View/Download: Conversions You Should Know
Tuesday, October 31, 2017
Rational Number Conversions to Memorize
My students have been working on rational number conversions. They need to know how to do these conversions by hand, but when they're actually using them, it's faster to just have some conversions memorized. I gave my students this chart for their notebooks and had them fill in the equivalent decimals. I told my students that these are conversions worth knowing, and they should work on memorizing them.
View/Download: Conversions You Should Know
View/Download: Conversions You Should Know
Monday, October 30, 2017
Real Number System Auction
Last week, I held a silent auction in class to give my students a chance to review classifying real numbers before their quiz. This activity was based on the Function Auction I first heard about from Sarah Carter. Check out her post for all the details!
Students were split into groups and each group was given the auction handout. First my students spent 10-15 minutes deciding with their groups which statements were true and which were false. I also encouraged them to decide in advance how much they were willing to spend on a single statement. I reminded them to make these decisions quietly so that they didn't tip off any of the groups around them.
When it was time to begin the auction, I reminded students that they only wanted to bid on the true statements. They asked what happens if they win false statements. In the past, I've said that it counts against them, but this year I told them that all it really meant was that they had less money to buy true statements.
The opening bid for each statement was fifty dollars and each subsequent bid had to raise the previous by $50 increments. Each group recorded the statements they won and how much money they spent on the bottom of the auction handout. One thing I have learned after doing several auctions with my classes is that students are much better at keeping track of the statements they win and how much money they have if I give them fake money to play with. If you hold an auction review with your students, I highly recommend giving each group fake money to use! I use money I created with the name of my school and our school mascot on it, but I also created generic money featuring famous mathematicians.
Two of my classes really enjoyed this activity. Although I had to remind them often that it was a silent auction, they quieted down so that we could review each statement after it was won. One of my classes got too excited by this activity. They continued to talk during the bidding and when I tried to review statements after each was auctioned off. In anticipation of this, I had an independent activity copied and ready to go. After some warnings and three strikes, I stopped the activity after auctioning off only two statements. Groups had to return their money and paddle and students worked silently and independently for the rest of class.
Although I was disappointed we didn't get to finish the auction in that one class, I was pretty proud of myself for sticking with the three strikes and packing up the activity when students didn't follow my directions. They couldn't stop talking during the auction, but they knew I was serious when we packed up and they worked silently for the rest of class. Slowly but surely I am making progress with classroom management.
View/Download: Real Numbers Auction Handout and Auction Money
Students were split into groups and each group was given the auction handout. First my students spent 10-15 minutes deciding with their groups which statements were true and which were false. I also encouraged them to decide in advance how much they were willing to spend on a single statement. I reminded them to make these decisions quietly so that they didn't tip off any of the groups around them.
When it was time to begin the auction, I reminded students that they only wanted to bid on the true statements. They asked what happens if they win false statements. In the past, I've said that it counts against them, but this year I told them that all it really meant was that they had less money to buy true statements.
The opening bid for each statement was fifty dollars and each subsequent bid had to raise the previous by $50 increments. Each group recorded the statements they won and how much money they spent on the bottom of the auction handout. One thing I have learned after doing several auctions with my classes is that students are much better at keeping track of the statements they win and how much money they have if I give them fake money to play with. If you hold an auction review with your students, I highly recommend giving each group fake money to use! I use money I created with the name of my school and our school mascot on it, but I also created generic money featuring famous mathematicians.
Two of my classes really enjoyed this activity. Although I had to remind them often that it was a silent auction, they quieted down so that we could review each statement after it was won. One of my classes got too excited by this activity. They continued to talk during the bidding and when I tried to review statements after each was auctioned off. In anticipation of this, I had an independent activity copied and ready to go. After some warnings and three strikes, I stopped the activity after auctioning off only two statements. Groups had to return their money and paddle and students worked silently and independently for the rest of class.
Although I was disappointed we didn't get to finish the auction in that one class, I was pretty proud of myself for sticking with the three strikes and packing up the activity when students didn't follow my directions. They couldn't stop talking during the auction, but they knew I was serious when we packed up and they worked silently for the rest of class. Slowly but surely I am making progress with classroom management.
View/Download: Real Numbers Auction Handout and Auction Money
Sunday, October 29, 2017
Photo of the Week - #SundayFunday
This past week my school participated in Red Ribbon Week. Each student and faculty member was given the opportunity to anonymously write how drugs and alcohol have affected their lives on a paper "brick." Hundreds of these bricks were then displayed down a high-traffic hallway for students and staff to read and know that they are not alone.
Here are some of the ways drugs and alcohol have impacted my school:
- neglect by parents who were drunk or high; feeling like they can't talk to their parents; feeling unsafe around their parents
- moving to a new state because of drug problems; living with a foster family due to drug issues at home
- deaths of family members and friends; family members being revived multiple times from overdoses; being encouraged to commit suicide by a family member who was high
- family members who were or still are in jail; awareness of an increase in drug-related crime; awareness of financial trouble related to drugs
- friendships that have ended because of drug use; friends that skip school or come to school high; encouraging a friend to stop doing drugs
- neighbors who do drugs; restrictions on places to play outside due to high drug activity in some areas
- family members in rehab; family members who are sober now for: 21 days, 1 year, 8 years
Saturday, October 28, 2017
Rational Number Conversion Question Stack
Last week my students practiced rational number conversions. That meant a review of long division. This year only a few of my eighth graders needed a refresher on how to set up a problem for long division. We put this reminder in their notebooks and a few students in each class walked us through the three examples.
