A little something I noticed
On the last day of our winter break, starts my planning for quarter 3. Actually before I can start my daily lesson planning I have to pace out my quarterly standards. I have a simple week by week homemade word document that I write a general idea of what we will be covering.
On the back goes the second half of the quarter. As I was pacing I found myself noticing something that I always ask myself to do when teaching a concept.
“What is the difference between…..?”
“What would it look like if it was NOT….?”
“Give me an example of what is NOT….”
“What are similarities and differences between this and what is NO this…..?”
After noticing this I realize the difference it has made in my student’s thinking.
We learn from Newton: “For every action, there is an equal and opposite reaction.” Hence my reasoning for asking students to justify what is the opposite of what we are learning.
It might seem a waste of time or you might be thinking….”yeah right not another thing to ADD into my lesson planning” Tell you the truth it takes about 5-8 mins of lesson time and it makes a world of difference. All it takes is asking a question similar to the ones above. Don’t have a homework for a certain day??? This makes an easy and attainable homework for all students to accomplish. When they come back with their homework done (cross your fingers) have them share their answers on the board (or on their whiteboards). There is the beginning of your discussion and also a way for other students to see what they might not have noticed. I don’t do the venn diagram thing but it is definitely usable here. The important thing is that students are being asked to really grasp what something is by also looking/figuring out what it is NOT!
The Day in the Life of Hana High School’s 0.5 teacher
Quick explanation, I am a half time teacher (0.5). What that means in a nutshell: Half the salary of full time teacher (NOT hourly), benefits available, work HALF the amount of classes as full time teacher. Full time teachers at my school teach 7 classes (6 classes with students and 1 collaboration period with another teacher (i.e. ELA/Soc Stud, Math/Sci, etc.)). If you can’t do the math that means I am supposed to teach 3.5 classes (I know right? what does that MEAN???)
Our school schedule is specific to our student’s needs. We have a combination of 50 min periods daily (Periods 1-5, 7:45-1) AND 100 min blocks every other day (Periods 6, 7, 1-2:40, M/W, T/Th)
6:15am – My eyes snap open because I have been dreaming about what I forgot to plan for this week. THEIR TESTING GROUPS!! I have to start this today! I don’t have enough time in the quarter not to start. Oh man when am I going to fit this in this week’s plan. I have to give up my precious teaching time in order to have students do state testing. (actual thinking going on in my head)
6:30-7:30 – Get ready, decide on my professional outfit (I like to dress up because I feel like if I take my job like a serious profession others might also)
7:30-9am – I receive work emails sporadically throughout the morning because I don’t have a working computer at school so in order to read and respond to my work emails (Lotus Notes) I must forward my emails to my work gmail account. So during this time at home while I am getting ready I am responding to work emails regarding my principal’s substitute administrator, student technology contracts being turned in, spam email from companies trying to sell me crap.
8:50 – Must leave house because it is my nieces birthday and I have to stop by and give her the lei (plumeria) that I made for her to wear. I normally leave 5 mins later.
8:57am – Park, reach to classroom, throw bag on desk, grab number talk book from cabinet, don’t forget your keys (I ALWAYS lock myself out). Stop by front office to sign in and make my way down to our 5th grade classroom to do a 20 min number talk (volunteer time because my real class doesn’t start until 9:50).
9:03am-9:28am – 5th grade class number talk begins with a reminder of reason for doing number talk, reminding them about taking risks by trying new strategies, not be afraid to make mistakes, etc. Number Talk set begins with: 90-79= the next 20 mins proceed by having students work on problems posted using mental math and showing me they are ready by putting thumbs up on their chest when they have one strategy. I then pick students to share their different strategies in order to “discover” other math strategies.
9:28am-9:30am – Walk back up to my classroom (5th grade class is at the bottom of campus, my classroom is right next to the front office), remind some students about getting into class and walk with them to their classroom. Continue walking to my classroom…..
9:32am -Check in with front office about school portrait pickup status (I am in charge of school portraits because I am yearbook teacher). Phone call comes in for me. Its the sales rep that I have been trying to get in touch with (timezone problems east coast, west coast). ”Aunty, forward this phone call to my classroom, give me a second to run to my classroom!” **Running down the hall to my classroom**
9:32am – Bell rings for first recess
9:32am-9:45am – Recess is used up talking with sales rep about sending me quotes of technology devices that my technology coordinator needs me to order for him.
9:45am – Just got off the phone with sales rep, PCNC is here to see me about changing our quarterly parent night meeting to January and show’s me the email that the elementary Grade Level Chair sent her. ”Yup that sounds good, just keep me in the loop on those emails.”
9:45am – Bell rings (but it’s not the right bell we have to wait 5 MORE mins for the right bell), oh wait windows aren’t open must open bottom windows because last time I tried to close my top windows I smashed my finger in the window and had to pull it out without opening window because I can’t reach window opening latch.
