There's an applet on this page that I like to use as a visual for demonstrating the effects of outliers on the mean. There's a few things that need to be improved though. I don't like how it's a little too small and I think there should be an option to hide the mean and median values (I'm thinking check boxes in Geogebra).

I'm a Geogebra rookie and don't have any idea where to start with this project. Some of you probably could make this in 10 minutes. Any takers? I will forever be grateful!

Edit: Maybe I'm better at this than I thought, but this took me well over an hour to make and now I'm stuck. I'm not sure how to get the median value calculated the same way that I was able to get the mean value calculated. Thoughts?

### Adding and Subtracting Integers

Posted by
Craig
on September 23, 2012

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Comments: (3)

Adding and subtracting integers is probably the only concept that I have taught differently every single year that I've been teaching. I always make modifications to my lessons from year to year, but it seems like my lessons on adding and subtracting integers get a major overhaul every year just because I'm never happy with how it goes.

I've done them on separate days and in unison; I've taught the number line method, counting chips method, and using money to help think about the solutions. Ultimately, it always boiled down to subtraction being the culprit of my frustrations. Students always seem to understand addition easier because it is more intuitive; subtraction is not. Of course, I could just tell them to add the opposite of the second number or to "Keep-Change-Change," but the students would never understand why it works.

The counting chips method has always been my favorite, but students have a hard time knowing when to add zero pairs. Then I saw this blog post along with this video:

I tried the Sea of Zeros method out this year and was happy with the results. With the Sea of Zeros already available, the trouble of knowing when to add zero pairs and how many to add was not a problem.

I will admit that this method was not as fool proof as I had hoped. I started off by giving the students this handout. There are 20 problems and I wanted the students to solve all of them by writing down what they thought the answer might be using their intuition. Next, I introduced the Sea of Zeros method by doing a few problems on the SmartBoard (here's the file; chips in the lower right are infinitely cloned) that were similar to the problems in the video. After that, I had the students partner up and gave them a set of counting chips to work out the previous 20 problems to see if they were correct.

I definitely made a mistake turning them loose right away. As I walked around, I observed most of the groups failing to create the Sea of Zeros for each problem (even though I stressed that it was necessary). I should have done two or three problems along with them on the document camera so they could transition from modeling the problems on the SmartBoard to modeling them using the physical chips on their desk. As a result, I had to backpedal the next day and do this with the students. Once I did this, the students were realizing the point of the Sea of Zeros and had a lot of success in understanding why 12 - (-4) equals 16 and not 8.

In the end, I think this is a method that I can hopefully stick with as long as I don't make the same mistakes I did during this lesson. If you're looking for another method to use, give this one a try.

The original blog post has a file to use for printing out counting chips, but it wasn't quite aligned correctly when I printed it back to back. I made one similar in Word and cut them out 1" by 1" squares. Here's the file in GDocs. The formatting doesn't look right, so download it if you want to use it. Cutting out all the counting chips takes FOREVER. Using big whiteboards to just draw positive and negative signs might be just as effective and less time consuming, but something can be said about having physical models in the student's hands.

I've done them on separate days and in unison; I've taught the number line method, counting chips method, and using money to help think about the solutions. Ultimately, it always boiled down to subtraction being the culprit of my frustrations. Students always seem to understand addition easier because it is more intuitive; subtraction is not. Of course, I could just tell them to add the opposite of the second number or to "Keep-Change-Change," but the students would never understand why it works.

The counting chips method has always been my favorite, but students have a hard time knowing when to add zero pairs. Then I saw this blog post along with this video:

I tried the Sea of Zeros method out this year and was happy with the results. With the Sea of Zeros already available, the trouble of knowing when to add zero pairs and how many to add was not a problem.

I will admit that this method was not as fool proof as I had hoped. I started off by giving the students this handout. There are 20 problems and I wanted the students to solve all of them by writing down what they thought the answer might be using their intuition. Next, I introduced the Sea of Zeros method by doing a few problems on the SmartBoard (here's the file; chips in the lower right are infinitely cloned) that were similar to the problems in the video. After that, I had the students partner up and gave them a set of counting chips to work out the previous 20 problems to see if they were correct.

