MTBoS Blogging Initiative - Better Questions

Boy...when I look at the prompt for this blog post my mind goes in so many different directions. I wrote this post in which I discussed trying to use "quality questioning" in my classroom. I was not really talking about questions to put on an assignment, quiz, or test. I was thinking about questions used to do the following:

• guide students to think deeper during discussions
• guide a struggling student toward understanding a concept 
• scaffold and access prior knowledge
• defend and/or explain answers or reasoning

The prompt seemed to be more along the lines of writing questions for assignments or quizzes. I happened to attend a PD today on Webb's Depth of Knowledge (DOK) in which we discussed asking more level 2 and 3 questions when we assess our students. Of the 4 levels of questioning we were told that the ACT and the ASPIRE assessments have very few questions that are level 1 (basic recall or computation) and the majority of questions are levels 2-3 (harder stuff...HAHA!). Anyway, the majority of textbooks are filled with level 1 questions but not many that are levels 2 and 3. 

For those of you who want to know here is a VERY brief description of Webb's DOK:

Level 1 - Recall and Reproduction - "Right there" questions where you can look it up in a book or follow steps from an example
Level 2 - Skills and Concepts - "think and search" questions where you have to put information together or categorize - these may be open to using different approaches and explanations are often required
Level 3 - Strategic Thinking and Reasoning - More than one way to approach and more than one possible answer - non-routine problems are often used here - often asked to state and support with evidence
Level 4 - Extended Thinking - Extended thinking that takes more time - possible products would be films, plays, research reports (with multiple sources), video games, documentaries, newspaper articles, etc...

(source: A Guide for Using Webb's Depth of Knowledge with Common Core Standards by Karin Hess, E.D - copyright 2013 Common Core Institute)

We were given some strategies on things to do in order to use our textbooks and resources that we have and take the questioning up a notch. One example of moving into the Level 2 questioning is to ask for "non-examples." We often ask our students to give an example of a _________ but they can demonstrate an even greater understanding of concepts if they can also give a non-example.

I had the pleasure of using two non-routine tasks with my algebra classes this week. Both of the tasks seemed impossible at first but when we continued to work toward the solutions we found that there were ways to arrive at a solution.

The first task was the Shuttling Around Problem of the Week #13 in my IMP Meaningful Math Algebra book. It is actually a puzzle where you really have to get out manipulatives to work through it. On the day we introduced the problem only one student found a solution. It took him a while but he finally videoed it so that he could email it to me as part of his POW write-up. The funny thing is that even though I stood there and watched in order to verify that he had a valid solution...I could not do it myself. So, today I allowed another class some time to work on the task and I was going to sit down and figure it out myself so they would see that it was possible...but I couldn't. I called down to the classroom where the guy who found the solution was and he came to my class and showed us the solution again. After watching him do it I had several students go back and work to figure it out themselves...he and I went around the room trying to help and I FINALLY got to where I could do it. The task asks them to investigate other problems too so we weren't taking away all of their fun. It was a great way to end the week! The coolest part of this is that the student who really excelled is not an A/B student. He is rarely ever one who aces a quiz or test. He has an incredible work ethic and tries to do every thing that I ask of him. It was so rewarding for him to have an opportunity to shine!!

The other task was A Mini-POW About Mini-Camel again from our text. One of the great things about our text is the "key questions" in the teacher resources which helps you have ways to guide the students. In this one all I had to say was, "Who says you have to go straight there?" and I had students to begin to find possible solutions. I even had multiple students to go to the board to try to prove to everyone else that their answer was correct. (Here is a link to my Instagram where I posted a video of them.)

I had one student ask me why we had to do these types of problems and I told him that it is important for him to realize that just because something seems impossible at first glance it does not mean that a solution can not be found. I even told them that I may be helping to save their future marriages (haha!) because they may think one day that the only solution is to give up but remember that one time in algebra class they kept on trying and working at a task that seemed impossible only to find that there was a solution!! I know that is goofy but I got some giggles and I do hope that these problem solving skills stick with them after they leave my class.

I love that I have these tasks included in our textbooks! I wrote my last MTBoS blog about how my textbooks are my favorite tool that I use in my classroom here.

Intro to Systems of Equations with Gallery Walk

This year I ran across a document in my Google Drive that Sonya New and I made in order to introduce solving systems of equations. I decided to do this on the first day back after Christmas break in order to get us "back on track." We have solved systems algebraically and had begun discussing the substitution and elimination methods the week before school let out.