9:50am – REAL BELL RINGS (now I have to time them 5 mins because there is no tardy bell). Kids start filing in…. “Circle Ms. Sadie?” ”Yes, P, we do circle everyday.”
9:52am – Don’t forget the sign in sheet, open up on iPad so students can sign in. Look in Dropbox to read over lesson plans before I give iPad to students. Oh yes, “counting down by 15 mins, starting at 600 mins”. Draw number lines on the board.
9:55am – “Ok who is starting today?” Loud students by the door “Oh wait who are we missing? Oh great! No, you need to go get your guy’s tardy passes. You guys are late”
9:56am – Tardy passes put on desk, late students have joined the circle and are somewhat ready to go.
9:56-10am – Discuss the weekend happenings with students and my co-teacher, the auto tech teacher (my co-teacher) participated in a stock car race/demolition derby over the weekend and many students went out to town to watch. Lots of fun!
10-10:15am – Start counting circle, we are counting with new strategy (down by 15 mins). We have a new starter today! Go ahead my dear…We proceed to count around the circle practicing adding strategies, converting mins to hrs, etc.
10:15-10:25am – We need to make new seating arrangements based on testing groups. We discuss the reason for having these new assignments (because we need to not disrupt class when we leave or come from testing). Ok now we are waiting for students to pay attention. We wait 2 mins for everyone to be back on task and paying attention. Back to testing groups….grumbling about people in groups, moving to new seating assignments slowly, ok now we are settled.
10:25-10:30am – We discuss who has their technology contracts signed. Who knows how to log in to computers or who has their pw to log into computers. Ok two students still missing tech contracts. Ok now for the prep for testing on computers: ”So what do we need when we do our math in class?” Brain, calculator, paper, pencil. “ Yes, which ones do we need to provide for ourselves?” Paper, pencil, brain. Yes, “let’s get our packets of scratch paper together, do you think they will ask you to graph? do you want graph paper?” Ok make your scratch paper packet. Staple it together! Let’s put it in our folders for the first group that will be going tomorrow.
10:30-10:35am – Filing papers, tomfoolery and silliness between immature boys. More waiting by me for them to be ready. WAITING, WAITING, WAITING. Discussion about who will be starting tomorrow, starting the practice test and practicing with the calculator.
10:35am – Bell rings (not the right bell, we have 5 more mins) “Ms. Sadie do we have homework?? Are you going to give us homework?” **Ignoring** ”Ok get your notebooks out, and turn to thursday’s notes. What did we do on thursday? Remind K what we did on thursday, what are we working on?” Slope and y-intercept from different representations (graph, table, equation, situation).
10:40am – REAL bell rings. Walk over to the door and close it because my next period is waiting outside the door and distracting other students. ”The bell rang Ms. Sadie can we go?” ”Nope, you can’t go you wasted my time so now I get to keep yours, sit down and lets discuss Thursday’s work” 1-2 more min of this and then I have to let them go so they won’t be late to next class. ”No, no, no homework, except for K and S who have to get their technology contracts signed” ”yes you may leave”
10:42am – Open door to let one class leave and another come in. ”Here’s the iPad to sign in, get in our circle.”
10:45-11am – After erasing last period’s counting circle numbers (but keeping the number lines) we are ready to start. ”Counting down by 15 mins, starting at 675 mins, who wants to start?” We start our counting circle and we proceed with questions and answers. We had quite a discussion today because I gave them a wrong answer and it took us a while to figure that out. ”You know who’s wrong you guys?? ME!! hahaha!”
11am-11:30am – Go to seats, get out notebook and turn to skills tracking log, as they are doing this and getting colored pencils I am passing back last Thursday’s assessment. Up to the board to write down name of 3 standards that were assessed for them to add to skills log. Questions about the assessment, comments about why I liked the questions, comments about why it was hard for them. More talk about what answers look like to get a “green” (meet proficiency). Reassessments were discussed, the process of reassessments, more questions about grading, mid quarter reports and their grades.
11:30-11:40am – “What skill(s) have we been working on?” Yup, slope and y-intercept from a representation (graph, table, equation, situation). Has anyone come up with a way to figure out the y-intercept and slope for a certain representation? Any ideas of EXPLAINING HOW to figure out slope and y-intercept?” ”Yes, I just ask myself those same questions for every representation” Get our notes down for today (we are totally rushing this). ”Turn to next clean sheet of paper in notebook, here is your title….” ”yes you will have homework so right underneath your notes write this title…..”
11:40am – Bell rings (the wrong one, we have 5 more mins)
11:45am – Finish writing homework in notebook, pack up and leave for lunch time.
