I was just thinking about some great movies that I like to show in my classroom. My favorites are:

Stand and Deliver

October Sky

The Freedom Writers

Pursuit of Happyness

The Blind Side

Notice a theme? They're all based on a true story.

What are your favorites?

## Monday, December 31, 2012

## Wednesday, December 26, 2012

## Saturday, December 22, 2012

## Thursday, December 20, 2012

### Shifts in Classroom Practice - Stepping Out Of My Comfort Zone

In my department, we have PLCs (Professional Learning Community Meetings) lead my an outside group called PARLO. We meet once a month and sometimes our coach assigns us something for the next meeting.

This past month we have been given the assignment of attempting to make a shift in our classroom: "From mathematical authority coming from the teacher or textbook toward mathematical authority coming from sound student reasoning."

I don't know about you, but I'm hurting here. If you read my last post about the real world sucking, this is right up there with that. I'm one of those people, who needs (I mean NEEDS) validation. So, in my classroom there are my students who want validation and have always received validation, and there's me who wants to give validation.

So, I need help with my assignment here. I can't wrap my head around this and could use some advice.

2) Students can look over each other's work and offer comments and advice.

Perhaps this assignment was made for me. We don't grow unless we step out of our comfort zone.

That's all I have. Any thoughts? What does this shift mean to you? Do you do this in your classroom? How did the students respond?

This past month we have been given the assignment of attempting to make a shift in our classroom: "From mathematical authority coming from the teacher or textbook toward mathematical authority coming from sound student reasoning."

I don't know about you, but I'm hurting here. If you read my last post about the real world sucking, this is right up there with that. I'm one of those people, who needs (I mean NEEDS) validation. So, in my classroom there are my students who want validation and have always received validation, and there's me who wants to give validation.

So, I need help with my assignment here. I can't wrap my head around this and could use some advice.

#### My ideas so far:

1) Students should try to make an educated guess right after reading a problem. This way when they finish, they can validate their answer on their own.2) Students can look over each other's work and offer comments and advice.

Perhaps this assignment was made for me. We don't grow unless we step out of our comfort zone.

That's all I have. Any thoughts? What does this shift mean to you? Do you do this in your classroom? How did the students respond?

## Friday, December 14, 2012

### The Real World Sucks

Yesterday I finally did my own 3-act math task with the students. We have been studying linear programming and this past summer, my son and I created a little movie to help with this topic.

Here is act 1:

And act 2:

Here is act 1:

And act 2:

## Tuesday, December 11, 2012

### No Seating Chart Update

I haven't updated you on my lack of a seating chart since the beginning of the school year, and I think it's about time. You can read the original post here.

I don't have a seating chart for any of my classes. Nope. I have class lists for substitutes, but that's it. What's the point anyway? The students think that it's funny to switch seats on a substitute teacher, so then a seating chart is useless.

I started the year with seating activities where the students would have to work together in order to find their seats. Things like sitting alphabetically or by height. It was fun, the students were engaged and working together. Everyday before they came into the classroom, I would write the directions on the board.

My intentions were to do this the first week, so that I would remember the students faces rather than their desks. One day everything changed, a student walked into the room, immediately looked at the board and asked, "What are we doing today?" I remember wishing that the students would do this with my bell ringers. All they would do was sit in their seat and ignore the warm-up problems. So, I put the two ideas together and no one has ignored the problems to date.

As the students walk into the room, I hand them an index card with a problem on it. The students need to answer the problem in order to find their seat. I didn't think I would last this long with this idea, but a few things are keeping me going. The obvious, the students are finally doing the bell ringers without begin begged. Also, once I make a set of cards, I can use them over and over because the chances of a students getting the same problem twice are rather small.

The types of cards that I have are mostly multiple choice in order to prepare for the state tests. I write on the board that students are to sit in row 1 if their answer is A, 2 if B, etc. I sometimes instruct the students to get into groups so that each group has an A, B, C, and D.

I also have cards where the answers are an integer from 1 - 24 and then the student sits in the corresponding seat. OR if I have 24 students, I will tell them they need to sit in groups of four so that the sum of their answer is 50.

There are my logic puzzle cards. I try to find logic puzzles with 3-4 clues. Each clue is written on an index card and students need to create a group making sure they have all the clues within their group.

A few things I like about this idea are the flexibility and control that the students still have with this arrangement. If a students gets an answer of A and has to sit in the first row, he can sit in the front or the back of the row. And with groups, the students still have a little control over which group they form. I may say they all have to have different clues, but they have some say in it too.

I still have some students who complain, but I'd have that regardless. At least I have cooperation. I will work on the complaining next.