I definitely made a mistake turning them loose right away. As I walked around, I observed most of the groups failing to create the Sea of Zeros for each problem (even though I stressed that it was necessary). I should have done two or three problems along with them on the document camera so they could transition from modeling the problems on the SmartBoard to modeling them using the physical chips on their desk. As a result, I had to backpedal the next day and do this with the students. Once I did this, the students were realizing the point of the Sea of Zeros and had a lot of success in understanding why 12 - (-4) equals 16 and not 8.

In the end, I think this is a method that I can hopefully stick with as long as I don't make the same mistakes I did during this lesson. If you're looking for another method to use, give this one a try.

**How to get counting chips**The original blog post has a file to use for printing out counting chips, but it wasn't quite aligned correctly when I printed it back to back. I made one similar in Word and cut them out 1" by 1" squares. Here's the file in GDocs. The formatting doesn't look right, so download it if you want to use it. Cutting out all the counting chips takes FOREVER. Using big whiteboards to just draw positive and negative signs might be just as effective and less time consuming, but something can be said about having physical models in the student's hands.

### #msSunFun First Week Activities

Posted by
Craig
on August 5, 2012

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Comments: (2)

I don't have a lot of time to go in depth about what I do with all of this, but here's a compilation of some of the activities and problems my 6th-8th graders do on the first few days.

The 6th graders get a little bit of story time with the book

All my grades dive right into some challenging problem solving tasks. Here's the 6th grade task (taken from Exemplars).

The 8th graders work on finding the location of the safe in Dan Meyer's safe problem from

With all of these tasks, I have them work with partners, try to find multiple solutions, and explain their strategies in front of their peers. It immediately gets them in the mindset that I am expecting them to use think every day and be able to justify their thinking.

The 6th graders get a little bit of story time with the book

*Math Curse*. It's a good read if you haven't had the pleasure.All my grades dive right into some challenging problem solving tasks. Here's the 6th grade task (taken from Exemplars).

Penny a DayYou have just won a contest! You must choose between 2 prizes. You may choose $.75 a day for 15 days or you may choose a penny the 1st day, which doubles every day for 15 days. Find out which prize you would choose.

Please do a writing (using good math language and symbols), which tells how and why you made your choice. Include a chart, graph or table that helped you solve the problem.The 7th grade task is a fairly recognizable problem (also taken from Exemplars). I love it when the students discover the pattern to figuring out this problem rather than counting all the squares.

Checkerboard InvestigationWhile watching a couple of students play checkers one day, I wondered, "Just how many squares are on that board?" I thought and thought and came up with a number greater than 200! Is that possible?

Your task is to find out exactly how many squares are on that board. Be creative and thoughtful about your mathematics. Show all of your work, explain all of your thinking and identify all the strategies you use to solve this problem.

The 8th graders work on finding the location of the safe in Dan Meyer's safe problem from

*The Italian Job*.With all of these tasks, I have them work with partners, try to find multiple solutions, and explain their strategies in front of their peers. It immediately gets them in the mindset that I am expecting them to use think every day and be able to justify their thinking.

### DIY Standards-Based Report Cards

Posted by
Craig
on July 25, 2012

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Comments: (0)

If you are starting or have started standards-based grading with your students, one of the things that you will need to think about is how to effectively report the grades to the students and to the parents. If your school uses a gradebook program like ActiveGrade, then I envy you and you can skip the rest of this post. If not, here's a few things that I do to help with the communication of grades.

Just a few pieces of background info to mention:

1. I will be using a 5-10 grading rubric for each learning target for the upcoming school year.

2. I have a spreadsheet that lists each learning target. You might want one of those to make your life a little easier if you choose to create these documents. Copy and paste is your friend!