11:45am-12:15 – It is lunch time for all students, now is the time I try to take roll (oh no internet is too slow can’t do it now must wait til after school, hope to remember). Put away representations in envelopes for assessments next week. Check student sign in sheet, check emails, respond to emails regarding students, get ready for graphic design class starting at 1pm. Student stops by on his lunch hour to schedule a reassessment date.
12:05pm – Bell rings (wrong one we have 5 more mins). I need to go home for lunch already….Keys, classroom keys, glasses, purse….BRB.
12:07-12:55pm – lunch time at home with my doggies. Out of crates, barking, barking, warming up my food, reading my book, Around the Horn on ESPN, more reading, twitter time, catch up (yeah right, fast scrolling through), back into crates with treats.
1-1:20pm – Its graphic design time (no I don’t even have a degree in this). Oh yes I forgot college/career fair so a little over 50% of class (all seniors) are not here. Meeting that happens at the beginning of each class period to update all students on jobs and what they are working on today. 2 photographers working on editing pictures and prepping them for page designers to use. 2 page designers finishing up laying out templates for grade level spreads.
1:20-1:30pm – Show my 4 students the process for using Adobe Bridge and how we will identify pictures that are used.
1:30-1:40pm – look through submitted Illustrator brushes, fonts and Photoshop brushes. Decide which ones I will install.
1:40-1:50pm – get the Olelo Noeau book for my page designer to go through and pick out ones we will vote on.
1:50-2:20pm – install brushes and fonts on 3 other open computers, help students with some page designing and picture editing.
2:20-2:40pm – remind students to save documents, turn off computers, bells rings (it is the right one, PAU SCHOOL!!)
Afterschool time….
2:45-3:25pm – My niece comes in for homework session. Ooooh we have math today….Getting out ten frames and counters. We basically do a math exchange as she works on her homework.
What is this??? FIRST STUDENT TO COME IN AFTER SCHOOL TO GET HOMEWORK HELP!! I’M SO EXCITED! ”The homework is pink on the board. Oh you forgot to write it down? Ok well there it is go ahead….” Some questioning with student about showing their work, how do they know that is the answer, etc.
3:25pm – “Bye niece, good luck at soccer practice. Good job getting your homework done!”
3:25-3:35pm – we have a consulting team visiting our school, consultant stops by my classroom to discuss issues we are seeing in some of our elementary classrooms.
3:35pm – yelling at student through window…”K did you find your soccer shoes?” He forgot about them….
3:40pm – “Thank you Ms. Sadie for reminding me about my shoes!”
AAHHHH!! I have #globalmath!!! Hurry up! ”yes, yes, no, no!” I have to go I have a meeting right now!
Safely get home (about 30 secs away), turn on computer, headphones, let dogs out, #globalmath time.
4-5:15pm – discuss homework concept with other math teachers around the world. Great discussions, sharing of pros and cons, goals, it was awesome!
5:15pm – #globalmath is done and now it is time to get some personal stuff done. Finish instrument for hula tomorrow: sanding, sanding, by hand. Check my garden, lettuce starters are coming up *YES*
Hope my lesson plans are ready for tomorrow **crossing fingers**
I will probably dream about it or wake up early and think about the lesson plan for tomorrow. Many things to update and change based on what happened today.
Oh yeah tomorrow is Wednesday my morning is the same routine however the afternoon is my elementary time. Math exchanges here we come!
Qtr 2: Relationships and Multiple Representations
That is our Big Idea for Algebra 1 class this quarter.
In the past couple of weeks we have been focusing our counting circle on time (minutes). Counting up/down by 15 mins and starting whatever I chose (most likely multiples of 60).
After we practiced counting a few times (couple days) I started asking questions to have students convert total minutes into hours and minutes. I then asked the question:
“Do you know what else people say for 2:15pm instead of just ‘two, fifteen’?”
Students: “Quarter after?” (as anticipated)
Me: “Why do they say that? QUARTER AFTER? what does that mean? I thought a quarter was $0.25?”
Students: “Well but its different…” (somewhat confused faces)
Couple of students: ”Well yeah but $0.25 is with money, this is time.”
Me: “Can anyone tell me why its different? What is the base number for time?”
S: “60, that is why it is different because 60 mins is 1 hr”
Me: “What is the base number for $0.25?”
S: **crickets** (many students don’t know our number system is base 10)
S: “$1.00?”
Me: “nope not $1.00, the numbers we use everyday (0, 1, 2, 3…) what are they all based on?”
Students: “100, 5, 2, …” (randomly yelling out answers so of course 10 comes out)
Me: “YES! 10 base 10 that is what our number system is based on”
Now continues a little history lesson (~3 mins long) about sexagesimal (my favorite word to teach teenagers) and decimal number systems. Including a little mention about Babylonians and why I love to teach them this word. We closed up that discussion with 1/4 not necessarily equal to $0.25 but means different things based on the number we are working with. ”A quarter of what?”