I don't have a seating chart for any of my classes. Nope. I have class lists for substitutes, but that's it. What's the point anyway? The students think that it's funny to switch seats on a substitute teacher, so then a seating chart is useless.

I started the year with seating activities where the students would have to work together in order to find their seats. Things like sitting alphabetically or by height. It was fun, the students were engaged and working together. Everyday before they came into the classroom, I would write the directions on the board.

My intentions were to do this the first week, so that I would remember the students faces rather than their desks. One day everything changed, a student walked into the room, immediately looked at the board and asked, "What are we doing today?" I remember wishing that the students would do this with my bell ringers. All they would do was sit in their seat and ignore the warm-up problems. So, I put the two ideas together and no one has ignored the problems to date.

As the students walk into the room, I hand them an index card with a problem on it. The students need to answer the problem in order to find their seat. I didn't think I would last this long with this idea, but a few things are keeping me going. The obvious, the students are finally doing the bell ringers without begin begged. Also, once I make a set of cards, I can use them over and over because the chances of a students getting the same problem twice are rather small.

The types of cards that I have are mostly multiple choice in order to prepare for the state tests. I write on the board that students are to sit in row 1 if their answer is A, 2 if B, etc. I sometimes instruct the students to get into groups so that each group has an A, B, C, and D.

I also have cards where the answers are an integer from 1 - 24 and then the student sits in the corresponding seat. OR if I have 24 students, I will tell them they need to sit in groups of four so that the sum of their answer is 50.

There are my logic puzzle cards. I try to find logic puzzles with 3-4 clues. Each clue is written on an index card and students need to create a group making sure they have all the clues within their group.

A few things I like about this idea are the flexibility and control that the students still have with this arrangement. If a students gets an answer of A and has to sit in the first row, he can sit in the front or the back of the row. And with groups, the students still have a little control over which group they form. I may say they all have to have different clues, but they have some say in it too.

I still have some students who complain, but I'd have that regardless. At least I have cooperation. I will work on the complaining next.

## Wednesday, December 5, 2012

### Sabotage

I have this game in mind, but there's something missing.

I call the game SABOTAGE. The game helps students to practice solving linear equations.

Download the game and instructions here.

Here is a quick rundown of the game:

Each team is given an equation that is written on the board, 4 operation cards, and 5 number cards.

On each turn the team uses one of their operation cards along with a number card to get one of the equations closer to being solved.

When an equation is finally solved the scoring goes as follows. If x is negative, the team that "owns" that equation will get that many points. If x is positive, then the points (value of x) is split between the team that solved the equation and the team that owns the equation.

For example, suppose that team A solves team D's equation and x = -6. That means that team D loses 6 points. And suppose that team B solves team C's equation and x = 3. That means that both team B and C will receive 1.5 points.

Initially, I told the students that they could work to solve equations or sabotage equations. What happened was a bunch of sabotaging and only one equation was solved the entire period. So, I changed the rule so that a team must "help" and equation if possible. If they cannot "help" an equation, then they may sabotage. What do you think? Or should I change it so that if they cannot "help" an equation, then they may forfeit their turn to trade in cards?

I'll try play testing again and see what happens.

Your thoughts and suggestions are MORE than welcome.

I call the game SABOTAGE. The game helps students to practice solving linear equations.

Download the game and instructions here.

Here is a quick rundown of the game:

Each team is given an equation that is written on the board, 4 operation cards, and 5 number cards.

On each turn the team uses one of their operation cards along with a number card to get one of the equations closer to being solved.

When an equation is finally solved the scoring goes as follows. If x is negative, the team that "owns" that equation will get that many points. If x is positive, then the points (value of x) is split between the team that solved the equation and the team that owns the equation.

For example, suppose that team A solves team D's equation and x = -6. That means that team D loses 6 points. And suppose that team B solves team C's equation and x = 3. That means that both team B and C will receive 1.5 points.

Initially, I told the students that they could work to solve equations or sabotage equations. What happened was a bunch of sabotaging and only one equation was solved the entire period. So, I changed the rule so that a team must "help" and equation if possible. If they cannot "help" an equation, then they may sabotage. What do you think? Or should I change it so that if they cannot "help" an equation, then they may forfeit their turn to trade in cards?

I'll try play testing again and see what happens.

Your thoughts and suggestions are MORE than welcome.

## Monday, December 3, 2012

### Slope Christmas Tree

This is my classroom Christmas tree, totally decorated by the students. My Algebra 1B students decorated it using slope. I created two types of ornaments where students use slope to create the them. The paper chains are created by solving linear equations.

The tree is a Walmart special $20!!