I loved doing the assignment. I only had 6 groups but I still wanted to have them graph all 8 systems so a few groups had 2 systems to graph. I did not call them systems. I just told them to graph both lines on the same coordinate grid. I first allowed them to graph the lines on graph paper and then I had them put them on chart paper. Afterwards I assigned each group a different color marker to write with and had them do a gallery walk and put feedback on the graphs. If they agreed with the graph they put a check mark. If they thought there was an error they had to place an x and then tell what they thought was wrong. The last direction I gave them was to write down the solution to the system of equations. (We have been talking about solutions for systems of equations ALOT in class. I have even OPENED and CLOSED class MULTIPLE TIMES by randomly calling on a student and asking them, "What is the solution to a system of equations?" AND offered candy when they get it correct!! Many of them still don't know. I accept various answers: an x and a y that make both equations true, the point of intersection, an order pair that works for both.... It hurts my feelings but I still haven't gotten it to "sink in.") I had one student in the room that asked me if I meant for them to write the ordered pair down so eventually everyone caught on. Almost every group asked me what I meant by the solution but I would not tell them. I told them to discuss it within their groups because we had talked about it in depth before Christmas. Anyway...after they completed their gallery walk we "debriefed" as a class and settled any differences of opinion. It was a wonderful way to review graphing and reintroduce them to solving systems of equations - we had one no solution and one infinitely many solutions so we also discussed what those would look like algebraically. I did have them solve a couple of the solutions algebraically (using substitution) at the end of class.

Here is the document if you would like it.

OBSERVATIONS:
1. Even my best students needed the graphing review. I had one of the top students in my class put his y-intercepts on the x axis!! I want to do a better job of spiraling my algebra class. I love that our Meaningful Math Algebra books include graphing in every single unit! I hope to incorporate more spiraling review as my warmups this semester.

2. It scares me how much my students forget AND it bothers me that I have to move on when I have so many who have clearly not retained what we have learned.

3. Many of them wrote that the solution was 5 and 2 when they really meant (5,2). They think I am being picky when I make them write the answer as an ordered pair.

4. Students like the opportunity to get out of their seats! I did have some really good student dialogue and I feel that it was a productive first day back after Christmas:)

Problem of the Week success:)

This week I graded what I think was the third POW writeup that I have assigned. Once again (even though I dread grading them) they provided "teacher encouragement." My 2 favorite comments in the "what I learned" portion were:

If you listen to the teacher she will give you hints that really help you. 

My parents said they didn't get to do fun assignments or sit in groups in their math class. (She thinks math can be fun??? = total success!!) 

I think the one about listening to the teacher is funny; the truth is many of my students tune me out while I am addressing the class as a whole. Then when the realize I've stopped talking they look around and say, "What are we supposed to be doing?" Ugh! I am trying some tricks to try to improve my students listening skills. One is to randomly call on a student at the end of class and ask them a question that they should know the answer to if they listened in class. I don't always ask them a math question either. I reward them with candy or letting them leave the room first.

One other thing that encouraged me this past week was noticing that I had one student use tables to graph lines. As a math teacher I think that is strange because I used to always put my equations in slope-intercept form to graph. Teaching from the IMP Meaningful Math Algebra book has helped me to allow students to discover the way that works best for them (believe me I always tell them the way I think is easier!! Haha!). I taught slope-intercept form (conceptually first in Overland Trail), graphing by intercepts, and graphing using tables almost simultaneously. I would stress the easiest way depending on the way the equation was written but told them over and over to use the way that makes the most sense to them. Out of 21 students I had 1 girl get 8 out of 9 graphing questions correct using tables. Even though it was only one student who chose that method it really encouraged me to see that some students really do benefit from the "alternate" approach. I have spent many years teaching them with the methods that I think are the most efficient. I feel like what I am doing now benifits my students more.

Hey...I still love math:)

I know this is a strange comment for a math teacher to make. For years I have just taught math. I chose to become a math teacher because I love math but to be honest all the years of teaching math to people who do not really want to learn it had just "sucked the life" right out of my math enjoyment! I was covering the standards but rarely ever used any activities that peaked the curiosity of my students.

Thanks to our "Meaningful Math adventure" (see this blog post for an explanation) I am having fun teaching math again. I see my students having more fun learning math. Last week I had a student to tell me that she had fun in class that day. I also had some students tell me that we do the most work of any of their classes but my class is also the most fun. I read Teach Like a Pirate this Summer and I have come to realize that it is okay to have a goal of having fun with your students...as a matter of fact we need to throw in some activities that the students will consider a "fun break" from "regular math."