Next I had my students do some practice with a Question Stack. I first heard about Question Stacks from Sarah Carter and I love using this practice structure. I had my students create their answer bank with the decimal side up so that when they flipped a card to reveal a fraction, they would have to do the long division to find the equivalent decimal.
If you wanted your students to practice converting decimals to fractions, they should create their answer bank with the fraction side up. This question stack includes both terminating and repeating decimals and some of the repeating decimals only repeat the last digit. That means your students will have to know how to change repeating decimals to fractions and not just the 9s in the denominator trick if you use this with them to practice decimal to fraction conversions.
I have done many a question stack with my classes over the last few years and one of the things that has always bothered me is the number of paper clips that are lost when students spread out the cards for their answer bank. I think I've finally solved that problem! This year I laminated the Question Stack Explanation Mat that Sarah shared and I drew a paper clip on the top-right corner. I explained to students that while they are working, they should clip their paper clip to the mat. Having a designated place to keep the paper clip worked because I didn't lose a single one that day with 85 students using the question stacks!
View/Download: Converting Fractions Notes and Question Stack here
Next I had my students do some practice with a Question Stack. I first heard about Question Stacks from Sarah Carter and I love using this practice structure. I had my students create their answer bank with the decimal side up so that when they flipped a card to reveal a fraction, they would have to do the long division to find the equivalent decimal.
If you wanted your students to practice converting decimals to fractions, they should create their answer bank with the fraction side up. This question stack includes both terminating and repeating decimals and some of the repeating decimals only repeat the last digit. That means your students will have to know how to change repeating decimals to fractions and not just the 9s in the denominator trick if you use this with them to practice decimal to fraction conversions.
 |
| Fraction Side |
 |
| Decimal Side |
I have done many a question stack with my classes over the last few years and one of the things that has always bothered me is the number of paper clips that are lost when students spread out the cards for their answer bank. I think I've finally solved that problem! This year I laminated the Question Stack Explanation Mat that Sarah shared and I drew a paper clip on the top-right corner. I explained to students that while they are working, they should clip their paper clip to the mat. Having a designated place to keep the paper clip worked because I didn't lose a single one that day with 85 students using the question stacks!
View/Download: Converting Fractions Notes and Question Stack here
Saturday, October 21, 2017
My Teaching Story - #SundayFunday
This week's #SundayFunday prompt is to tell your teaching story. I'm in my fourth year of teaching middle school math. I started because I love math. I continue because I couldn't imagine my life without these kids. In just the first month and a half of school this year, twelve of my former students have already managed to sneak back into the middle school to say hi and tell me about high school and their lives. And I am filled with such joy and gratitude that they are a part of my life. But I didn't always think it would be this way.
I never expected that I would be a teacher. I was (and I guess I still am) painfully shy and soft-spoken. I've always been a behind-the-scenes kind of person. But I've also always loved math and sharing my love of math seemed to make interacting with other people easier for me.
In college I studied Math Education and Spanish. I tutored for the Athletic Department and volunteered in local schools. I went through a five-year program to get my Master's in Secondary Mathematics Education. I spent my fifth year completing a year-long student teaching internship at an inner-city middle school - a completely different setting from the small town school where I grew up. At the end of the internship, I still wasn't sure if I wanted to teach. I knew that I liked working with kids, but I didn't know if being a regular classroom teacher was the best fit for me.
I didn't send out any applications until July of that summer. The only classroom teacher position I applied for was in the same district where I did my student teaching. I applied for paraprofessional positions in other districts and an AmeriCorps position at an inner-city high school in a neighboring state.
I interviewed for the AmeriCorps position first. The position was basically for an in-school math tutor at the high school level. I would be working with small groups (2 or 3 students each period) to do re-teaching and pre-teaching. More than 50% of the students at the school were Hispanic, which meant I would also get to use my Spanish. I was very excited about the position - a feeling I had not had when I thought about having my own classroom. Being a certified teacher in another state, I was more than qualified for the position and at the end of my interview I was offered the job on the spot. I had until the end of the week to decide.
Three days later, I had my only interview for a regular classroom teacher position. It was at a different middle school in the district where I student taught. I sent in my application so late that they actually had to pull the interview team together again a week after they had held all other interviews for that position. An hour after my interview, the principal called to offer me the job of the math teacher on a 7th/8th grade split team. By then, I had one day to make my decision.
I went back and forth so many times. I wanted to take the AmeriCorps position because it was high school. It was small groups. I would get to use my Spanish. It felt more comfortable to me. On the other hand, was I going to be able to figure out if I really wanted to teach by taking a job as a math tutor? The regular classroom teacher job was going to challenge me more. I would be working at the middle school with the greatest percentage of students eligible for free/reduced lunch in the entire state. I would have classes of 25 or 30 students. I would be working with a team, but I'd be on my own in the classroom.
Both jobs were one-year positions. Ultimately, I was going to be in the same position the next summer with regard to finding a job, and I decided that taking the regular classroom teaching job was going to be the best move for deciding if teaching was really for me. I knew I would do my best for those students for that one year, and after that, I had an out if I determined that regular classroom teaching wasn't for me.
That first year was tough. We were a brand new team at our school, a team formed to alleviate large class sizes in the seventh and eighth grades. Our team consisted of two first-year teachers and two veteran teachers who hadn't been part of a team in a long time. On top of that, one of the sixth grade teachers told me that my incoming seventh graders had been her worst year of teaching in 19 years! Man, do I have stories about that first year!
Despite all the discipline issues and stories of horrible home lives, I have really great memories of that first year as well.
