. The coach in me says the more times they think about it the better they will understand. Letting them use it as a resource on their pending assessment hopefully will result in them personalizing it, and giving it a bit more importance than just another review to turn in.

Christ,

Excellent lessons! I would honestly love to have you as a teacher. You are refreshing and fun to learn from. I love your questions in the first lesson. I feel more confident in my abilities to facilitate a Chalk Talk because of the questions you provided. It seems like you’ve tapped into some great YouTube examples. I’d recommend being more selective and having less links to share. This might be a “less is more” kind of thing; I’d hate for people to skim through any part of your work. I also love the RESIZING of the post-it-notes based on the students’ interpretation of the relevance to the concept. This is GOLD. You aren’t looking for right answers and they just get the freedom to make their thinking visible. Great work!

Kenzie, thanks for the kind words. I have to admit the Chalk Talk is something I think the students will really enjoy. I have written myself several notes about places I can use it, particularly when starting new units, throughout the year. I prefer the whole-class on the white board in most instances, but thought since this review covered so much material, breaking it into both methods was warranted. I can’t take all the credit for the post-it notes. Being new to the social media world, I went through a lot of different videos and I noticed in a picture that went with a video for one of the other thinking routines that young kids were using them on the board and I just thought that it would enable students to adjust their thinking without having to rewrite things or start over. On review, I agree I should have been more selective with links. I am not a person real comfortable with all the different media options and overdid it a bit. Lesson learned for the next round. Thanks again.

Hi Christ!

I enjoyed reading over your two lessons. In your second lesson using the Generate, Sort, Convert, Elaborate strategy for quadratics I think that the web ideas is great. Having the students go through each step in the strategy seems that it would add to there understanding of each step far beyond just writing it down. Is it possible to have students make a web after they learn each method? Could this help them see the steps in each method? Or is this area of math not conducive to being broken down in such a way? I especially like that you plan to allow students to use their map on future assignments, giving them an extra tool in their tool built outside of just regular notes.