Today I also found myself sitting at my desk working on the High-Low Differences activity in Overland Trail's supplemental activities. I was "noticing and wondering" myself! I was thinking that I really need to find some extra time to investigate why this works like it does. Then I was so ambitious that I answered one of the questions (in a survey I had to take) to indicate that I considered myself to be a mathematician! (HAHA!) I have found value in addressing problems from a student's perspective. Our new textbooks from It's About Time give me many opportunities to have fun working on math and then turn it around to my students as an opportunity to problem solve and enjoy themselves while they do it. I asked them a few times last week if they wanted me to "introduce" them to the activities or let them just try to figure it out on their own. I was amazed at the number of students who wanted to try it without any assistance.

Now, don't get me wrong. I still have students who sit there like "knots on logs" and wait for the problems to be presented to the class so that they can write down the answers - they just hope that when I roll the dice to call on someone that their number is not called. And when I do call on them they tell me they didn't do that problem...and then I talk them through it until I pull the answers out of them...in some cases it would be easier to pull their teeth without anesthesia. I also still have students who gripe and whine and ask for help before I even get the page number out of my mouth. However, it is so cool to catch that student who says he hates our textbooks truly engaged and enjoying himself during an activity (because he figured it out by himself!). This certain student that I have in mind was "called on the carpet" when I told him that I noticed he had fun working on the activity for the day - which just so happened to be "Getting the Gold" that I blogged about here.

I would like to end this blog with a funny picture of what some of my students did last year after I had gotten onto them for sitting there like "knots on logs" instead of doing their work.

Comedians!! 

Students teach the class - IMP Mini POW About Mini Camel

Today I decided to do the Mini POW About Mini Camel activity from The Pit and the Pendulum. We decided to skip Corey Camel POW and do this one first. I had not worked through the problem myself prior to doing it with my Algebra IB class today. Please don't judge me on this. Haha! I find that I do not lead the students quite as much when I don't know the answer myself. Actually, the teacher's guide does give you the highest possible answer but doesn't tell you how to arrive there. It does give you the hint to ask the students if the camel has to go straight to the market. (In other words...can he go part of the way and put a portion of his bananas down?)

I knew that the camel had to have some "pitstops" along the way but I had not sat down myself and figured out the problem. I gave the students some manipulatives and gave them approximately 20 minutes to work. I walked around and helped them to model their ideas with the counters. When I had one of  the boys in my class tell me he figured it out I was skeptical and made him show me. He and his partner talked me through the situation (which involves the camel only traveling distances of 1 mile at a time - and is pretty cool!!) I was amazed. I often find that my students are better than me at logic problems. I told the student that he had taught me something today and he was so proud.

Typically if my students do not come up with and defend a solution I will work through the problem with the entire class. If no one had come up with a valid solution I would have done that today. Also, if I model the problem solving process with the entire class and we don't come to a solution right away I just tell the class to help me think about the problem and let's see if we can work on it again the next day. It is so exciting to me when my students do it on their own.

IMP Pit and the Pendulum Days 1-2 - The Question and Initial Experiments

On the first day of Pit I was actually issuing books. Therefore I used the WONDERFUL advice of Jim Roebuck and we listened to a Youtube video in which the entire story was read. If it were not for the fact that I needed the time to issue books anyway I probably would have gotten too impatient and skipped to the portion that read the excerpt from our algebra books.

After the story I assigned The Question where they draw a sketch of the situation and look for information in the story to answer the big question...does the story's hero really have time to carry out his escape plan? On the first day we didn't completely finish the sketches and didn't even start the discussion so we continued it on the 2nd day. We made a list of what we know from the story (especially the items that are mathematicaly relevant). They include the following:

• The ceiling is 30-40 feet high
• The pendulum swings perpendicular with his body
• The pendulum was 3 inches from his body
• He thinks he has 10-12 sweeps or vibrations (back and forth) before it will touch him
• It will take the rats one minute to eat through the rope (yuck!!)

Then we arrived at a "revised question" - How long does it take the pendulum to make 10 swings? We are also going to use the assumption that the ceiling is 30 ft high. 