3. My school uses PowerTeacher to report grades. I set up my gradebook in way previously described by Matt.

4. My school still relies on traditional grading. I've modified my SBG system every year (hence the change to the grading rubric) to get the best representation of overall grades while still dealing with percentages.

My students know their grades on each learning target at all times. When I hand back each assessment, they fill out a tracking sheet to monitor their own progress. Here is a copy of the one I use (borrowed and modified from Dan Meyer). The copy that my students receive at the beginning of the year has each learning target already typed. Just as in Dan's post, I have my students fill in the boxes that correspond with their scores. They get a sticker for Mastery - they freaking love stickers!

PowerTeacher allows parents to access their child's grades from home, but not many of them take advantage of this. Even fewer will take the time to analyze their child's grade to see why they are getting a B-. If they do, they still might not understand what they are looking at ("What are these learning target things?!?).

While I send out a blurb in my syllabus about SBG, it usually doesn't make sense until they take several assessments. By then, what was read in the syllabus has been forgotten. As a result, I decided to create my own standards-based report card for each grading period. After all, what good is a report card if it only gives a letter and a percent?

The first thing I did was type up a letter to help the parents understand and interpret the report card. Here's a copy of what I wrote (this letter is based on how I graded last year...I am no longer grading homework and the rubric is changing).

The second step is to download a copy of all the grades from your gradebook. For you PowerTeacher users, click on "Reports" and then "Scoresheet". Make sure the Output Type is CSV. This will allow all the data to be in a spreadsheet format. Here's what a copy of mine looks like:

The final step is to compile the information from the parent letter and the spreadsheet into one document. Here's where doing a mail merge can be your friend. Don't worry, it's actually pretty easy. Here are the steps for how it's done in Word 2007. I'm sure the steps for Word 2010 are pretty much the same.

From here, you can preview all the copies to make sure it's working correctly and then print. This looks like a lot of work, but it really isn't. In fact, once you get the initial parent letter typed up, creating and printing these report cards takes about 15-20 minutes. That's a lot quicker than typing up all those comments!

Just a few pieces of background info to mention:

1. I will be using a 5-10 grading rubric for each learning target for the upcoming school year.

2. I have a spreadsheet that lists each learning target. You might want one of those to make your life a little easier if you choose to create these documents. Copy and paste is your friend!

3. My school uses PowerTeacher to report grades. I set up my gradebook in way previously described by Matt.

4. My school still relies on traditional grading. I've modified my SBG system every year (hence the change to the grading rubric) to get the best representation of overall grades while still dealing with percentages.

**Communicating Grades with Students**My students know their grades on each learning target at all times. When I hand back each assessment, they fill out a tracking sheet to monitor their own progress. Here is a copy of the one I use (borrowed and modified from Dan Meyer). The copy that my students receive at the beginning of the year has each learning target already typed. Just as in Dan's post, I have my students fill in the boxes that correspond with their scores. They get a sticker for Mastery - they freaking love stickers!

**Communicating Grades with Parents**PowerTeacher allows parents to access their child's grades from home, but not many of them take advantage of this. Even fewer will take the time to analyze their child's grade to see why they are getting a B-. If they do, they still might not understand what they are looking at ("What are these learning target things?!?).

While I send out a blurb in my syllabus about SBG, it usually doesn't make sense until they take several assessments. By then, what was read in the syllabus has been forgotten. As a result, I decided to create my own standards-based report card for each grading period. After all, what good is a report card if it only gives a letter and a percent?

The first thing I did was type up a letter to help the parents understand and interpret the report card. Here's a copy of what I wrote (this letter is based on how I graded last year...I am no longer grading homework and the rubric is changing).

The second step is to download a copy of all the grades from your gradebook. For you PowerTeacher users, click on "Reports" and then "Scoresheet". Make sure the Output Type is CSV. This will allow all the data to be in a spreadsheet format. Here's what a copy of mine looks like:

The final step is to compile the information from the parent letter and the spreadsheet into one document. Here's where doing a mail merge can be your friend. Don't worry, it's actually pretty easy. Here are the steps for how it's done in Word 2007. I'm sure the steps for Word 2010 are pretty much the same.