## Saturday, December 1, 2012

### Assumptions and Graphing Lines

In our state (Pennsylvania), we are gearing up for the first round of state tests which are next week. Yikes! Right now our state is switching to only an Algebra 1 exam for high school math. Between classes a few of my colleagues and I were discussing the tests and how we were going to spend our class time the last two days before the exams begin. We had mentioned skipping a review in classes like Calculus and Pre-Calculus. After all, it's only an Algebra 1 exam. But, we backtracked quickly. It has happened in the past where a Calculus student failed the exam! Algebra 1!

I teach Pre-Calculus and here are some assumptions that I had that were wrong!

1) Students can order numbers when they are given in different forms, like this.

I teach Pre-Calculus and here are some assumptions that I had that were wrong!

1) Students can order numbers when they are given in different forms, like this.

What I found was that students didn't realize they needed to convert all the numbers to the same form (decimal) in order to compare. They thought they should know just by looking at them, and of course felt stupid when they couldn't. Some students didn't know how to convert the numbers to decimals even with a calculator.

2) If students can factor, then they can simplify a rational expression like this.

In problems like this, students are looking to cancel individual terms rather than factor then cancel.

3) In my Algebra 1 class: If I teach students how to find slope given two ordered pairs, then they can find slope given a graph.

Again, I discovered that students aren't comfortable with converting forms without instruction. To take a graph and, on their own, find ordered pairs, then find the slope, was something they didn't think was "allowed".

This year I decided to teach graphing lines to my students a little differently based on these incorrect assumptions that I've been making year after year.

First, I can't teach topics in isolation, I need to help students make connections between the methods of graphing. I always assumed that students were making these connections because they were obvious to me, so they should be obvious to the students.

I started teaching graphing of linear equations with tables. To me, that seemed to be the easiest entry point into this topic to help the students feel comfortable with graphing. Once students were proficient with this I asked them to start picking out patterns in their tables. I encouraged them to keep their tables organized. We discussed the change in y (delta y). We discussed the change in x (delta x). We looked for these numbers in the equation. Low and behold, the students noticed that delta y over delta x was the fraction next to x in the equation (after we solved for y).

Next, we went over how to graph by finding the intercepts. We noticed that this was very similar to graphing with tables, except that we filled in two zeros in the table immediately (one for x and one for y). Discussions on why to use zero were completed.

Now we're back to slope. We know that we can find slope from a table and from an equation when it's in slope-intercept form. What about other forms? What if I give you two ordered pairs? One student suggests putting those numbers in a table **Angels start singing**. We discovered the slope formula. Next I give them a graph and ask how we can find the slope. Another student says, find two ordered pairs and use the slope formula **An entire choir of angels sing**. We discover rise over run.

Helping students make connections is time consuming, but oh so worth it.

## Friday, November 16, 2012

### Make Learning Visible - Part 2

I know it's hard to imagine, but I have students who will try to do nothing on a Flashback Day (a Flashback Day is a day where I allow the students to practice and reassess on previous outcomes). Last year I had this student who made it well known that he was intent on earning exactly a 70% in my class (the lowest possible passing grade in our district). That pissed me off. However, instead of directing my anger at him, I thought maybe the other students in the class could get on his case.

I told the class that once every single student is proficient in every single outcome for the first quarter, we would have a party. I didn't care how long it took for this to happen. If it happened in May, then our party would be in May.

The next time we had a Flashback Day, nothing changed. That student still did nothing and his classmates didn't care. I reminded them of my promise, and still nothing.

That afternoon after school I created the following chart. It is numbered 1 - 60. Why 60? That's as many numbers that would fit on my cabinet door. I made a magnet for each class and placed their magnet next to number of outcomes they still needed to be proficient in as a whole. For example: If there are 20 students in a class and a total of 7 outcomes in the first quarter, that's a class total of 140 outcomes to pass.

When the students came in the next day, they knew I meant business. Not in a "She's mad, let's do some work" kind of way, but in a "Oh, she's really going to let us have a party." kind of way. The next time we had a Flashback Day, the students did not let me down. Peer pressure is such a great thing.

I'm happy to report that last year, all of my classes earned at least one party. The class with that lazy student, earned two parties. That class was totally proficient in every outcome for the first two quarters. The lazy student earned a 78% for the year, not what he's capable of, but better than 70%.

Lesson learned: You can say it all you want, in any tone of voice you want. But until you make it visible, the students won't believe you. If you're committed, they're committed.

## Tuesday, November 13, 2012

### Graphing a Story

As an introduction to graphing I completed an activity with my students that I call

Students are put into pairs and asked to pick one paper from each bag and tape them to their graph.