And that was just the first year! I knew I wanted to teach. The connections I made with my students were so important and inspiring. It must have been meant to be, because my one-year position was extended to a permanent position at the end of that year. The following year, we followed the bubble of seventh graders up to eighth grade and looped with many of our students - an experience I absolutely loved and for which I am so grateful. I also taught a Functional Math class that year which provided a whole new set of challenges. Since then I have switched teams, but still teach eighth grade and that Functional Math class. I spend my summers teaching Algebra 1, Geometry, and Algebra 2 to satisfy that itch to teach at the high school level. Maybe one day I'll move up, but for now I'm really loving my eighth graders!
I never expected that I would be a teacher. I was (and I guess I still am) painfully shy and soft-spoken. I've always been a behind-the-scenes kind of person. But I've also always loved math and sharing my love of math seemed to make interacting with other people easier for me.
In college I studied Math Education and Spanish. I tutored for the Athletic Department and volunteered in local schools. I went through a five-year program to get my Master's in Secondary Mathematics Education. I spent my fifth year completing a year-long student teaching internship at an inner-city middle school - a completely different setting from the small town school where I grew up. At the end of the internship, I still wasn't sure if I wanted to teach. I knew that I liked working with kids, but I didn't know if being a regular classroom teacher was the best fit for me.
I didn't send out any applications until July of that summer. The only classroom teacher position I applied for was in the same district where I did my student teaching. I applied for paraprofessional positions in other districts and an AmeriCorps position at an inner-city high school in a neighboring state.
I interviewed for the AmeriCorps position first. The position was basically for an in-school math tutor at the high school level. I would be working with small groups (2 or 3 students each period) to do re-teaching and pre-teaching. More than 50% of the students at the school were Hispanic, which meant I would also get to use my Spanish. I was very excited about the position - a feeling I had not had when I thought about having my own classroom. Being a certified teacher in another state, I was more than qualified for the position and at the end of my interview I was offered the job on the spot. I had until the end of the week to decide.
Three days later, I had my only interview for a regular classroom teacher position. It was at a different middle school in the district where I student taught. I sent in my application so late that they actually had to pull the interview team together again a week after they had held all other interviews for that position. An hour after my interview, the principal called to offer me the job of the math teacher on a 7th/8th grade split team. By then, I had one day to make my decision.
I went back and forth so many times. I wanted to take the AmeriCorps position because it was high school. It was small groups. I would get to use my Spanish. It felt more comfortable to me. On the other hand, was I going to be able to figure out if I really wanted to teach by taking a job as a math tutor? The regular classroom teacher job was going to challenge me more. I would be working at the middle school with the greatest percentage of students eligible for free/reduced lunch in the entire state. I would have classes of 25 or 30 students. I would be working with a team, but I'd be on my own in the classroom.
Both jobs were one-year positions. Ultimately, I was going to be in the same position the next summer with regard to finding a job, and I decided that taking the regular classroom teaching job was going to be the best move for deciding if teaching was really for me. I knew I would do my best for those students for that one year, and after that, I had an out if I determined that regular classroom teaching wasn't for me.
That first year was tough. We were a brand new team at our school, a team formed to alleviate large class sizes in the seventh and eighth grades. Our team consisted of two first-year teachers and two veteran teachers who hadn't been part of a team in a long time. On top of that, one of the sixth grade teachers told me that my incoming seventh graders had been her worst year of teaching in 19 years! Man, do I have stories about that first year!
Like the time I had to call the office to say that there was a student sitting on the roof of the school outside my window.
Or the time one of my students told me that he wears multiple pairs of socks as a cushion because his father makes him stand in the corner for hours at home.
Or the first time there was a fight in my room.
And the time I stepped in between two boys about to get into a fight, and then realized that they were both much bigger than me and I'd better hope they just take a step back and not start swinging.
Despite all the discipline issues and stories of horrible home lives, I have really great memories of that first year as well.
Like the time we were practicing finding measures of central tendency and one of my students refused to do any work at all until I told him to look up the prices of five of his favorite pairs of Jordan's and use that data for his calculations. He was done in less than ten minutes!
Or the time when the principal told me that one of our most difficult students said that I was his favorite teacher. When he was in school, he usually spent his lunch in my room and would come talk to me during my prep period when he was having a problem.
Or the times when another challenging student who rarely lasted a full period in my class due to such serious behavior issues would come to my room after school to talk with me and get his homework done.
Or all the times when my student and I shared a laugh about how we were wearing the same sweater on the same day again!
Or the laugh I got when a parent emailed me, saying, "Apparently my son thinks he's a duck!"
And that was just the first year! I knew I wanted to teach. The connections I made with my students were so important and inspiring. It must have been meant to be, because my one-year position was extended to a permanent position at the end of that year. The following year, we followed the bubble of seventh graders up to eighth grade and looped with many of our students - an experience I absolutely loved and for which I am so grateful. I also taught a Functional Math class that year which provided a whole new set of challenges. Since then I have switched teams, but still teach eighth grade and that Functional Math class. I spend my summers teaching Algebra 1, Geometry, and Algebra 2 to satisfy that itch to teach at the high school level. Maybe one day I'll move up, but for now I'm really loving my eighth graders!
Sunday, October 15, 2017
Math Games - #SundayFunday
This week's #SundayFunday topic is Math Games. Here's a list of some of the games I like to use in class.