Initial Experiments pg. 201

Okay...the fun part was then asking the students what we needed to know to answer this unit question. I had one boy who instantly said that we needed to know how long it took the pendulum to make one sweep. We had a class discussion about all the things that might effect this time and we narrowed it down to 3 things that we could actually test in class: weight of the bob (end of pendulum), length of pendulum (which is the height of the ceiling in the problem), and the angle of release (amplitude??) of the pendulum. I am not used to using the word amplitude for this type of problem. I keep picturing the perpencicular distance between opposite sides of a parallelogram!

Anyway...the students enjoyed building pendulums. I assigned each group one variable to test but I didn't give them any guidelines other than to test each weight (or length or angle of release) 10 times. Therefore they did 30 total trials. Also they only timed one sweep. After the experiments they decided that the angle of release didn't matter but that the other 2 variables did. Then we discussed issues that may have effected our data like not using the same angle or pendulum length when you were trying to test different weights. Or not using the same pendulum length and weight when testing angle of release. Also, some student held the pendulums in their hands and kind of helped the swing by moving their hand up and down. I look forward to doing more investigations and tying in the statistics as we go!

Students working on their sketches

P.S. - Thank you Jim Roebuck for giving us helpful hints on how to best teach this unit!

First days of school ideas - adapted from basketball camp!

My son and husband have attended a basketball camp this week. There are a couple of activities they have done in the classroom sessions that I want to adapt for the first days of my algebra classes.

First idea:
Explain a little about what makes a good group member or leader, an average group member, and a bad group member (my students sit in groups of 4)...then give the students some classroom scenarios and ask them to work in their groups to decide how the 3 types of group members would respond.

Example scenario:
The teacher puts a problem on the board and tells you it is review and you should all know how to do the problem. However, no one in your group knows how to do the problem.

Sample reaction of a good group member/leader: "Well, let's look in the book for similar problems."

Sample reaction of average group member: Raises his/her hand and waits for the teacher to come to their group.

Sample reaction of a bad group member: "She's crazy! What's for lunch today?"

I think this has a lot of potential. I want to improve my 3 names of types of group members and I want to come up with some GREAT scenarios! Also, I want to record the students' responses on chart paper and post them in my room as "rules" so I can ask them which category they fall under as we do group work throughout the year.

Second idea:
Next, I want to do a "4 corners" activity where I give the students 4 different characteristics and ask them to determine which one is the most important one for a great student to have. The 4 characteristics (or however many you want) need to all be good...therefore there is no wrong answer. After the students go to the location for the characteristic they feel is most important each group brainstorms why they feel the way they do and then selects one person to "share out" and defend their answer.

I hope these activities will help establish a culture of good communication and quality group work. Who would have thought these ideas would be learned second hand from a basketball camp?!?! If you have any ideas please email me (towens@attalla.k12.al.us) or send me a tweet (@owensteri). I will add them to this post :)

**I tweaked this idea a little but and Mrs. New and I created this presentation for the 1st day of school. Mrs. New had a great idea to use "Which one doesn't belong" activities for the 4 corners. Also, we are doing Jo Boaler's week of math activities from youcubed.org.

The Pirate's Life for Me!

Thank you Robin Bynum for letting me read your Teach Like a Pirate book by Dave Burgess. I must admit I was a bit skeptical at first. I mean....I'm a math teacher! I thought the book was only going to be about dressing up as historical characters and other "history-specific" hooks. However, as I got deeper into the book I found myself becoming re-energized for this coming school year. Here are some of my take aways:

• If your students aren't engaged don't get mad at them. See it as feedback.
• It's okay to spend some time on activities that loosely tie into the curriculum yet promote creativity and fun in the classroom! 
• Ask yourself the right questions about how to "hook" your students into a lesson.
• Pursue excellence as an educator. It is okay to want to be great at what you do!
• Don't let fear of failure, perfectionism, or fear of criticism hold you a back. Failure is a part of growth.

I know I have left out way too much. However, I believe every teacher -no matter the subject area or grade level -can benefit from this book. It may not all apply to you...or you may not agree with all parts of the book...but I think anyone who reads will find at least a few ideas for the next school year. I believe that each time you read a book or hear a speaker at a conference you can learn something.  I am probably not going to wear costumes or redecorate my room for certain lessons...but I still have many other ideas knocking around in my head because of this book.

So...I will accept the challenge to go daringly into next year and try some things I have never done before - a "pirate's life for me!"