Next, I give each pair of students a die. The first roll of the die will complete the ordered pair (0, ). The next roll will complete the ordered pair (1, ), etc. The students plot the points and connect those points. I tell students that the scale of each axis does not have to go by 1.

Finally, students create a story that would "fit" the graph. My hopes for this activity were to determine if students could read a graph. As you can see from one story below the students believed that each point was a sum of the previous points, something I need to fix. Below are a few samples of students' work, worts and all. Here is a link to the file if you are interested.

*Graphing a Story*. I have two paper bags. In one paper bags are units of time that are used to label the horizontal axis. In the other paper bag are different things to represent the vertical axis.Students are put into pairs and asked to pick one paper from each bag and tape them to their graph.

Next, I give each pair of students a die. The first roll of the die will complete the ordered pair (0, ). The next roll will complete the ordered pair (1, ), etc. The students plot the points and connect those points. I tell students that the scale of each axis does not have to go by 1.

Finally, students create a story that would "fit" the graph. My hopes for this activity were to determine if students could read a graph. As you can see from one story below the students believed that each point was a sum of the previous points, something I need to fix. Below are a few samples of students' work, worts and all. Here is a link to the file if you are interested.

## Monday, November 12, 2012

### Survival of the Fittest

Imagine being able to send your students away to a remote island and be the stars of a new reality show called

I put students into teams of 3 (or 4) and "flew" them to an island to play a game where the last team alive is the winner.

Each day I taught a short lesson and allowed the students to work in their teams to complete practice problems. Each member of the team had to make sure everyone knew the lesson because their survival depended on it. I circulated around the room answering questions only if no one in the group was able to come up with the answer.

Once all the groups were satisfied that each member knew the lesson, I gave an exit ticket that the students had to complete individually. Each exit ticket had three questions of different difficulty level. The problems that they students got correct dictated what supplies they received in order to survive on the island.

Once the teams started collecting supplies, the fun began. I would randomly pick one of the "Survival Scenario" cards and read it to the students. A card might read that the game-creators are playing with the temperatures at night and a team would need a sleeping bag in order to stay healthy. Each team needed to hand in a sleeping bag or lose a health level.

Alliances and rivalries started to form and an atmosphere of 'survival' was in the air. The entire unit took 7 days to complete start to test. In those seven days, I heard students talking at their lockers about their health levels and making deals for trading supplies that were needed. My other classes noticed the posting of the teams' health levels and want to know when I'll be sending them to a remote island. Oh if only!! But more importantly than students talking about the game, was the conversations that happened during the practice problems. Students didn't want to let their teammates down. They asked each other questions, offered advice, and I noticed a sense of urgency in learning the material.

This is the most fun I've had teaching in a long time and I cannot wait to send my students to the island again!

*Survival of the Fittest.*That's exactly what I did and the students LOVED it.I put students into teams of 3 (or 4) and "flew" them to an island to play a game where the last team alive is the winner.

Each day I taught a short lesson and allowed the students to work in their teams to complete practice problems. Each member of the team had to make sure everyone knew the lesson because their survival depended on it. I circulated around the room answering questions only if no one in the group was able to come up with the answer.

Once all the groups were satisfied that each member knew the lesson, I gave an exit ticket that the students had to complete individually. Each exit ticket had three questions of different difficulty level. The problems that they students got correct dictated what supplies they received in order to survive on the island.

Once the teams started collecting supplies, the fun began. I would randomly pick one of the "Survival Scenario" cards and read it to the students. A card might read that the game-creators are playing with the temperatures at night and a team would need a sleeping bag in order to stay healthy. Each team needed to hand in a sleeping bag or lose a health level.

Alliances and rivalries started to form and an atmosphere of 'survival' was in the air. The entire unit took 7 days to complete start to test. In those seven days, I heard students talking at their lockers about their health levels and making deals for trading supplies that were needed. My other classes noticed the posting of the teams' health levels and want to know when I'll be sending them to a remote island. Oh if only!! But more importantly than students talking about the game, was the conversations that happened during the practice problems. Students didn't want to let their teammates down. They asked each other questions, offered advice, and I noticed a sense of urgency in learning the material.

This is the most fun I've had teaching in a long time and I cannot wait to send my students to the island again!

## Thursday, November 8, 2012

### Heheheheheheee wipe oooout!

We have been whiteboarding in my Algebra 1B classroom.

I've been wanting to try whiteboarding for a while, but when I saw the prices of a large whiteboard, I almost passed out. I would need about 8 boards, and at about $20 a pop, that $160 I didn't have. My school issues us $115 per year for classroom supplies. So, I turned to donorschoose.org and the students' parents and complete strangers came through for us.