Review Games: can be used for any topic
Review Games: can be used for any topic
- Trashketball - compete as teams
- MATHO - compete as individuals
- Snowball Fight - students write their own review problem, crumple the paper, and have a "snowball fight" before picking up a "snowball" and answering that review problem
- Kahoot - online review game; search for a topic or write your own quiz
- Slope Dude Says (from Sarah at mathequalslove) - practice classifying the slope of a line
- Dance, Dance, Transversal (from Jessica at Algebrainiac) - practice angle pair relationships when parallel lines are cut by a transversal
- Zero Game (from Denise at Let's Play Math) - practice adding integers and finding absolute value
- 24 Game - practice the order of operations
- Eleven (I've seen it so many places that I forget where I first read about this one) - the class must count to 11 (or a number that you choose) while following these rules:
- no talking/hand signals/communicating a strategy to classmates
- students must count in order
- no student can say more than one number
- if more than one student says a number at the same time, the class must start again from the beginning
- Petals Around the Rose - you roll 5 dice and tell students the score; they must figure out the rule
- Tangrams
- Blokus
- Make a Million (from Julie at fractionfanatic)
- Set
- Rubik's Cubes
Saturday, October 14, 2017
A Call for Advice
For several years, my last period class has been my worst behaved. I've always boiled it down to, "it's the last class of the day and they're tired." Also, "it's my last class of the day and I'm tired." I know that my last period class gets away with murder compared to my earlier classes. I feel like I say the same things all day to get students back on track that by the last class, I already feel defeated and like my students are not going to listen to me. I forget that those are not the same students I saw earlier in the day who I've already told to change their behavior. I know that by the end of the day, I am tired and sometimes frustrated just like my students. Instead of getting stricter, I get more lenient when I'm frustrated.
I recognize all these things in myself, but I don't know how to change. My classroom management has improved since I started teaching, but I've still got so far to go.
I recently covered a class period for two teachers on a day that we didn't have enough subs. The first was a sixth grade computer class. That class ran itself. I was so impressed. Every student came in and sat in their assigned seat. Every student wrote the homework in their agenda book before I even prompted them to do so, and one student had the job of stamping everyone's agenda book when the homework was written down. After their typing practice, we read an article together and the students were to answer the questions independently; and there wasn't a single student who tried to get away with working with someone during that time.
The second class I covered was for the social studies teacher on my team. This experience puzzled me the most. I was covering a class full of my own eighth graders. They all sat in their assigned seats without complaint. They did all the work expected of them during class and were SILENT during the guided reading activity that they were completing. I had to prompt some students to keep working and I did take a phone away that period, but for the most part, the kids were fantastic. At the end of that period, many of the students in that class followed me down to my room for math. And it was like they were completely different people. They had a warm-up to do that was projected on the board the same as every other day, and yet the students came in and wandered around the room talking to their friends, ignoring the work that they'd been expected to do every day at the start of class since the first day of school.
I need better procedures. Or maybe just a better way to enforce them. The number one piece of advice I got from my students at the end of last year was to "stop being so nice, especially to the bad kids." I'm not trying to be nice. I'm not trying to get kids to like me. I am trying to be patient and understanding, but at times I take it too far and at the expense of other students' learning. And that's not fair to anyone.
I'm looking for advice - mostly proactive, but also some reactive. What can I do to make my class run more smoothly and to better convey my expectations to my students so that I don't end up with so many discipline problems? But also, how do I regain control of my class when behaviors have gotten out of hand? Even something as minor as how to get the attention of the class when they have gotten too loud during an activity. I'm not supposed to yell and I'm not supposed to flick the lights; ideally we'd never get to that point, but what can I do when they do get too loud, and I just need to get their attention to remind them of the noise level they should be working at?
I know what works for one teacher may not always work for another, but any and all advice would be appreciated! I'm open to trying just about anything, because I know that I haven't yet found what works for me.
I recognize all these things in myself, but I don't know how to change. My classroom management has improved since I started teaching, but I've still got so far to go.
I recently covered a class period for two teachers on a day that we didn't have enough subs. The first was a sixth grade computer class. That class ran itself. I was so impressed. Every student came in and sat in their assigned seat. Every student wrote the homework in their agenda book before I even prompted them to do so, and one student had the job of stamping everyone's agenda book when the homework was written down. After their typing practice, we read an article together and the students were to answer the questions independently; and there wasn't a single student who tried to get away with working with someone during that time.
The second class I covered was for the social studies teacher on my team. This experience puzzled me the most. I was covering a class full of my own eighth graders. They all sat in their assigned seats without complaint. They did all the work expected of them during class and were SILENT during the guided reading activity that they were completing. I had to prompt some students to keep working and I did take a phone away that period, but for the most part, the kids were fantastic. At the end of that period, many of the students in that class followed me down to my room for math. And it was like they were completely different people. They had a warm-up to do that was projected on the board the same as every other day, and yet the students came in and wandered around the room talking to their friends, ignoring the work that they'd been expected to do every day at the start of class since the first day of school.
I need better procedures. Or maybe just a better way to enforce them. The number one piece of advice I got from my students at the end of last year was to "stop being so nice, especially to the bad kids." I'm not trying to be nice. I'm not trying to get kids to like me. I am trying to be patient and understanding, but at times I take it too far and at the expense of other students' learning. And that's not fair to anyone.
I'm looking for advice - mostly proactive, but also some reactive. What can I do to make my class run more smoothly and to better convey my expectations to my students so that I don't end up with so many discipline problems? But also, how do I regain control of my class when behaviors have gotten out of hand? Even something as minor as how to get the attention of the class when they have gotten too loud during an activity. I'm not supposed to yell and I'm not supposed to flick the lights; ideally we'd never get to that point, but what can I do when they do get too loud, and I just need to get their attention to remind them of the noise level they should be working at?