Gary Webb's reflection of 1st year teaching Meaningful Math Algebra

There are 2 other math teachers who have gone through IMP Meaningful Math Algebra with for the first time this year. I have mentioned them both from time to time in my blogs. One of them is Gary Webb. We were asked to write a testimonial about our first year's experience. I thought another teacher's perspective might be interesting. Here are his thoughts:

I really enjoyed teaching from the Algebra I Meaningful Math book this past school year. It was quite different than traditional math text books. The books have few examples, fewer problems, require deeper thinking, and don't have answers in the back either.

One takeaway I have is that your best students will do whatever you ask them to do. Some of the students are not going to do anything no matter what. These are the ones who complained most about the book. However, these are the same students who might do 5 traditional math problems in 30 minutes and complain about having homework.  The many students who are in the middle were the ones that I was able to reach. Students were more engaged because they were able to use their creativity in the math classroom, were in groups much more often, and were encouraged to discover mathematical concepts on their own.  I loved watching my students think and not be a robot and follow set procedures.

Gary Don Webb
Etowah High School

STUDENT End-of-Year Reflections on IMP Meaningful Math Algebra

Wow! What a year it has been! It has been a while since I have written a blog post due to the craziness of the end of the school year. I have so much that I would like to share.

Here are the student responses I got from the end-of-year review questions in the Fireworks portfolio. We did not have time to do the complete portfolio so I just had them answer the questions on pg. 421 in the book. I feel like what they have to say is more important than anything I could add. I only had one student to just absolutely say that he wishes he was taught out of the "old" type of textbook. Of course the responses I am sharing below are the "fun" ones for me to read as a teacher. There were some students that talked about how they didn't like that the book was so "wordy" but those same students later admitted to growing more confident and learning how to work in groups. I also had a few students to tell me that they still preferred to work alone but the overwhelming majority had positive things to say about group work. I told my students to be honest with their responses and give good explanations to support their comments. I told them I really wanted to know what they thought.

The first question set included the following:

How was this experience different from your previous work in mathematics? Did you learn the mathematics differently? How was the math itself different? 

Here are some of the responses: (I really wanted to fix all the grammatical errors...but I didn't because I didn't want to put my "spin" on what they said.)

• The books we used this year was all word problems and that will help me during high school and college. 
• Working in a group helped me understand better cause some of them understand better than I did and they helped me understand it better. 
• It was more fun with the activities and been taught different.
• ...the mathematics itself was longer and a bit harder also
• My past experiences I didn't understand anything but now everything seems a lot easier. (this is a repeat algebra student)
• This book is also different because it never (is) just straight on work it always has a fun story. Also it helps you a lot more than any other math book.
• We actually learned about real work stuff. We did a POW about having a house, paying bills, etc...

The second question set included the following questions:

How have you changed personally as a result of your experience? Has your confidence in your own ability grown? How has your experience of working with others changed?

Student responses:

• Working with others - I've started talking about it more than just trying to work on it.
• I'm more conficent in math now than I ever was. (this comment was repeated by several students)
• All year I've had a group to work and to collaborate with so I do believe I have gotten better working with others.
• My confidence in math has grown a lot because at first I never answered out loud, but now I know that I can do it.
• I don't hate math as much. It's not as hard as it was. My experience of working with others has grown alot and I can talk better with other people. (this student is a very quiet and shy young lady) 
• I like working with other people. You get to see what everybody thinks and their ideas. My personality has grown to like math a little bit more. I still kinda don't like it, but I like it more than I did.
• I think I have become more confident. I think I have learned to work with people that I normally don't talk to.
• It's changed (experience working with other) cause if I need help then I can ask my group members.
• It has helped me change by helping me with the word problems to look for clues through the paragraph. I myself had a hard time on word problems till this book helped me out.
• Personally I changed mathematically. My math skills have grown and so has my confidence in my own ability. My experience of working with others has changed like now I can work better with others. I can cooperate with others better. (This student stated in his answers to the first question set that he didn't like the book. I sure did like the results he got though!!)
• Yes my confidence has grown going into ninth grade. I never like working in groups but now I do.
• From a special education student: My confidence grown alot since last semester. It change because I use to just copy people because I didn't know how to do it but now I work together to figure out the answer.
• Working with others gave me more confidence and helped me understand something I didn't know and I could just tell my group and see if they know so we could help each other out.

The last question set had these questions:

What are your mathematics goals for the rest of your high school years? How have those goals changed over the past year and why?

Student responses:

• I also would want to keep learning more math cuase it can actually be fun to do.... But this year in math it has been easier for me and I'm getting higher grades.
• My goals have changed because I feel like I'm trying in my math classes and not just copying.
• I wanna keep improving my math skills for the rest of my high school years and beyond that. My goals have changed over the past year because I learned that I can keep improving my math skills. 