We finished a lesson on graphing lines when given an equation in slope-intercept form. The next day I put them in groups of 2 or 3 and gave them the following 3 equations and asked them to graph them.

They still asked me questions, but I wasn't giving in (showing off). I assured them that although I wasn't being very helpful at the moment, that I would indeed answer all their questions if they were unable to come to a conclusion. That seemed to appease them.

I've been wanting to try whiteboarding for a while, but when I saw the prices of a large whiteboard, I almost passed out. I would need about 8 boards, and at about $20 a pop, that $160 I didn't have. My school issues us $115 per year for classroom supplies. So, I turned to donorschoose.org and the students' parents and complete strangers came through for us.

We finished a lesson on graphing lines when given an equation in slope-intercept form. The next day I put them in groups of 2 or 3 and gave them the following 3 equations and asked them to graph them.

I loved the conversations that I heard throughout the lesson. "In number 1 after we multiply by one-half, what do we add?" "What do we pick for x in number 3?" "How do we find y in number 2?"

They still asked me questions, but I wasn't giving in (showing off). I assured them that although I wasn't being very helpful at the moment, that I would indeed answer all their questions if they were unable to come to a conclusion. That seemed to appease them.

I found the one above interesting. This group believes that the equations x = 3 will produce a point rather than a line.

The photo above needs to be rotated if you want to see the top graph correctly.

In the group that made the above graphs, one student seemed to really know what he was doing but seemed "too nice" to correct the other students. Eventually he won, and was able to convince them to graph x=3 correctly!!

Would I do whiteboarding again? In a heartbeat. The students loved it, I loved it, the conversations were amazing, and no paper waste. Win, win, win!!!

Suggestion: Have different color markers. One color for each graph, or students, or just to make it more interesting. I went out and purchased my own, but of course forgot them at home. *Sigh*

## Monday, November 5, 2012

### Completing the Square Story - by a Student

For your reading pleasure: A story created by a student of mine about Completing the Square...

(I know there's an error in her math (+2 instead of -2) but the story is great!)

## Thursday, November 1, 2012

### Solving Systems of Equations: Foldable Booklets

*Update* (10/18/16) - Some people are having difficulties with the download below. Try this one instead.

What you see here are little booklets with tabs. One each for solving systems by graphing, substitution, and elimination.

No staples or glue required to make these. See how....

1) Download and print the documents back-to-back

2) Cut the foldable:

2) Cut along dotted lines:

3) With Example 1 facing you roll the left side of the paper.

4) Insert the rolled paper into the other paper with Example 2 face up.

5) Fold into a booklet.

All three booklets will fit on a 8.5 by 11 sheet of paper.

## Friday, October 26, 2012

### I'm a Believer: #75FACTS Comments-Only Marking

I've been doing comments-only grading since the beginning of this school year and it has completely changed my students' attitudes.

When I first heard about comments only grading I was in a Standards-Based-Assessment Conference/Workshop and we were learning about traffic light grading as well. This year I had an epiphany and realized that grading was grading no matter how you tried to sugar-coat it. Numbers, letters, colors, they're all the same. A grade is a grade is a grade. No more. I only grade tests.

When I first heard about comments only grading I was in a Standards-Based-Assessment Conference/Workshop and we were learning about traffic light grading as well. This year I had an epiphany and realized that grading was grading no matter how you tried to sugar-coat it. Numbers, letters, colors, they're all the same. A grade is a grade is a grade. No more. I only grade tests.

#### Standards for Mathematics Practices:

I feel this FACT is closely ties to 1. Make sense of problems and persevere in solving them. I've seen this in action. Students are willing to try problems more than once, knowing that they are not being judged on their work. I've written about this earlier. You can see that post here.

#### Planning to Use and Implement FACTS:

One thing that I keep in mind when creating assignments is how I'm going to give the comments with my limited time. If the assignment is something that would be difficult to comment on, I would only assign a few problems because I would have to do the commenting by myself. However, if the students could comment on each other's work, then I could assign a few more problems.

In the post that is linked above, I allow space for students to make corrections and time to make those corrections.

#### Small Steps:

Were your students engaged?

*Yes, I found that the students are more cooperative this year with the comments only grading. Students want to know "why" so they are ready for the test, rather than copying assignments to just complete them.**Note - I don't penalize students for not completing an assignment, their penalty is less knowledge.*

Were you confident and excited about using the FACT?

*When I first decided to do this I was scared that students would rebel, I have an entire post about that as well. In general, the students like not having the comments. They tell me the class is more relaxed and less stressful than the classes that grade every single paper.*
How did use of the FACT affect the student-to-student or student-teacher dynamic?