Following this “Math Exchange” we start this week’s succession of counting circles (we only spend ~15 mins each period on these):
Monday: counting up by 15 mins, starting at 65 mins (not divisible by 60 but 60+5).
Tuesday: No school.
Wednesday: counting up by $0.25, starting at $1.05 (I hope you see where I am going with this). After our counting circle on this day, I asked them if they think there is a relationship between Monday’s counting circle and today’s counting circle? They were very familiar with counting by $0.25 because we did that for the most part of quarter 1.
So we discussed the “quarter” idea that we have been mulling over since last week. We also discussed how $1.05 is kind of like 1 hr and 5 minutes (65 mins). Before they went to their seats to start our math lesson for the day I told them “You need to think about these relationships because tomorrow I am going to give you an assessment that asks you to describe the relationship between two situations like these. They probably won’t be the same situations but they will be mins and $ so be prepared for tomorrow”
THAT SAID………
Thursday: Assessment (see picture below) I gave them 2 different counting circle scenarios with a number line like we would normally come up with if we did the counting circle. Then I asked them those 3 questions. Notice how the questions successively get harder as you go down. I really love how only Q#1 has one answer but the other 2 questions have multiple answers and ways to prove their answers. I love how most students would be able to answer Q#1 (getting them started) and then move their way down the ladder. I also love how Q#3 basically wraps Q#1 &Q#2 up in a beautifully wrapped math present for them.
I will admit this assessment wasn’t a piece of cake. But we have been working on these connections and counting circle numbers for quite some time now. I discussed it with them yesterday!! I EVEN TOLD THEM WHAT WOULD BE ON THEIR ASSESSMENT!!
Did they struggle with it? ABSOLUTELY!
Would I change anything? NO WAYS!
Do I think these discussions are happening too late in their math career? WHOLEHEARTEDLY YES!!
When do I think they should be discussing these relationships between number systems and fractions?? Somewhere around Grades 3-5 and continue them throughout their years in math class.
Are they happening in my school’s Grade 3-5 classrooms? HECK NO!
Will I stop asking my students to look for and point out these relationships? HECK NO!
Do I love my job? HECK YES!!
This is what I want to be when I grow up
“What do you do out there?”
“I am a teacher, a math teacher.”
**wide eyed shock**
“OH WOW! Really? What grade do you teach?”
“I teach high school mathematics.”
**picking jaw off the floor**
“WOW! Well that is…..good??? How are the kids out there? How do you like it?”
And that is basically the way every conversation starts when people ask me about my job. Did I think I was going to be a teacher when I graduated from high school? HELL NO! To endure what I put my teachers through when I was in school hehehe! There was NO WAY I was going to be a teacher.
Then I got to college and SURPRISE SURPRISE what I thought I wanted to be since the 5th grade was not all it cracked up to be. Most people THINK they know what they want to do but the truth is at that age you HAVE NO IDEA!
Then I chose mathematics teacher because I have always been good in math (I followed my teachers directions well). I wasn’t totally sold on the idea when I started taking my lower division Linear Algebra class at my junior college. I did it, jumped through the hoops and finally got into the college of my DREAMS……….
University of California San Diego
Trimesters went by, upper division math classes were tackled, some I loved (Number Theory), some I hated (Differential Equations) but as all this was happening I was swimming in a sea of math lovers. They loved math for its beauty, its difficulty, its straight up “mathyness” and within this sea of lovers I came to find out that I. LOVE. MATH. Wow! Did I just say that? (my first thought when I first heard myself say that out loud). YES I DID! And dab nabbit am I proud to say that I. LOVE. MATH! I AM A MATH NERD! (hence my blog title).
My senior year in college I got to start taking my TEP classes (teacher education program). If you are not familiar with UCSD’s program check it out it is different than some other programs I have been a part of. We took teacher ed classes, we got to student teach our senior year (this is the prep work to get you ready for their EDS M.Ed./Single Subject (secondary) program). It was pretty cool. I got paired with an interesting mentor teacher, I got to tutor in an AVID classroom, I got to observe a friend of mine who taught at a school 20 mins from the border. All together I was learning about teaching and I was somewhat sure that I wanted to do this (going with the flow).
Graduation time came upon me quick and I was so home sick that I was ready to go home no matter what it took. My teachers at UCSD were waiting for me to apply to their program. They even pulled me aside after the deadline and asked me if I was REALLY sure I didn’t want to be a part of their program. Long story short…I went home (not a good idea based on teacher program options) but I finally got my teaching credential (after much jumping through hoops).