The Four 4s - an activity from Jo Boaler's book

Today I spent most of my day in the computer lab where my Algebra IB students took a "mock" end-of-course exam. Those days are so draining for some reason! I am happy that it gave me the opportunity to finish reading Jo Boaler's What's Math Got To Do With It? which I believe every math teacher should read! Thankfully one of the last chapters discusses some puzzles and number talk activities that are good for students. I was so tired I could not imagine having a "normal" class with my 5th period today. Instead I gave them The Four 4s to do as an activity. The task asks them to try to make every number between 0 and 20 using only four 4s and any mathematical operation. The directions for the task gives one example and then asks them how many of the numbers between 0 and 20 they can find.

At first my students wanted me to give them more examples but I refused by telling them I didn't want to rob them of the opportunity to get them on their own (haha!). I finally got a few of them moving by telling them to just write four 4s on their papers and then put some operation signs in between them. Once they did this I told them to evaluate the expression making sure they used the order of operations correctly. This really got them rolling. A cool thing about this task was that everyone worked on it. At the beginning I had to seperate a few that were totally off task but once they saw that they could get some of the numbers they worked on their own.

I think that you need to have variety in your classes. I have many students who do not enjoy an activity when they view it as purely mathematical but when you give them a puzzle to solve they engage. I intend to use activities like this more often. One of the discussions on Boaler's website (youcubed.org) talked about how they just listed the numbers 0 thru 20 on a board in the back of the room and allowed students to write their expressions and put their name beside it. That way all of the classes throughout the day could contribute until all of the numbers are found. This task will engage some students that are bored with the normal daily routine!

Just in case you read this blog because you are using the IMP Meaningful Math textbooks, Jo Boaler has a list of 3 curricula that she recommends for use in 9-12 and the Interactive Mathematics Program from It's About Time is on that list. After I started reading her book I realized that she was one of the keynote speakers at NCTM this year. I learned so much about what the research says about the best ways to teach math for student success!

IMP Fireworks - Parabolas and Equations I, II, and III and The Vertex Form of a Parabola

I am absolutely loving the way Meaningful Math develops the Fireworks unit. These graphing activities go through each of the ways that parabolas are transformed using phase shifts. The students explore each of the phase shifts using graphing calculators. They start with different equations to enter and analyze and then they are given a picture of multiple graphs on the same coordinate plane. They areasked to create the picture by typing equations into the calculator.

The first few activities I gave each student a TI-83 and each group also had an Ipad. Once they figured out the correct combination of equations the group displayed their graphs on Desmos which I projected on the board using Airplay. This was a neat way to have the students to "show off" their work. However, as we were going through the activities I noticed that many of the students were just waiting for the person with the Ipad to type in the equations. They were not using their calculators like I had intended. I wanted them to use the calculators first and then display their findings using Desmos. Therefore, today I had the students to let me know when they got each of the pictures correct. I initialed their papers where they had written down the equations that gave the picture. We did not use the Ipads today. I liked the change - especially since we were working on the activity that pulls all the shifts together. By requiring initials for each of the problems I was able to formatively assess each individual instead of each group. Since each graph took a good bit of  time to create it was feasible for me to initial.

Today's activity introduced the students to the vertex form of a parabola. It combined all the pieces that we have been working on in the last few days. I feel that after working on getting the equations that generate the pictures the students were beginning to demonstrate a firm understanding of the phase shifts. 

On a side note...Thursday Tom Laster and Laura Murphy from It's About Time came to our school to observe our classes and discuss plans for next year. Observe is really the wrong word...they actually came into my class and sat with my students and participated in the graphing activity. My students really enjoyed this and I was honored that they came to visit!

IMP Fireworks Day 1 - Victory Celebration

I am excited to be "switching gears" and starting a new unit today. We did the Victory Celebration activity which introduces students to the unit problem for Fireworks. I love that the activity asks students to sketch the situation - this gives students with an artistic flair the chance to "show off" in class! There are 4 questions in the activity so I had each group split up. In my 2nd block class I had groups of 4 so I told them to let 2 people sketch the situation while the other 2 started working on the other questions. This worked out well because there was not more than 1 or 2 students in each group who were interested in drawing.

Some groups took longer than others on their sketches so I had everyone who was finished to get a graphing calculator and showed them how to enter the height equation into the calculators. It was necessary to also talk about how to adjust the window for the graph. We played with the tracing features on the calculators in order to look at approximations for the maximum height and the time the rocket was in the air.