I know what works for one teacher may not always work for another, but any and all advice would be appreciated! I'm open to trying just about anything, because I know that I haven't yet found what works for me.
Sunday, October 8, 2017
Integer Operations in Eighth Grade
It can be so difficult to teach kids what they think they already know. Every year, integer operations seems to be one of those things. Many of my students come to eighth grade knowing, "Same signs add and keep, different signs subtract, take the sign of the bigger number, and then you'll be exact" to the tune of "Row, Row, Row Your Boat." Unfortunately, that doesn't always translate to accuracy when working with integers. They know that "two negatives make a positive," but overgeneralize that rule to include integer addition. I've struggled with helping my students build a conceptual understanding of how to work with integers when all they want to do is try to remember the rules they were taught.
Zero Game
To see what my students remembered about adding integers, I started with some problems where my students had to determine what value must be added to make zero. I wrote problems on the board like the following:
Positive/Negative Chips for Adding/Subtracting
The next day we began modeling how to add integers using positive and negative chips. We modeled problems adding all positive integers first and my students did a Think-Pair-Share about their observations when adding all positive numbers. Next we modeled adding all negative integers. After a few examples, we did another Think-Pair-Share about what they noticed when adding all negative numbers.
Finally, we modeled adding numbers with different signs. We moved all our zero pairs to the Sea of Zeros on this Integer Work Mat from Sarah Carter at Math Equals Love and students made observations about what happens when you add positive and negative numbers together.
Next we modeled subtracting integers using counters, adding in zero pairs as needed. I tasked my students with using pictures to model what we had done in class for homework.
Adding/Subtracting on a Number Line
I love using a number line to think about adding and subtracting integers. Adding means you move toward that end of the number line and subtracting means you move away from that end of the number line. I like that this gets students thinking about why adding the opposite works for subtraction.
We did a few examples together and then my students completed this packet on their own. The problems are paired so that students see an addition expression and its equivalent subtraction expression, and how the same movement is shown on the number line. I wrote this packet up a few years ago and I'm not completely satisfied with it; however I haven't yet figured out how to change it. All suggestions welcome!
When we reviewed this packet as a class, we spent a fair amount of time rewriting more examples of subtracting integers as adding the opposite.
Multiplying Integers Desmos Investigation
Next we explored multiplying integers. This was my first time using Desmos with my students and I blogged more about that experience here. We did Andrew Stadel's Multiplying Integers investigation. Students modeled multiplication on a number line, looking at groups of positive or negative numbers and the opposite of groups of positive or negative numbers. I've always been a fan of saying, "the opposite of" instead of "negative" and that tied in well with this lesson.
Integer Operation Rules Foldable
After four days of what I hoped was a more meaningful look at working with integers, we were finally ready to summarize the rules for integer operations. We put this foldable in their notes and did a few order of operations examples. This foldable is available to download below.
One Incorrect Order of Operations Practice
The next day my students worked on this "One Incorrect" worksheet from Greta at Count It All Joy. What I liked most about this worksheet was that my students knew that if they didn't get an answer of -13, they had most likely made a mistake somewhere since only one of the eight problems had an answer other than -13. This was our first #VNPS day, and I let my students choose to either pair up or work individually around the room.
One extension to this activity was shared with me on Twitter: have students write their own set of "One Incorrect" problems. I'm excited to try that the next time I use this practice structure.
Two Truths and a Lie
Sarah Carter shared this template for a Two Truths and a Lie activity. For homework, I had my students write their own statements about integer operations. Some students chose to write about the rules, while others wrote numerical examples of using integers. On the day of the quiz, we spent about half of the class reviewing the student-generated Two Truths and a Lie homework. This gave us a chance to clear up some misconceptions as some papers had two or even three lies.
Integer Flashcards
Finally, I gave my students about ten minutes to quiz themselves using these integer operations flashcards from Sarah Carter before the actual quiz.
View/Download: Integer Operations Files
Zero Game
To see what my students remembered about adding integers, I started with some problems where my students had to determine what value must be added to make zero. I wrote problems on the board like the following:
-4 + ____ = 0
7 + ____ = 0
12 + (-9) + ____ = 0
-14 + 8 + ____ = 0
15 + (-20) + ____ = 0
We then played the Zero Game from Denise at Let's Play Math via Julie at I Speak Math. The game is played with a deck of cards where red cards represent negative numbers and black cards represent positive numbers. Cards are dealt to each player and the object of the game is to get a sum as close to zero as possible. Read either of the posts above for more complete directions. My students then completed this check for homework.
Positive/Negative Chips for Adding/Subtracting
The next day we began modeling how to add integers using positive and negative chips. We modeled problems adding all positive integers first and my students did a Think-Pair-Share about their observations when adding all positive numbers. Next we modeled adding all negative integers. After a few examples, we did another Think-Pair-Share about what they noticed when adding all negative numbers.
Finally, we modeled adding numbers with different signs. We moved all our zero pairs to the Sea of Zeros on this Integer Work Mat from Sarah Carter at Math Equals Love and students made observations about what happens when you add positive and negative numbers together.
Next we modeled subtracting integers using counters, adding in zero pairs as needed. I tasked my students with using pictures to model what we had done in class for homework.
Adding/Subtracting on a Number Line
I love using a number line to think about adding and subtracting integers. Adding means you move toward that end of the number line and subtracting means you move away from that end of the number line. I like that this gets students thinking about why adding the opposite works for subtraction.