Now that I started my 8th year of teaching I realize this is what I want to be when I grow up….” A MATH TEACHER” There is not another job in this world that I can see myself doing. Every day I wake up and get ready to go to school because I know I have students to “torture” with math. <–that is a joke people! Students are my motivation….NO STUDENTS=NO SADIE
There are not many people that can say they LOVE what they do. That they are excited to get up in the morning to get to work. That they will get paid half time but work full time (yup that is me). Yes I have those bad days (who doesn’t) but all the good days outweigh them. I have students arguing about math for 50 mins in a class period (it happened again today, wish I could have recorded it). I have students JUMPING out of their chairs to answer questions. I have students who aren’t running out the door when the bell rang but instead didn’t even hear the bell ring. I have students that grumble about math so much that they have me in tears over the conversations taking place. There are no words to describe the joy and happiness that I get out of teaching my students (even the naughtiest ones). I don’t know how I got to this point but I do hope that I continue to learn how to keep up the successfulness of students at this level or beyond. I hope to not get worn out by the constant bureaucratic bologna (Oscar Meyer brand) that continues to happen at the state and federal levels. I hope one day that the answer to the last questions in my conversation that I opened with “How are the kids out there? How do you like it?” changes from “I. LOVE. IT! The kids are FANTASTIC its the adults above me (my DOE) that I am not sure about” to “I. LOVE. IT! The entire system is working great…kids are feeling successful and the DOE is making the right decisions to support their successes”.
This is what I want to be when I grow up…..”A MATH TEACHER” and most of you might not be able to relate to that but I just hope that your child’s teacher does because when students feel successful in school they want to come to school, they want to be in the class, they want to learn and be a part of their classroom environment. These are the students I strive to produce and I am proud to say that no matter how my government (state or federal) decides to treat me with salary, teacher accountability ideas or curriculum ideas that non-teachers create I am still sure that being a math teacher is the best job on this planet. I. LOVE. MY. JOB
.
The LONG awaited post…..
I’m finally going to attempt to post about the success of using “magic tricks” to teach (mainly) solving linear equations in one variable.
Disclaimer: most of you might not know that I’m not the best with the English language and I am so much better at describing stuff like this by showing/doing so I know that I won’t be able to get across to you my full intentions but at least you can get a better idea and maybe experience as much success as I have with magic tricks.
To start off, this wasn’t my original idea. I learned of magic tricks after downloading and glancing through Dan Meyer’s Algebra curriculum. I took his idea and modified it to meet my student’s needs. So essentially my students last year, helped me design our “table”. In addition, in this post I am attempting to explain reasoning for important pieces of the lesson that is crucial for student’s success. I apologize for its lengthiness.
We start with me trying to “perform a magic trick” on my students. Some of them realize what I am doing instantly and once I get them hooked with this I have them start creating their own magic tricks (using whiteboards) and perform tricks to their partner. They are just mentally practicing to guess their partner’s number but they are also required to write down some math work to show me the thinking that happened in their head. 
This part might not seem too important but it is VERY important for the success of magic tricks. This mental work will be the safety net for students to fall back on when they start to venture into the linear equation portion. We all know linear equations are scary for ALL students so I use this mental part to be their strength and to give them that feeling of success so they feel confident enough to move towards (in their mind) THE……
DREADED LINEAR EQUATION!
This leads us towards an exit card or homework where students have to perform a trick to someone at home (great parent involvement) and guess their number. Students are also required to have their math work to show their thinking (basically mirroring our classwork).
We now move from only the steps of the magic trick and the math work (sometimes called “In My Head”, “Magician’s Work”) to “How do we write these steps using math symbols?” I’ve also used lies like “I want to do this magic trick to a friend who is in another country, is there some type of universal language I could use to describe the trick to my friend?” Another route: I am very adamant about kids “becoming mathematicians” in my class so I’ve asked them “On our journey to become mathematicians how can we write these magic trick steps? That is where the 3rd part of the table comes in “Math Notation” (we also break down the definition for notation). Most of them want to write the number THEY picked in this first step but then I start asking a bunch of kids their numbers and say “how do I write all of your numbers?” another route: switch gears and ask them to be the magician now and express the number someone picked, which you don’t know, as a number. At this point most students will know variable.
Now we get into translating verbal mathematics into math notation. Great discussions have come from this part of magic tricks: regarding 2*a or a*2, the need for the multiplication symbol, which notation is “right”? Which ones do we use and why? Which ones do you as the teacher prefer? etc. We also discuss differences between (I create a whole day lesson around this one) 2a+3 and 2(a+3) why the need for the parentheses? Does it produce different results? Order or operations, etc. we discuss the last step of the “result is” what does that mean in math? Also what does the equal sign mean? You can guess that the homework/exit card that might come from this is the independent practice of math notation. I like to have them use the SAME magic trick as previous homework (gives a need for homework to be done and connection between homework and classroom).