- Open up a copy of your parent letter. Click on the "Mailings" tab.
- Click on "Start Mail Merge" and then "Normal Word Document".
- Click on "Select Recipients" and then "Use Existing List".
- You should have the spreadsheet with all the student grades saved. Find it and click "Open".
- A window will pop up asking you which sheet you want to use. For example, I have all my 6th graders on one sheet, all my 7th graders on another, and so on. If I want to do just the 6th grade class, I will select that sheet.
- Now it's time to start formatting the report card. Go to the second page of the parent letter; it should be blank. I put the student's names at the top so it's easy to pass them out. To do this, click on "Insert Merge Field" and then click on the appropriate header. For me, it's "First_Name". Enter a space, and then insert the student's last name.
- Format the rest of the report card the way you want it to look. Here's a final copy of mine:

From here, you can preview all the copies to make sure it's working correctly and then print. This looks like a lot of work, but it really isn't. In fact, once you get the initial parent letter typed up, creating and printing these report cards takes about 15-20 minutes. That's a lot quicker than typing up all those comments!

### Intervention Time Resources Needed

Posted by
Craig
on January 12, 2012

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Comments: (0)

My school is going to be starting a scheduled intervention time for students soon. Our entire middle school has been split up into four academic groups based on MAP scores and classroom success. Since I will be taking the students that need extra help in math, I am still kicking the tires on how I want to approach this situation.

I am probably going to have around 30 kids between myself and a teacher's aide for the intervention time, but the students are a mixture of 6th grade math, 7th grade math, pre-algebra, and Algebra 1 students. Since I do standards-based grading, I will be having the students work on the learning targets they have struggled with during the school year. Some reteaching will be necessary, but for the most part, these students will be just doing some skill-based practice. This is where I am hitting a few snags.

There's no way that I will be able to individualize the problems that each student needs to work on every day without using technology. I also think that this will be the quickest way for the students to receive feedback on the problems. I have a short list of some resources that might help me in this situation, but I'm wondering if anyone else has a better suggestion. Here are a few of the resources that I have looked at with a few pros and cons listed:

Khan Academy: I don't think there is a large enough database of skills to meet the concepts that all my students need to work on. Most of the skills seem to fall in the K-5 range, so it's not much of a help.

TenMarks: I like this site as it is pretty customizable and has a large selection of questions (many of which even focus on problem solving). The good thing is that it's free, but several times during the year when I have wanted to use it, the website is down. I cannot use this resource if it is not reliable.

IXL: This would also be a good resource to use, but it's expensive. I might try the 30-day trial and see if my principal could spring for a subscription, but I'm not sure that will be possible.

ALEKS: I supervised a high school make up course last summer with students who used this program. It was pretty detailed and doesn't have multiple choice answers (which is an anomaly), but since it is a program, it doesn't allow the students to have a free-range choice of all the concepts. It also costs money.

Manga High Math: Although it is mainly a math games website, it does have skill-based questions. I've had a couple students use it this year, but the questions are pretty bad and I probably shouldn't even consider it.

Those are all the resources I have experience with. Does anyone have any insights to another website similar to these that might meet my needs or any other suggestions based on the ones I have listed?

I am probably going to have around 30 kids between myself and a teacher's aide for the intervention time, but the students are a mixture of 6th grade math, 7th grade math, pre-algebra, and Algebra 1 students. Since I do standards-based grading, I will be having the students work on the learning targets they have struggled with during the school year. Some reteaching will be necessary, but for the most part, these students will be just doing some skill-based practice. This is where I am hitting a few snags.

There's no way that I will be able to individualize the problems that each student needs to work on every day without using technology. I also think that this will be the quickest way for the students to receive feedback on the problems. I have a short list of some resources that might help me in this situation, but I'm wondering if anyone else has a better suggestion. Here are a few of the resources that I have looked at with a few pros and cons listed:

Khan Academy: I don't think there is a large enough database of skills to meet the concepts that all my students need to work on. Most of the skills seem to fall in the K-5 range, so it's not much of a help.