*I believe that the students are less competitive with each other because there is no grade to compare. They are more willing to help each other and ask for help.*
Was the information gained from the FACT useful to you?

*Yes, looking at students' work with commenting on my mind is so much more useful that having grading on my mind. I know how to better serve my students.*
Would you have gotten the same information without using the FACT?

*No, when everything is graded, some students shut down. Once they've lost their confidence, you've lost them. With comments only grading, I continuously get information from students because they are not afraid to give it.*
What added value did the FACT bring to teaching and learning?

*I believe my students are more focused on what they know rather than how much they do. They are more concerned with knowledge and what have more value than that in a classroom?*
Did using the FACT cause you to do something differently or think differently about teaching and learning?

*Yes! I use to think that grades were the great motivator, but they're not. Students don't like to feel stupid. You want to motivate your students, find a way to show them how smart they are.*
Would you use this FACT again?

*Everyday!*
Are there modifications you could make to this FACT to improve its usefulness?

*I like the book's modifications for codes. I think I may incorporate that.*#### Using Data from the FACTS:

When I create problems for commenting, I try to make ones that will tell me if the students learned the major points of the lesson. In most cases that is only 2 - 3 problems. I leave time in my lesson plans for the students to make corrections based on my comments. The students who know what they are doing are asked to help struggling students. If I find that I was making a certain comment often, I would address the entire class and reteach that part of the lesson.

## Saturday, October 20, 2012

### Create the Problem #75FACTS

This past week I attempted "Create the Problem" (#11 page 80) as my #75FACT. In this FACT students are given a solution and they need to create a problem that would be solved using that solution.

Here is my solution for Create the Problem:

Here is my solution for Create the Problem:

#### Eight Standards for Mathematical Practice:

Math Standard #1: Make sense of problems and persevere in solving them. In this problem student need to create a problem that would be modeled with quadratics and would be solved by finding the vertex.

#### FACTS and Teaching Goals:

We just finished our lesson on applications of quadratics and I wanted to see if students understood when to find the vertex of a parabola and what that meant in different situations.

After teaching the lesson, I gave each student a copy of the solution and asked them to create the problem as an exit ticket. That afternoon I made copies of their problems and cut off their names. The next day I put students into pairs and had them write comments on the papers. We used the document camera to look at a few together and discuss our thoughts. That night I went through each problem and picked the ones that matched the work and made copies for each student to have.

Correct student problems:

After teaching the lesson, I gave each student a copy of the solution and asked them to create the problem as an exit ticket. That afternoon I made copies of their problems and cut off their names. The next day I put students into pairs and had them write comments on the papers. We used the document camera to look at a few together and discuss our thoughts. That night I went through each problem and picked the ones that matched the work and made copies for each student to have.

Correct student problems:

#### Small Steps:

Were your students engaged?

*Yes, many of the students were able to use their creative side when creating the problem.*

Were you confident and excited about using the FACT?

*Yes, I love a great lesson plan.*

How did use of the FACT affect the student-to-student or student-teacher dynamic?

*Student-to-student: I don't think students are use to commenting on each other's work. Also, not often do they have the opportunity to see what other students are doing in class unless the student himself decides to share his work. Student-teacher: The students are still in the zone where they need to ask me for assurance for everything they do. In this FACT, I tried to sit out as much as possible. Because of this I played a roll of more of a questioner rather than an evaluator.*

Was the information gained from the FACT useful to you?

*Yes. What I was looking for in this problem was "how high" and "when does it reach this maximum height". However, most of what I received was "when will it hit the ground?". Because I used this FACT I knew I had to review what information was given from a parabola's vertex.*

Would you have gotten the same information without using the FACT?

*Yes, I could have created problems that asked students to find maximum height, and when will it hit the ground to see if they would solve them correctly. But this FACT allowed students a nice entry point even if they didn't know how to find the vertex. This FACT allowed students to express that they knew what it meant.*

What added value did the FACT bring to teaching and learning?

*Because the students had more ownership in the problem they were more willing to figure out why it was correct or incorrect. Also, because the students' work was anonymous, they were safe in creating their problem.*

Did using the FACT cause you to do something differently or think differently about teaching and learning?

*Yes, I didn't realize that so many students didn't know what information was given from the vertex? I mean, I taught it, that means they learned it, right? <-- Sarcasm.*

Would you use this FACT again?

*Yes, I felt that it helped the students learn about the meaning of the vertex.*

Are there modifications you could make to this FACT to improve its usefulness?