After the success of these 3 parts we move to the real reason for this magic trick…..THE LINEAR EQUATION!! Now you might not have noticed how we setup the table here but you will now because this 4th part will go right underneath math notation. Reason for this is because there is a connection between the math notation and the linear equation and putting the equation right underneath tries to keep that connection visible for students. 
This last step is where it all comes together but it does not happen all on the same day. It takes time and patience!! It takes a lot of questioning and connection building through these questions for students to really see the connections. We start with a new magic trick and together we go through the math notation and then get started on the “In My Head” part by asking them “What do we start with here?” Most of them say the result number (“4″) but what I am really looking for here is THE WORDS “the result”. Why? because when we move over to using the equation where do we start? ”with the result” and what is the result in math notation? THE LINEAR EQUATION! *zing*
We show all our work for “In My Head” and then get started on to the equation. I hype the scary feeling that some of them (most of them) are feeling when they look at that linear equation. Why? because they will learn that it is not as hard as they think, it relieves their anxiety and embeds that feeling of success of something they thought they couldn’t do. Teacher questioning for equation part:
Soooo, where do we start?
OK….what do we do next?
So is that the same step we did with “In My Head”
Why isn’t the step different?
Do we get different answers between the two methods (in my head & equation)? Why not? How do you know?
Now I must mention here that this part gets a little tricky because teachers differ in words they use and notation they use to display the zero or one that is made. I am very picky about my words and my notation. I want them to see that it is ZERO or ONE and that it doesn’t just “cancel”. Why? because that is the truth of what we are doing….we are using the inverse properties of addition and multiplication and we really need to be specific to show them here. In addition, since we are doing the opposite steps of the original magic tricks steps it is important to discuss the inverse here and to show students this connection. As you can see I have students draw their zero and their one when they solve their equations. Another thing you may notice is how I have students write the equal sign between numbers to make a true statement. I don’t FORCE them to do it but I highly encourage them to do so…it is another one of those meticulous math things I have them do so they can justify each step they are performing. Many students get caught up on this and when I ask them about their “true statements” it instantly helps them see their mistake.
When it comes to homework on this lesson, I normally just have students do ONE step in the equation part of the table but are asked to finish the rest of the table. Reason for this is so that kids don’t get too frustrated and immediately get turned off…..remember I said time and patience is key here. It is important for students to feel successful for this to work. But some students ask if they can do the whole thing and I tell them why not but my min is ONE step.
Basically that is the ending of the setup for the magic tricks. The rest proceeds with practice in class, independent practice, going through notation specifics, discussion of variations we encounter, etc.
Lastly, I have some things that I want to mention that I have experienced in the past few years of using this to teach this concept.
Differentiation: Depending on what students can handle you are able to give students more (or less) magic trick steps to accommodate their capabilities. I have used operation and number dice to have students create magic trick steps in order to challenge their skills. I have also been able to modify tricks so that students who need to work with only whole numbers can and those who are ready for fractions are able to use them.
Other Ideas: I have thought about creating a couple more stations for practice but never got it done this year but would love to start it someday….matching station where they match equation to steps (this is to get students to start using ONLY the equation), cutting up parts of tables and have them match the 4 different parts to each other (i.e. steps, math notation, equation, in my head all need to match), same concept as matching up the parts but put into a game like memory where they flip four cards instead of two.
Equations only: Now many teachers are thinking well how do we get them to just use the equation and not the entire table? I have conversations with kids to try to do this but some of them just NEED that table. If that is the case then I don’t push them to NOT use it…Why? because there is nothing wrong with using the table to help you…yes it takes longer but the standard doesn’t say they have to solve a linear equation in x mins. In my mind, whatever it takes to make students successful is my goal and if this is what they need then so be it. I will continually push students to NOT use the table but again if they need it then they need it….Also, part of the table (steps –> math notation) is a benchmark that I am assessing so I make them use the table on a couple of problems to show me their level of mastery for that benchmark.
More Connections: The connection between the In My Head and the Equation is very crucial and I don’t discuss it much above. It is important for students to use the In My Head portion of the table to CHECK their answers. This is why it is important for them to be able to mentally be able to guess someone’s number because that is the part that they will be using to check their equations. They should see that there is NOT much difference between the two methods. We have discussions about this: What are similarities and differences? Why do I (Ms. Sadie) make them do both? What should they be using it for? How can you use In My Head part to tell if you did the equation part right? 