TenMarks: I like this site as it is pretty customizable and has a large selection of questions (many of which even focus on problem solving). The good thing is that it's free, but several times during the year when I have wanted to use it, the website is down. I cannot use this resource if it is not reliable.

IXL: This would also be a good resource to use, but it's expensive. I might try the 30-day trial and see if my principal could spring for a subscription, but I'm not sure that will be possible.

ALEKS: I supervised a high school make up course last summer with students who used this program. It was pretty detailed and doesn't have multiple choice answers (which is an anomaly), but since it is a program, it doesn't allow the students to have a free-range choice of all the concepts. It also costs money.

Manga High Math: Although it is mainly a math games website, it does have skill-based questions. I've had a couple students use it this year, but the questions are pretty bad and I probably shouldn't even consider it.

Those are all the resources I have experience with. Does anyone have any insights to another website similar to these that might meet my needs or any other suggestions based on the ones I have listed?

### Math Teacher Interview Questions

Posted by
Craig
on August 2, 2011

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Comments: (2)

Preparing for a job interview is not only important for the person being interviewed, but also for the interviewers. Asking all the right questions can get you a good idea of who the candidate is and how they operate as a teacher. Here is a list of good interview questions that Lisa and I gathered from the responses we received via Twitter.

- What would your dream school look like?
- Share with me what you think a good piece of mathematics is - something you really like.
- How would you make math class great for the students who feel like the "dumb kid?"
- Do you have any experience with Web 2.0 tools?
- Are you familiar with the Common Core State Standards for Mathematics? NCTM's Principles and Standards for School Mathematics?
- Why did you choose to become a math teacher?
- What is your relationship with mathematics? Why do you love it and why should anyone care about it?
- How do you make the content relevant and engaging for all learners? How do you make the content more accessible?
- Tell me about a lesson that went well and why.
- Tell me about a lesson that didn't go well and why. How might you improve that lesson?
- How do you use technology in the classroom? As a personal/professional learner?
- What skills and technologies are you most interested in improving upon or learning?
- Do you find any particular courses/subjects/topics intimidating?
- What professional materials (books, websites, blogs) do you read?
- Describe a typical day in your classroom.
- Which math is your favorite to teach and why?
- How do you teach coverage of all topics while teaching students how to think/problem solve?
- How would you work with a particularly difficult parent or student?
- How do you incorporate problems that promote reasoning and sense making into your classroom?
- How do you feel about implementing backwards design into your curriculum?
- How do you determine a student's grade?
- What is your homework philosophy?
- What do you do when a student doesn't understand a concept?
- How do you differentiate instruction in a class with students who can't multiply and students who understand complex math ideas?
- What were your favorite classes in high school and/or college?
- How do you determine what you teach?
- How do you get students to practice math?
- Give an example of a lesson when your students were really engaged.
- How do you get students interested in the problem solving process?

Hopefully some of you (interviewers and interviewees) will find this list useful in the future. Add any others that you can think of in the comments!

### Reaction Time Test

Posted by
Craig
on July 5, 2011

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Comments: (1)

I wanted to review mean, median, mode, and range with my students by having them use data that was meaningful to them. I saw this reaction time test and thought this would be fun way to review these skills. I also wanted the students to recognize how outliers affect the mean. I had them use this handout while working to keep track of the data.

The lesson went well, but a funny thing happened while the students were collecting their data. We've all had those unintentional things happen in a lesson that have turned out to a blessing in disguise and this was one of them. One student was collecting their data and forgot to record one reaction time. The website shows the mean reaction time after each click, so she had this information:

The lesson went well, but a funny thing happened while the students were collecting their data. We've all had those unintentional things happen in a lesson that have turned out to a blessing in disguise and this was one of them. One student was collecting their data and forgot to record one reaction time. The website shows the mean reaction time after each click, so she had this information:

What was the time for the 5th attempt? Behold a new, more challenging problem! I love it when these things happen.