We did a few examples together and then my students completed this packet on their own. The problems are paired so that students see an addition expression and its equivalent subtraction expression, and how the same movement is shown on the number line. I wrote this packet up a few years ago and I'm not completely satisfied with it; however I haven't yet figured out how to change it. All suggestions welcome!
Multiplying Integers Desmos Investigation
Next we explored multiplying integers. This was my first time using Desmos with my students and I blogged more about that experience here. We did Andrew Stadel's Multiplying Integers investigation. Students modeled multiplication on a number line, looking at groups of positive or negative numbers and the opposite of groups of positive or negative numbers. I've always been a fan of saying, "the opposite of" instead of "negative" and that tied in well with this lesson.
Integer Operation Rules Foldable
After four days of what I hoped was a more meaningful look at working with integers, we were finally ready to summarize the rules for integer operations. We put this foldable in their notes and did a few order of operations examples. This foldable is available to download below.
One Incorrect Order of Operations Practice
The next day my students worked on this "One Incorrect" worksheet from Greta at Count It All Joy. What I liked most about this worksheet was that my students knew that if they didn't get an answer of -13, they had most likely made a mistake somewhere since only one of the eight problems had an answer other than -13. This was our first #VNPS day, and I let my students choose to either pair up or work individually around the room.
One extension to this activity was shared with me on Twitter: have students write their own set of "One Incorrect" problems. I'm excited to try that the next time I use this practice structure.
Two Truths and a Lie
Sarah Carter shared this template for a Two Truths and a Lie activity. For homework, I had my students write their own statements about integer operations. Some students chose to write about the rules, while others wrote numerical examples of using integers. On the day of the quiz, we spent about half of the class reviewing the student-generated Two Truths and a Lie homework. This gave us a chance to clear up some misconceptions as some papers had two or even three lies.
Integer Flashcards
Finally, I gave my students about ten minutes to quiz themselves using these integer operations flashcards from Sarah Carter before the actual quiz.
View/Download: Integer Operations Files
Tuesday, October 3, 2017
Reflection by a First-Time Desmos User
Although my eighth graders have worked with integers before and should know the operation rules, experience has taught me that they don't. They remember some of the rules, but mix up and over-generalize others. I actually had to walk away from two students who were CONVINCED that when you add two negatives, you get a positive answer. I tried using examples like when you owe money or homework assignments, using positive and negative integer chips, and using a number line before I told them we'd come back to it the next day. It can be difficult to reteach students what they think they already know, so I was excited to have my students explore pictorial representations of multiplying integers before we reviewed the rule.
We did Andrew Stadel's Multiplying Integers Desmos activity. It was my first time ever using Desmos in class, and when I took to Twitter for advice, the most common thing I was told was to "just go for it!" So I ran my own class code ahead of time and switched between devices to log in as both a student and teacher to see the different interfaces, and when it came time for class, we just went for it!
Things That I Loved This Time
We did Andrew Stadel's Multiplying Integers Desmos activity. It was my first time ever using Desmos in class, and when I took to Twitter for advice, the most common thing I was told was to "just go for it!" So I ran my own class code ahead of time and switched between devices to log in as both a student and teacher to see the different interfaces, and when it came time for class, we just went for it!
 |
| It's surprisingly difficult to get a good photo of a projected image. |
- My students were leading themselves through the investigation rather than me guiding them.
- After students submit a written response, they can see the responses of a few other classmates.
- I can "anonymize" the names, which served two great purposes in my mind. First, when other students' responses appeared, they didn't know who said what, which in middle school can lead to a lot of unkind judgement. Second, I had students who finished early look up their mathematician to find out who they were and when they lived.
- Figure out how to use Pacing to keep the class on track. We didn't really have any whole class discussions on screens where I wanted to. I ended up projecting the teacher dashboard the next day to review responses as a class.
- Give more time for the activity (although I guess this may depend on whatever the activity is next time). I thought it was more important for my students to finish up the exploration and keep working right up until the bell, which meant that I was the one to put all the chromebooks away after class.
Monday, October 2, 2017
Better Than a Vent Session
You know those days when you can't help but focus on one frustrating or idiotic thing that happened with your students? And sometimes you just want someone to vent to so that you can get it out of your system and move on?
I had one of those days yesterday. Without going into too much detail and getting myself worked up about it again, I'll just say that I was grading quizzes and became overwhelmingly frustrated at the few kids who had so obviously cheated. I'm usually a glass-half-full, look-on-the-bright-side kind of person, but I couldn't seem to let this one go. I figured it was fair - healthy, even - to give myself five minutes to vent before getting on with my day.
Anyways, my go-to person to hear my thoughts on this, agree with me, and then let me move on, was not answering her phone. So instead I called a friend who either didn't understand or completely ignored the fact that I didn't want advice or a solution; I just wanted to rant and move forward.
Instead, he challenged me.
He reminded me that they are just kids. He reminded me of the unfair home lives of so many of my students and all the things they are thinking about besides their math quiz. He reminded me that many of them don't trust adults because they have been let down by parents and families and teachers that were supposed to take care of them and have their best interests in mind.
He challenged me to really figure out why I was so upset. Was it because of the poor grades? Because of the apathy toward learning?
One of the hardest things for me to hear was when he told me that I am certain to have students who don't trust me yet. It hurts to think that's true. But I also felt like it put me in my place a little bit. Just like I am still getting to know these kids, they are getting to know me.
He really put things in perspective for me. What I expected to be a five-minute vent session about quizzes and cheating turned into a fifty-minute conversation about kids. And isn't that how it should be? It should always come back to the kids. That's why we do this.