These are all strategies that you want students to start adopting so they they are not using the teacher as a person to validate their answers. I am a strong supporter of students being able to prove why their answer is right and to be confident in their work. Students love to ask the question: Is this right? My response: I don’t know, is it? How can you prove to anyone that your answer is right? Is there any statement you might have written down that is wrong? I don’t check students work I would rather have them check their own work or find ways to show they are right NO MATTER WHAT! Whenever we do assignments that might ask them to make posters where they could eventually share wrong answers I use these moments as ways to be learning moments for students. You can read more about this strategy in Peg Smith’s book 5 Practices for Orchestrating Productive Mathematics Discussions
I know I missed some of the connections I help students make so I am will probably be updating this post throughout the rest of the year with things that pop into my brain randomly!
Fake Magic Trick Post
I know I know…I SAID I was going to post about the magic tricks…Which I AM blogging about “magic tricks” but it is not the post you have all been waiting for. Sorry! When I blog about the magic tricks I want to have this whole line up that leads to all these things that I am testing right now in my class. With that said I wanted to share about this idea I had for magic tricks….I am really making this up as I go along (aren’t we all) so I decided to trick my students (I do this all the time) into thinking that some “other” student came to me and gave me an equation that “he said he used” for magic tricks. I told them I couldn’t figure it out and I wanted to know if they could help me. They instantly knew that they had to “Find a (number guessed)” but they were not really sure what to do. They squirmed a little bit, ok wait I’m lying, they squirmed A LOT! But I had my bag of questions ready for them….”So what do you notice about this equation? What do you KNOW how to do with magic trick equations?” With those two first questions said they were able to at least set up the subtract 5 to make 0. Then came their next dilemma: where does the -5 go on the “other side” of the equal sign? The next question from my bag “Well what do you think? Which number do you think it belongs with? The 4a or the 10?” They naturally went for the 10 (YES!) and of course I asked them why? ”Because they both are just regular numbers without a variable. Now we are at 3a=4a+5. So here is the tricky part because only NOW at this exact moment in the lesson and class do I realize that their next step HAS NOTHING TO DO WITH MAGIC TRICKS AND OPPOSITE! So I instantly mentally prepare for this one: “So now what do we do?” <–how many times have we heard this one? I play it cool: “I don’t know, what do you think?” Student response: “Well since you put the numbers together then you gotta put the ones with variables together??” Students nod and agree with her…with that figured out I ask them “So what do you want the 4a to BE?” *silence* (this is a hard one) “Well, do you want it there? What do you want it to BE if you don’t want it there?” response: “ZERO!” (YES!!) ”So how do you MAKE IT A ZERO?!” That gets the ball rolling again and they are off…..The rest of the equation is easy peasy for them because they are using their opposite strategy from our magic tricks.
At this point my students look up and ask me “So was his number -5?” My response “I don’t know I didn’t ask him that. I was so intrigued by his equation that I didn’t ask him what his number was.” They slump over…looking defeated….and then a student responds: “NO WAIT! we can check it!” She’s off again….doing some calculations in her notebook….and she’s back…”YES IT IS RIGHT!!” everyone is staring at her like what?? how do you know this? She shares with us that she plugged it in to the equation and it created a true statement (-10=-10).
From her idea I get an idea…”Ok so Katieanna showed us her way of proving it and we can agree that it makes a true statement but even without that confirmation are there any ‘moves’ or steps that we might have performed that were ‘illegal’ or untrue statements?” We go through our statements “is -5=-5?, is -4a=-4a?, is -1=-1?” We figure out (with many questions from my bag) that all our moves are “legal” and we don’t see how anyone can disprove our moves (divide by -1 because we must do the opposite according to our magic tricks, subtract 5 for the same reason, subtract 4a because we WANT a zero). So I ask the last questions before our homework: “So we don’t really KNOW if we did it correctly but without knowing, could anyone PROVE US WRONG?! Could any one accuse us of doing something that we did not justify with reason?” Students: “NO!” My response: “So are we right?” Student: “We have to be! There is no way to show that we are wrong.” They get their homework and everything/one is out the door but not without one student stating: “this is a tricky way to do a magic trick…this student who gave you this is smart and tricky…its good!”
We are back after last night’s homework. And of course they ask if I asked the student…I tell them I did (there really is no student I just made this up…I know I am evil) and yes his number was -5. But I had this idea and I wanted to talk to them about it. I told them how the student got his equation….I told them that the student took a number he guessed and did different magic trick steps to get the same result with two different equations. Then he realized that since both equations were equal to -10 then he thought that he would just let the two equations be equal to each other (3a+5=-10 and 4a+10=-10 are the two original magic tricks). They could understand that and it helped them see how “this student” got his equation. For some reason this kept them engaged because I gave them one more different type of magic trick and we practiced it together. I did pose the question about doing the opposite of add 2 or sub 10. Some students did add 2 some did sub 10 and we compared answers. In the end we realized it doesn’t matter which one we did first because we got the same answer (more than one way?! my fav).
