# One Good Thing: “I think we need to clap for that.”

I really enjoy reading Rebecka Peterson‘s posts over on the One Good Thing blog.  It’s encouraged me to look for my own good things after a tough day.  Today’s was easy.

Last week in one of my classes we played “Mathketball”  (I think most people call it trashketball.)  A student made the comment that we should play “Mathket-war”.  I said if someone wanted to create the game, we could play this week.

I honestly had forgotten about that conversation until Tuesday.  A student walks into my room and hands me a piece of paper,  “Here are the rules for mathket-war.”  Then, “And here are the cards for it.”

Yes, one of my students spent Memorial weekend creating mathket-war.  I wish I had a picture of my face when she shared this with me.  She told me her older sister who is in one of my other classes helped check her math for the problems.  Yet another reason I love this -her sister helped her out.  As an only child, I LOVE to see siblings get along.

Today she read the rules to the class and showed them the cards.  This was out of this girl’s comfort zone, but she did a great.  Hearing the other students appreciate what she had done was good for her.  They were excited she created this so they could play it and were impressed with all the work she had done.

At one point another student made a comment suggesting something that should happen in the game.  She replied, “Just wait.  That’s in the bonus points.”  She truly thought of everything.

When she finished a student raised his hand, “I think we need to clap for that.”

And they did.  🙂

# System of Equations: Substitution

Every once in a while I get excited to have my students do a worksheet.  This is one of those worksheets.  I’ve been waiting to get to this in 8th grade this year to see if it would go as smoothly as it did last year.  So far, it has.  🙂

Last year, I dreaded the thought of teaching solving systems of equation by substitution.  I envisioned my students getting frustrated by the long process involved -solving for a variable, substituting that expression into the other equation, solving for the remaining variable, plugging that back into the other equation to solve for the other variable…  These were all things that students knew how to do already, but putting it all together can feel overwhelming to them.  I didn’t want them to see this as a process to memorize, but rather see this as something that made sense based on what they already knew.

The result of my brainstorming on how to teach/introduce this to students is one of my favorite worksheets.  This worksheet is also an example of one of my favorite parts of teaching/lesson planning -taking a concept I’m dreading teaching and finding a way to smoothly get my students from where they currently are to where they need to be.

I don’t know if this is considered best practice or not, but basically my goal when creating this worksheet was to go back to the basics when it comes to evaluating an expression for a given value of a variable and simplifying expressions and slowly add one more step to the process until students unknowingly solve your typical system of equations by substitution type problem.

Should I help students make the connection to the graphs and the equations earlier than I do?  I don’t know.

The worksheet essentially goes from substitute and simplify to substitute and solve an equation.  Students start by substitution a numerical value and it moves to an algebraic expression.

After students complete the worksheet, I have them graph one of the last problems in Desmos and ask what they notice.  They are amazed when they realize that their answer is the intersection of the two lines.  The first time I had a student do this she thanked me for “tricking” her into doing this type of problem.  No joke.

# Surface Area & Volume Scavenger Hunts

How is it that even after several years of teaching 6th grade, I can still go to my old files looking for stuff to teach an upcoming unit and find pretty much nothing?  How?  How does this happen?  I know I taught it in the past, but what did I do?

This happened with a recent unit on surface area and volume, so I created two scavenger activities.  One on surface area and volume and another with word problems on the same stuff.

I’ve been using “loop” activities or “scavenger hunts” for a while.  I especially like them for the times when I need students to practice a specific type of problem.  It’s a great way to disguise a worksheet as an activity.  I love that they are self checking and get students up and moving around.

I have tried a few different ways of creating this type of activity up when making my own.  This is what I’ve found to be most efficient for me when I’m making the activity.  On the top of a sheet of paper I put the first problem.  Then I put the answer to that problem on the bottom of the next sheet.  It’s been a big help for students to make the font as big as possible so that students can see it from a ways away.  Then on the top of that sheet I put the next problem.  The final answer goes on the bottom of the first sheet.   At the end of the activity, I am able to check students’ work by checking the order of their answers.