*First, I would give the students examples of the correct work before they were to comment on other students problems. So, I would go in this order: 1) create the problem 2) discuss some problems together with the document camera 3) show examples of good problems 4) comment on other's*

*problems.*

*Second, I used a lot of paper to do this FACT. I completed this with two classes, a total of 43 students. Then I made two copies of each students work. Finally, I copied examples of correct problems. That's a total of 172 sheets of paper! Maybe to cut back on waste, I will scan their problems and put them in a google doc (can you do that). Other students can make comments on the google doc.*

## Monday, October 15, 2012

### Make Learning Visible

What you see here is a "Proficien-tree". When a student has proved himself to be proficient in a particular outcome I write his name on a leaf and the student puts it on their class tree. There is no competition, just a nice metaphor of how our knowledge grows and blooms.

I have 5 trees around my room (one for each of my classes). My students love them. After every test or flashback day, they go to their folders looking to see if they earned a leaf.

How to make your own proficien-tree:

Get one planter for each class.

Get rocks to hold your tree in place. Luckily I live near a river and collect free river rocks.

Cut some branches off a tree.

Make leaves.

I started by buying the scrapbook punches you see above ($16 each). However, the leaf punch has seen better days and I've only owned if for a year. I used the flower one in spring, so the students could put pink flowers on their tree. Then I found foam leaves from Oriental Trading. I can use most of those, but some are just too small to write on. $8 for 500 leaves....OK. It saves me time from punching out the leaves, it saves tape too since the leaves are stickers.

What I like most about the trees are the teachers who walk past my room, stop, and come back to ask about the trees. After a while, some will come back just to see how the trees are growing.

I also like to remind the students of how far they have come. They'll be struggling with something and get down on themselves. I say, "Look at your tree! Look how far you've come. We can get through this."

## Friday, October 12, 2012

### #75FACTS Week 4 - Human Scatter Plots Poster

This week I tried the Human Scatter Graph again, but using the modification. Read about that here.

Math FACT # 22 page 104.

Before teaching a lesson on patterns I gave the students a multiple choice problem and asked them to answer the question and rate their confidence on a scale of 1 - 10 (1 being a guess and 10 betting your life on the answer). I marked those results in pink.

I taught the lesson.

After the lesson I gave the students the exact same problem with the same conditions and marked those results in blue.

By the way, the correct answer was A.

Here is the question:

The first five terms of a sequence are given below:

10, 17, 24, 31, 38, ...

Determine which of the following formulas gives the nth term of this sequence.

A) 3 + 7n

B) 16 - 6n

C) 4 + 6n

D) 17 - 7n

#### Reflection Questions (Page 37):

Were your students engaged?

*Mostly, it was a multiple choice question. How engaged would you be?*

Were you confident and excited about using the FACT?

*Confident? Yes. Excited? No, not excited. I was looking forward to it, but it's not the excitement that's created when conducting and up-and-out-of-your-seat activity.*

How did use of the FACT affect the student-to-student or student-teacher dynamic?

*I don't think any of that was affected. I ask questions all the time in class. This was nothing new.*

Was the information gained from the FACT useful to you?

*Yes, I was able to see that the lesson was effective and that the students' confidence grew.*

Would you have gotten the same information without using the fact?

*I may have done a pre- and post- question to see what knowledge was gained, but I wouldn't have known how their confidence grew.*

What added value did the FACT bring to teaching and learning?

*I'm a big believer in student confidence leading to student learning. Because not only did the students state that their confidence grew, but they could see it in a visual representation. Maybe a few more students will start to think that they can learn math. For this lesson on patterns the students were especially whiny. Many times they complained that they didn't understand and that it was "stupid". But at the end of class when I showed them the chart, you could see their faces brighten up.*

Did using the FACT cause you to do something differently or think differently about teaching and learning?

*I like that this FACT asked students their confidence. I never thought about making that visible before.*

Would you use this FACT again?

*Yes, especially for those difficult lessons where students usually struggle. I like that even though the students feel like they know nothing, you can show them that they indeed do know something.*

Are there modifications you could make to this FACT to improve its usefulness?

*I wouldn't use a scale of 1-10 again. I would use this in conjunction with the FACT: Fist to 5 (#16 page 92), where the horizontal axis would be from 0 - 5 using the Fist to 5 descriptions.*## Sunday, October 7, 2012

### #75 FACTS - Week 3 - Chapter 3

Okay. I tried. I've been "attending" the twitter chat on #75 Math Facts, but I can't do it anymore. Not that I don't want to, but staying up that late has been messing with my whole week.

So, in an effort to stay in the loop, I will blog about my thoughts rather than participate in the chat :(

I tried out Human Scatter Plot (p 104 # 22) this week and thought I would speak about how it relates to chapter 3.