It wasn't what I expected when I called this person, and it wasn't what I thought I wanted to hear, but our conversation was exactly what I needed in that moment.
I had one of those days yesterday. Without going into too much detail and getting myself worked up about it again, I'll just say that I was grading quizzes and became overwhelmingly frustrated at the few kids who had so obviously cheated. I'm usually a glass-half-full, look-on-the-bright-side kind of person, but I couldn't seem to let this one go. I figured it was fair - healthy, even - to give myself five minutes to vent before getting on with my day.
Anyways, my go-to person to hear my thoughts on this, agree with me, and then let me move on, was not answering her phone. So instead I called a friend who either didn't understand or completely ignored the fact that I didn't want advice or a solution; I just wanted to rant and move forward.
Instead, he challenged me.
He reminded me that they are just kids. He reminded me of the unfair home lives of so many of my students and all the things they are thinking about besides their math quiz. He reminded me that many of them don't trust adults because they have been let down by parents and families and teachers that were supposed to take care of them and have their best interests in mind.
He challenged me to really figure out why I was so upset. Was it because of the poor grades? Because of the apathy toward learning?
One of the hardest things for me to hear was when he told me that I am certain to have students who don't trust me yet. It hurts to think that's true. But I also felt like it put me in my place a little bit. Just like I am still getting to know these kids, they are getting to know me.
He really put things in perspective for me. What I expected to be a five-minute vent session about quizzes and cheating turned into a fifty-minute conversation about kids. And isn't that how it should be? It should always come back to the kids. That's why we do this.
It wasn't what I expected when I called this person, and it wasn't what I thought I wanted to hear, but our conversation was exactly what I needed in that moment.
Sunday, October 1, 2017
Classroom Tour - #SundayFunday
It's not everything, of course, but here are some highlights from my 2017-2018 classroom for #SundayFunday. I had just finished painting when I took some of these pictures, so some posters are stuck in random spots on the wall or removed entirely.
Growth Mindset
I have these posters from Sarah Carter. Last year one of my students asked if we could include "him" on the poster that says, "I'll never be as smart as her," so we added that. I make my students repeat the growth mindset phrase if they ever say one of the fixed mindset phrases. When they whine, "Do I have to?" I threaten them with detention. They know I'm kidding, but I've since caught them warning each other to "say the colored one or else you'll get detention."
This year I added the Mistakes Grow Your Brain curtain. It hangs in the back of my room next to the Retake Request Forms. The plan is that when students receive back a quiz, they will add a post-it note to the Brain curtain with an error they made. I want to make time for students to reflect and respond to a post-it one of their classmates put up to really enforce the idea that we can all learn and grow from everyone in class.
Student Supplies
I recently blogged about this here, but I originally saw the idea from Sara Buck. I have 30 pouches filled with supplies that students may need on a regular basis. This includes a pencil, tape, glue stick, scissors, highlighter, dry erase marker with pom-pom eraser, regular pencil eraser, and a straight edge. Each pouch is numbered and the wall hooks are numbered to make it easy to hang back up at the end of class. I originally let students pick which pouch they wanted (some hang much higher than others, so I didn't want to assign alphabetically), and that has since become their assigned pouch. I have a list taped to the back of my clipboard so that I know who uses what pouch number in each class, and which pouches are not being used.
Play Table
Another new addition this year is the Play Table, an idea from Sara VanDerWerf. I LOVE HAVING A PLAY TABLE IN MY CLASSROOM!! If students get to class before the bell, I find them at the Play Table. When they finish their work in class, I find them at the Play Table. When they're waiting for a friend after school, I find them at the Play Table.
Kids have taken pictures of their creations and wanted to show me. They've spelled out messages and told me to make sure I read them before someone creates something new. So far, I've noticed significantly fewer phones coming out because kids have something interesting to do when they're done their work.
Library
This year I added a few more books to my classroom library. I had a few chapter books before, but it's not often that a student wants to borrow a book that would take some time to read. Usually, they're looking for something to read during the 20-minute enrichment period before lunch. The number of eighth graders who have asked me if I have picture books was always a little bit concerning to me, but I've since changed my mind about that. My library now includes nearly a dozen children's books about mathematicians and scientists. They are perfect for our enrichment period, because students can finish a book in one sitting. So far, I've found that kids are more likely to read a book during that time if they know they're going to finish it.
Posters
Many of my posters come from Sarah Carter. This year, I tried to be mindful of how much I put on my walls. When I thought about the posters I hung up, I realized that my students really do reference these during the year. Some of the most-referenced posters from Sarah are: Perfect Squares and Cubes (thanks as well to her husband, Shaun, for making the Geogebra files available to download to create posters that go higher than x=10), GEMDAS (plus a version from Shaun), and Vertical and Horizontal Number Lines. Some posters that sparked the most questions and curiosity are: Pythagorean Triples and Prime Numbers.
Some other posters I created include: The Mathematics Behind a Successful Student, Were You Up To PAR In Class Today?, Minds Are Like Parachutes, Play Quotes similar to the ones Sara VanDerWerf included in her post, Vertical and Horizontal Labels, and our Eighth Grade Team Expectations and SAHD Letters (Seat, Agenda, Homework, Do Now).
VNPS
I'm trying to incorporate more Vertical Non-Permanent Surfaces into my classroom this year. I moved my agenda board to a wall without a whiteboard. That meant I needed to create a make-shift erasable surface, and I was quite proud of my white-paper-in-sheet-protectors agenda "board" until it fell off the wall.