I pulled a piece of chart paper and started talking about sketching the graph on the chart paper so we could refer to it throughout the unit. This brought up a discussion about which quadrants were needed. We also talked about labeling the axes and how we needed to be careful about drawing the graph because we didn't know how to scale the axes until we knew the maximum height and the amount of time it took for the rocket to land. (This is when we started playing with the tracing feature on the calculator but we ran out of time.)

Also, we discussed what the height of the rocket was when time was 0 seconds and what the height of the rocket was when the rocket hit the ground. These concepts are common sense really but it takes a few seconds for the answers to "hit" them.

Another cool thing that happened today was that my 4th block came in excited about getting to draw in math class. They took so long with their sketches that we didn't get as far with our discussions...but it was worth seeing them so invested in the activity.

After writing this post today I had an afterthought. I know that many people may ask, "Why are you drawing in a math class?" I told the students today that when people in the "real world" have large problems or projects to solve they often draw sketches or models in order to visualize what is happening. I think it is neat that this activity leads the students to start with a sketch!

Solving Equations Scavenger Hunt - Thanks Mr. Webb

It is great to have fellow algebra teachers that share their fun activities! Mr. Webb is another algebra teacher at Etowah High School and he made a scavenger hunt using QR codes in which the students had to solve equations in order to find the missing digits in the next room number. He bought cupcakes for the winners and we also awarded bonus points to the top 2 teams (everyone got a grade for participating). So during 5th period today we combined our  classes and created random teams of students.  Each team got a paper with a QR code that gave them an equation to solve in order to get the next room number.  They ran all over the school!

They had to get the room numbers in the correct sequence to win so they often returned to my checkpoint a little frustrated...

They do eventually get the hang of it though and they seemed to have alot of fun too! This was a great way to spend the last class of the day on the Friday before Spring Break! (And I got to eat a cupcake too!!)

Thank you again Mr. Webb for creating this activity and sharing with us!

Winners eating their cupcakes:)

IMP Alice Days 6-7 - Piece After Piece, Many Meals for Alice, and In Search of the Law

For Many Meals for Alice and In Search of the Law I really put my Ipads to use. I am learning better ways to implement using the Ipads. I gave each group a few minutes to brainstorm on each problem and then told them that at the end of the allotted time they had to put SOMETHING on the Ipad (using the Educreations app). The Airserver app allows you to project up to 10 Ipads at a time so I have an Ipad in each group (sometimes more). I had told my students that if you have an Ipad you HAVE to be mirroring the screen. I can see all the screens on my computer. This has been a tremendous help for keeping my students from using the Ipads for purposes other than the math! When I turn on my projector where the students can see everyone else's work it is interesting. I am still amazed how my students will approach problems so differently when I don't stand at the board and show them an example of what to do (which causes them to all try to do it my way). We have an easy way to compare and critique the work without it being totally obvious whose group it came from. Then they are able to edit their work when it is needed. Formative assessment on the fly!!

I had a student volunteer to "teach" - she was great!

The context given in All About Alice provides such a neat alternative to simply just giving the students the rules of exponents. Piece after Piece establishes the rule for multiplying powers with the same base. Some of my students wanted to ADD 2^3 and 2^5 so to help them I told them to remember that we are always looking at what we are MULTIPLYING Alice's height by. I am interested to see how other IMP teachers handle this...

Many Meals for Alice establishes the rule for raising a power to a power. The original power is for the number of ounces of cake she eats at each meal - #1 is 3 ounces of base 2 cake so it is actually 2^3. Then the students figure out what is happening to her height after certain numbers of meals. In the end they have hopefully developed the idea that (2^3)^4 means that Alice ate 4 meals where she had 3 ounces of base 2 cake. It takes a few times of looking at it to start making the connection. I LOVE #3.

In Search of the Law actually has the students to explore exponent rules that I have not usually put much thought into. It took me a minute or two of exploring myself - I actually had to tell my students to start working on #1 while I went to read the teacher's guide! When I glanced over the activity the day before I taught it I didn't realize it was going to throw me a curve. Anyway...this activity is actually not difficult AT ALL. It gives the students several scenarios to just work with exponents.