The Human Scatter Plot is where students are given a multiple choice question and asked to stand somewhere in the room according to their answer and confidence in their answer. I placed tape on my classroom floor to create 4 lines. One each for the answer choices A, B, C, D. If the students were confident in their answer, they were to stand on the line but closer to the door, if they were less confident, they were to stand farther away from the door. I had 10 questions ready for the lesson but that was more than enough.

Chapter Three: Considerations for Selecting, Implementing and Using Data From FACTs.

####

So, in an effort to stay in the loop, I will blog about my thoughts rather than participate in the chat :(

I tried out Human Scatter Plot (p 104 # 22) this week and thought I would speak about how it relates to chapter 3.

The Human Scatter Plot is where students are given a multiple choice question and asked to stand somewhere in the room according to their answer and confidence in their answer. I placed tape on my classroom floor to create 4 lines. One each for the answer choices A, B, C, D. If the students were confident in their answer, they were to stand on the line but closer to the door, if they were less confident, they were to stand farther away from the door. I had 10 questions ready for the lesson but that was more than enough.

Chapter Three: Considerations for Selecting, Implementing and Using Data From FACTs.

#### Eight Standards for Mathematical Practices

I felt this FACT was closely tied to Mathematical Practice #3: Construct viable arguments and critique the reasoning on of others. Once the students were standing where they wanted to be I asked them to explain to the rest of the class their reasoning. It was very interesting to see what was going on in their minds. I liked when the class was split between two answers and students were jumping out of their skin to explain why their reasoning was correct.

#### Facts and Teaching Goals

My goal for this lesson was for students to get better at solving literal equations. This was the second day of the lesson and I felt they were mostly okay to do some problems on their own. I wasn't sure if their mistakes would be in the order of operations (SADMEP or SMEG if you will), or somewhere else in their reasoning. I selected this FACT so I could watch as they walked to their answer. Who got there first? Did anyone follow someone else? How confident is each student in their answer? Did students get more confident as the class progressed? What incorrect answers are they selecting?

I also learned who was not only able to solve literal equations but was also confident. I used this information in the next class to select the students who could coach other students. I have to admit, it wasn't the usual students who knew what they were doing. It showed some other students who normally aren't in the spotlight to shine through.

#### Planning to Use and Implement Facts

One of the reasons I selected this FACT was because it got the students up and moving. I started class by telling the students that I have never done this before and it was be a huge success or a complete failure, but I was counting on them to be honest with me about their thoughts.

#### Small Steps

Were your students engaged?

*Oh yeah, they were definitely engaged. Every student was completing every problem.*

Were you confident and excited about using the FACT?

*Yes, I usually look forward to my day when we try something new.*

How did use of the FACT affect the student-to-student or student-teacher dynamic?

*The students relied on each other to determine if they were correct or not. I found students discussing a solution before they would go stand somewhere. If students were sitting at their desks completing problems, they rarely discuss it with their neighbors. I think this activity encouraged discussion because their answers were visible to everyone.*

Was the information gained from the FACT useful to you?

*Yes, you can read about that above.*

Would you have gotten the same information without using the FACT?

*Yes, but not as quickly or easily.*

What added value did the FACT bring to teaching and learning?

*First, excitement over something new. Second, the students learned the material faster than going at it alone.*

Did using the FACT cause you to do something differently or think differently about teaching and learning?

*The information that I gathered from the FACT inspired the next lesson. I wouldn't have had this information if I didn't use a Formative Assessment.*

Would you use this FACT again?

*Yes.*

Are there modifications you could make to this FACT to improve its usefulness?

*I like the activity the way it is. However, if I want to do something similar that doesn't require too much time, I may have a warm-up question were the students will place their initials on a poster, teach the lesson, then have the student do the same problem, initial the same poster at the end of the class in a different color. This way the students can see how their knowledge or confidence changed throughout the lesson.*

#### Using Data from FACTs

The information I gained from using this FACT motivated the next lesson. I knew who was knowledgeable and confident, those students coached other. I also included more problems like the ones that the students were struggling with during the FACT.

### Relations and Functions Foldable

Common Core Standard:

A1.2.1.1.2 - Determine if a relation is a function given a set of points or a graph.

In an effort to teach my students about what makes something a relation or a function, I created this foldable. It's just a 4-door foldable, glued to an 8.5 x 11 sheet.

It took us the entire period to create this. And I feel that students were bored out of their minds. Does anyone else get that vibe from their students when filling in foldables?

Anyway, we haven't done anything with it yet, so I'm hoping they see the usefulness of it and aren't so bored the next time we create one.

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