I finally got around to painting that area of the wall with whiteboard paint after school last Friday. It needs to cure for three days, but I'm excited to start using it again. This has freed up a real whiteboard on the side of the room for students to use (see photo above of whiteboard near student supply pouches). I also have a coordinate plane that I created on sheets of laminated paper on a wall in my room.
Additionally, I used the extra whiteboard paint to cover the doors of my wall locker and a table top. I don't know that I really intend that students write on these surfaces, but at the very least, I think the white paint looks nice. The wall locker is home to my Prime Numbers and Pythagorean Triples posters (at least, it will be again once the paint dries!).
Desk Arrangement
I'm excited about the way I arranged desks this year. Student desks are in groups of four, but in an L-shape, rather than a typical rectangular group. The L's on each side of the room face each other, with pairs of desks in the middle, which creates a U(ish)-shape. I like that students are in groups, but that they also fit into a whole class structure and fewer than half have their backs to anyone else.
I feel as though my classroom is always a work in progress and I think that's a good thing. It may not be the most important thing about teaching, but our classroom environment does affect students and I think it's important that we show flexibility and growth in that aspect as well.
Growth Mindset
I have these posters from Sarah Carter. Last year one of my students asked if we could include "him" on the poster that says, "I'll never be as smart as her," so we added that. I make my students repeat the growth mindset phrase if they ever say one of the fixed mindset phrases. When they whine, "Do I have to?" I threaten them with detention. They know I'm kidding, but I've since caught them warning each other to "say the colored one or else you'll get detention."
This year I added the Mistakes Grow Your Brain curtain. It hangs in the back of my room next to the Retake Request Forms. The plan is that when students receive back a quiz, they will add a post-it note to the Brain curtain with an error they made. I want to make time for students to reflect and respond to a post-it one of their classmates put up to really enforce the idea that we can all learn and grow from everyone in class.
Student Supplies
I recently blogged about this here, but I originally saw the idea from Sara Buck. I have 30 pouches filled with supplies that students may need on a regular basis. This includes a pencil, tape, glue stick, scissors, highlighter, dry erase marker with pom-pom eraser, regular pencil eraser, and a straight edge. Each pouch is numbered and the wall hooks are numbered to make it easy to hang back up at the end of class. I originally let students pick which pouch they wanted (some hang much higher than others, so I didn't want to assign alphabetically), and that has since become their assigned pouch. I have a list taped to the back of my clipboard so that I know who uses what pouch number in each class, and which pouches are not being used.
Additional supplies are found on a back shelf next to the cart holding papers for each class.
Play Table
Another new addition this year is the Play Table, an idea from Sara VanDerWerf. I LOVE HAVING A PLAY TABLE IN MY CLASSROOM!! If students get to class before the bell, I find them at the Play Table. When they finish their work in class, I find them at the Play Table. When they're waiting for a friend after school, I find them at the Play Table.
Kids have taken pictures of their creations and wanted to show me. They've spelled out messages and told me to make sure I read them before someone creates something new. So far, I've noticed significantly fewer phones coming out because kids have something interesting to do when they're done their work.
Library
This year I added a few more books to my classroom library. I had a few chapter books before, but it's not often that a student wants to borrow a book that would take some time to read. Usually, they're looking for something to read during the 20-minute enrichment period before lunch. The number of eighth graders who have asked me if I have picture books was always a little bit concerning to me, but I've since changed my mind about that. My library now includes nearly a dozen children's books about mathematicians and scientists. They are perfect for our enrichment period, because students can finish a book in one sitting. So far, I've found that kids are more likely to read a book during that time if they know they're going to finish it.
Posters
Many of my posters come from Sarah Carter. This year, I tried to be mindful of how much I put on my walls. When I thought about the posters I hung up, I realized that my students really do reference these during the year. Some of the most-referenced posters from Sarah are: Perfect Squares and Cubes (thanks as well to her husband, Shaun, for making the Geogebra files available to download to create posters that go higher than x=10), GEMDAS (plus a version from Shaun), and Vertical and Horizontal Number Lines. Some posters that sparked the most questions and curiosity are: Pythagorean Triples and Prime Numbers.
VNPS
I'm trying to incorporate more Vertical Non-Permanent Surfaces into my classroom this year. I moved my agenda board to a wall without a whiteboard. That meant I needed to create a make-shift erasable surface, and I was quite proud of my white-paper-in-sheet-protectors agenda "board" until it fell off the wall.
 |
| The old make-shift agenda board. |
I finally got around to painting that area of the wall with whiteboard paint after school last Friday. It needs to cure for three days, but I'm excited to start using it again. This has freed up a real whiteboard on the side of the room for students to use (see photo above of whiteboard near student supply pouches). I also have a coordinate plane that I created on sheets of laminated paper on a wall in my room.
Additionally, I used the extra whiteboard paint to cover the doors of my wall locker and a table top. I don't know that I really intend that students write on these surfaces, but at the very least, I think the white paint looks nice. The wall locker is home to my Prime Numbers and Pythagorean Triples posters (at least, it will be again once the paint dries!).
Desk Arrangement
I'm excited about the way I arranged desks this year. Student desks are in groups of four, but in an L-shape, rather than a typical rectangular group. The L's on each side of the room face each other, with pairs of desks in the middle, which creates a U(ish)-shape. I like that students are in groups, but that they also fit into a whole class structure and fewer than half have their backs to anyone else.
I feel as though my classroom is always a work in progress and I think that's a good thing. It may not be the most important thing about teaching, but our classroom environment does affect students and I think it's important that we show flexibility and growth in that aspect as well.
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