Kahoot! - educational and fun - especially for reviewing

Today we were delayed for 3 hours so there were several students who were absent. Also, we did not meet with all of our classes and I like to keep my classes together (for my sanity!) so I did not want to move forward with the next lesson. I was thinking about pulling some standardized-test style questions and reviewing. I was just going to project them on the board and have them work on them using the ipads (educreations app) or the small whiteboards. BUT then I remembered how much fun my students from last year had playing Kahoot! for reviewing.

Coach Whitt explaining a problem from a Kahoot!

Fortunately I ran across a wonderful Kahoot when I did a "public search" for graphing equations. It had 16 questions that reviewed finding slope, graphing, finding intercepts, and evaluating functions. I was able to use it with my Algebra IB for review and in my Algebra IA to reinforce concepts we are currently working on.

These 2 guys were working together:)

I realized last year that when we worked through Kahoots which makes the review feel like a game the students invested in trying to learn how to get the correct answer so they can get the points for the next question. After each question the game shows who the leader is and you also have the opportunity to stop and go over the question. Today I gave the winning player 2 pieces of candy and all the other players on the "leader board" 1 piece of candy. It was a fun and productive day.

If you have never used Kahoot! it is great for all subjects and grade levels. You can create your own reviews or you can do a public search for ones that have already been created. There are sometimes mistakes in the public reviews but I just use them and then address any mistakes as they come. My husband showed me last year where the writers of the Kahoot! website even recommend you have students to create their own reviews for the class to play. That is also a great way to see if your students have a clear understanding of the material. Last year I had the students to use their own smartphones. There is a code that they use to log into the game - they do not have to have an account to play. I let students share if they needed to. Today I had 9 ipads for the students who didn't have smartphones so it went great!

IMP Cookies - Solving Systems of Equations (Only One Variable and The Classic Way to Get the Point)

I love the way the Cookies unit starts with solving systems of inequalities and then works into solving systems of equations. In the Cookies and Inequalities portion of the unit the students are introduced to "real-world" problems where systems of inequalities can be used for solving them. The students practice writing constraints and then graphing the inequalities that go with them. In the real world problems often have more than one possible answer - much like is true of the feasible regions you get when graphing systems of inequalities.

Then, as you try to solve the Cookies unit problem or other problems in the unit involving minimums and maximums you discover that you need to find the "corners" where the lines intersect. We had our students just estimate using their graphs in order to find the points of intersection. However, it is neat to be able to introduce the topic of solving systems of equations by talking about how we really need to be more precise when we find the "corners" of the graph. For a couple of days this week our classes worked on an additional activity that helped them to explore the elimination method.

Today I first had my students do the Only One Variable activity. We had alot of fun with it because we integrated some technology too. Each group had an Ipad and they were projecting their screens using air server/airplay. I gave the group 3 minutes to work on the problem and then after the time was up they had to put something on their screen (they were using the Educreations app). It is so cool to be able to see several samples of student work on the board at the same time. We can critique the work without the class knowing whose work it is. We are able to celebrate different approaches for solving the problem. Also, we are able to talk about common mistakes. They love when they are working on a problem and I point out their work. I can say, "Hey, this person is really moving in the right direction."

Each group's problems projected simultaneously! Cool stuff!

Next we worked on The Classic Way to Get the Point which introduces the substitution method. Mrs. New and I had looked through the rest of this unit and we saw so many activities that give the students the opportunity to practice solving systems again and again. I used to teach these two methods of solving systems of equations separately. Then after covering each method I gave them some "mixed practice" where they had to choose the method to use.  However, I now like the idea of giving them some time to practice a few of each type and then let them decide which method to use as we go. The ACT and other tests are not going to tell them which method to use so they need to learn how to choose which method works better for each type of problem. There are several activities in this portion of the Cookies unit that give them a few more systems of equations to practice solving so hopefully by the time we revisit the topic several times my students will retain the information.

My #KidsEnjoyingMath post

My math teacher "twitter friend" Justin Aion has challenged math teachers to post pictures of students enjoying math in this blog post. Here are some pictures of my students having math fun.

Well, I take alot of pictures of my students! I better stop here! This year I have started using Twitter and Instagram to post pictures of things going on in my classroom and school. I started with Twitter but some of my students talked me into getting an Instagram because they used it more. I love that you can set up an account on both of these and people can "follow" you and you don't have to follow them back. It seems more appropriate for teachers and students. I sometimes have the students to ask me to take their picture when they are proud of what they have accomplished! I am their proud math mom! We also started a school hashtag. Anyway...that is why I had so many pictures for this #KidsEnjoyingMath post. I think this is a wonderful idea! Thank you Justin!