Students can start at any card.  They solve the problem and find that answer on another sheet.  This continues until they have done all the problems.  If they do everything correctly, they will end up back where they started.

Because this is a self checking activity for students, I tend to be “less helpful” to students while they are working on activities like this.

And an added bonus is that you can hang the problems just as well to the outside of the school as you can the walls of your classroom.  So when it’s beautiful outside and your class has been awesome all week, you take them outside.  🙂

Update:  I also uploaded an area review worksheet I used to intro this unit.  I’m trying to incorporate more self-check assignments for my students so they know whether or not they are on the right track while working on them.

I also thought I’d share the documents I used to create the images for these activities.  I recently discovered I can use Google Drawings to create prisms.  It works really well for triangular prisms and rectangular prisms.  It’s not quite as easy to create trapezoidal prisms, but it was the best I found.  Here is the link to the images I made for the surface area and volume scavenger hunt, and here is the link to the images for the word problem scavenger hunt.

# Exponent Unit

This was the first time I’ve taught exponents without explicitly telling students the “rules” at some point within the unit.  Many students still said things like, “Oh, so when you divide, you subtract the exponents.”  I have mixed feelings over this.  Yes, I want my students to notice patterns, but not at the expense of understanding the math they are doing.  This is one of the things I struggle ensuring as a teacher -that after my students have noticed patterns, they still understand what is actually happening.

I started the unit with a modified version of Andrew Stadel’s exponent mistakes worksheet.  (I know I found someone else’s version of this worksheet that I modified, but I can’t remember where I got it.)  This was something we came back to periodically throughout the unit.  On one of the last days of the unit, we went over the correct answers as a class for the first time.  After going over the sheet, I asked my students to think back to their reaction when I first gave them the worksheet.  Many sort of freaked out and several others were convinced that some of the problems were actually correct.  It was fun for me to see them realize they had learned something throughout the unit because they could now correctly do all of the problems.

The rest of the first day we focused on identifying the base and writing things in expanded form.  The next several days I spent at least one full day on the product rule, power rule, and quotient rule.  The link for the worksheets I used is at the end of this post.  Again, I know I modified those worksheets from ones I found somewhere online at one point, but I can’t remember where I found them.

I used this Which One Doesn’t Belong? as a warm-up one day.  I’ve really been loving using these as warm-ups this year.  I love how much vocab students use while doing these.

About this point in the unit, I was not in my morning class a few days in a row due to state testing with my 6th graders.  I was looking for self-checking practice for students on exponent problems.  The challenge for me was we hadn’t talked about the zero power yet or negative exponents.  Most everything I was finding online included those types of problems.  Here’s what I came up with.

I modified Kate Nowak’s row game to work for where my students were at.

I don’t know if “Two Truths and a Lie” is the correct name for the next worksheet I created, but I couldn’t think of another name and was running out of time, so I went with it.  Basically, students were to simplify 3 different problems.  Two of the problems would have the same answer (the two truths) and the other problem had a different answer (the lie).

I also had a sheet of Yohaku puzzles ready which I LOVED, but I didn’t end up using it then.  I did, however, use it later in a few of my classes.  I love that there are so many different solutions to these puzzles.  I definitely want to look at the other puzzles on that site for future use.

When I was finally back with all classes after state testing, we reviewed using this Desmos activity I created.

absolutely LOVE this Desmos activity from Mathy Cathy for an introduction to zero and negative exponents.

We ended the unit with some more practice combining all different types of problems.

Here is the link to download the worksheets from this unit.

# “I got it, and I feel amazing!”

As a teacher, one of my favorite experiences is watching a student struggle with a problem, persist, finally get it, and say something like, “I got it, and I feel amazing!”

That’s what I overheard one of my most challenging students say a couple weeks ago in my classroom.  About a math problem.  I’ll be honest, at first I thought maybe she was being sarcastic, but a little bit later she was telling someone else, “I did it, and it feels great!”  She was truly proud of herself and wanted those around her to know what she did, and it. was. awesome.