In conclusion, why am I writing about all these questions and responses from students? Because I feel like I just made this up (I did actually) and for some reason they went along with it. It perplexed them, they really wanted to know the answer they really wanted to figure it out. Truth be told I was really worried when I first posed the scenario with the fake student and it went a little rough but it had to go that way for them to squirm. But I also feel like it WORKED!! Now don’t get me wrong we are not done but I just used magic tricks to fake them out with math AGAIN!!
p.s. I will do a final post that pulls together all the ways I used magic tricks to make students successful.
My first date with SBG
I will admit it I was VERY nervous to start SBG. I might have seemed cool, I told myself I got this but it really hit me when I was forced to do mid-quarter reports for my students. Truth be told I am not a crazy grader, I don’t correct papers and put __/__ on the top in some colored ink. I used to check homework and gave points for homework but it was like full credit (for doing it), half credit (for attempting and doing half) or nothing. As for tests, 3/4 way through last year I decided I hated the way my students felt when they got their tests back so instead of correcting them I decided I would just put comments that told them what they needed to work on. I actually didn’t even write comments I wrote questions!! With that said I was still scared to start this new venture.
This week is our mid-quarter marker (hence our reports being due) and my students are almost ready to get assessed on their magic tricks. On Tuesday, the lesson plan was written to have students write down the benchmarks (more specific standard for our state) in their notebooks and to point out where they see us practicing/learning/working with these standards in our magic tricks.
I was very worried when I wrote up this lesson but I told myself it needed to be done. Students need to be aware of their learning, what they are learning, why they are learning it and if they can’t point out where the standard is in their own work how is this SBG thing ever going to work. So I dove in head first….
IT TURNED OUT AMAZING!!
Every student was able to point out that our equation part of our magic trick table was standard 10.1 I had a student ask “what does standard 10.2 mean?” So we broke it down and then I asked them if we are doing that in our magic tricks…. “YEAH, that is when we write the math notation for our steps” Standard 10.3 is harder to show but we talked about how can they justify working backwards and opposite when it comes to magic tricks? ”Because we have to undo what we did in order to find the number” That is a great start and of course that is not the only thing I will be requiring from them for justification but it is a start. Lastly, I passed out my rubric that I had decided on using this year. We talked about how to use it. How they can refer to their rubric to assess themselves. I know it is not the perfect rubric but for my first year starting SBG it was easier to use someone else’s instead of make my own (thank you SBG wiki). I will save that for next year.
Now to add to all this, the homework I gave them after this lesson was more procedural….”Go through your notebook and mark with post it notes or highlighters the problems that show your work towards mastery for the standards discussed in class today. Compare your mastery to the example mastery problem given in class today. Is yours exactly the same? Where would you fall on our rubric? What might you need to work on? Are you ready to challenge yourself with decimals and fractions?” BEST PART OF IT…..Majority of the class came back with highlighted/starred/bookmarked problems in their notebook and some of them even graded themselves based on our rubric!!!!!
OK WAIT! I know you are thinking “um yeah that is what you told them to do?” yeah but i have not collected or graded homework at all this year. I walk around sometimes and look over their homework and see what they did or sometimes I have them put it on their whiteboards and talk with their table partners about their homework. I know this is a honeymoon stage but I really feel like this group of students GET IT! I have put learning in their hands and they have GLADLY accepted it. This is a class of students who ask me, very often, “why do you make us do this?” ”what is this for?” I LOVE THESE QUESTIONS!! WHY you ask?!!! Because every thing they do in my class has a reason, I plan for students to learn from everything they encounter in my class. I also LOVE when students are so interested in their learning that they want to know why. Even better once you explain to them they agree and say “oh yeah that makes sense”. They are sold on it and they take pride in everything they do in class.
The last thing I want to address in all this is the magic trick “mask” that I have put over solving linear equations. I have to say thank you to Dan Meyer for sharing this idea with me. I have taken it and expanded on it and the tricks have evolved to be a great way to teach one of the hardest concepts of algebra that I have experienced in my 8 years of teaching. With the range of students that come into my class these magic tricks allow me to differentiate based on student’s skills. Every student that I have taught this to understands that if you take a number and add 4 to it if you do the opposite you will get the original number you chose. This is the ONLY previous knowledge that these tricks really require of students. The magic trick table that I have created allows students to use the steps to help them solve the linear equation. The “In my head” section allows them to just use numbers and to check their answers for the equation section. The steps and math notation allow them to translate verbal math into math notation AND if they get stuck in the equation section or are not sure they are able to use the steps to move backwards and opposite in order to solve the linear equation.
All in all my first date with SBG has left me with a sweet kiss on the cheek and I’m going home waiting for the next date (assessments/reassessments). I know nothing will be perfect, especially in my first year, but I believe in this method of grading and within the first month of using it, my students and I are starting to form this almost indescribable bond with it.