Here was the task students were working on.

The back side of the sheet had problems like this.

As I think back on this day, something stands out to me.  If this student had been in my classroom last year, she probably wouldn’t have had that experience.  Why?  Because I probably wouldn’t have put that worksheet in front of her, or any other student in my class.

This was a worksheet I created my first year teaching.  I had found a worksheet with similar problems in our textbook resources, loved how it went, and wanted more problems like it.  I was excited to have students work on this task, but that excitement quickly turned to frustration when I found that students struggled with these problems much more than the ones on the worksheet from the textbook.  They were frustrated, and I was frustrated.  I was frustrated that things weren’t going as I had planned and that I didn’t know what to do.  I was disappointed what I thought was a great idea, didn’t turn out so great.  So we moved on, and the worksheet found its way to the back of my filing cabinet.

I let that one bad experience with this impact decisions on what activities I would and wouldn’t do in my classroom for several years.

Rather than try to learn from that day and try again, I opted for more familiar activities where I could pretty much predict how the lesson would go.  I avoided activities where I anticipated a similar outcome and chose to use activities that were comfortable for me because I didn’t know if I was prepared to pick up the pieces of a failed lesson.

And then like Princess Mia in Princess Diaries (1:15), I realized how many stupid times a day I use the word I.

What about my students?  How often do I rob students of their own “I got it, and I feel amazing!” experience because I choose not to use a task I knew was good for fear of how the lesson might go simply because it was less familiar and more uncomfortable for me?

Probably more often than I want to know.  So next time I’m planning a “safe” activity, I hope I will remember to stop and think twice about it and think about my students.  Sometimes safe is ok, but sometimes safe doesn’t lead to “I got it, and I feel awesome!” moments for students, and I want more of those moments in my classroom.

Here is the link to download both the pdf and Word versions of the worksheet.

# A “One Problem Lesson Plan” that didn’t Go as Planned

I’ve been trying to incorporate more “one problem lesson plans” into my classroom this year.  My first few attempts were pretty successful.  My most recent one didn’t go quite as I had hoped.

I gave students this problem from 1 to 9 Puzzle.

I was disappointed at how many students had forgotten how to multiply fractions already, but at the same time I was happy to see them use their resources to figure it out before asking me how to.

I really didn’t expect this to be as much of a struggle as it was for students.  I don’t know if it was the fractions or what, but was like we were back to the first time I had given students a problem like this.  They didn’t know where to start, so many just sat there.  Ugh!

Shortly after students got in groups, I could tell this was going differently than the other times we did problems like this.  There were times throughout the class period that I thought about giving up, having students stop, and move on to the next lesson, but I decided to use this as an opportunity for myself to learn how to move students forward in situations like this.  I don’t know that this was the best approach to this, but here’s what I did.

1.  About five minutes into student work time on this problem when many students were “stuck on the escalator”, we talked about how students could get off the escalator.  They gave me a couple ideas of how to do this in the context of this problem.  (Scroll through this post from Sara Van Der Werf to read about the escalator and beagle video she shows her students.  I highly recommend using them in your classroom!)
2. A little while later when I noticed students getting “stuck on the escalator” again, I brought the class together and asked students to share anything they had figured out so far.  A few students shared fractions they had put in cells a and b.
3. A while later, I gave students one number in the puzzle – I think it was 7.  I told them I wasn’t sure if this was the only solution to the puzzle, there may be more, but for one of the solutions, this is where the 7 goes.  For whatever reason, this really got students going and excited to work again.
4. With about 5-10 minutes left in class and as the students energy started to work on the problem started to decrease again, I let students vote on what number they wanted me to give them next.  I think they voted for me to tell them where the 1 went.

By the end of class I think 2 groups out of about 10 had figured out the solution.

The homework for students that night was to spend 10 minutes working on the problem.

When we came back the next day, the majority of my students told me they spent 10 minutes on the problem, and in that time I think one or two students came up with a solution.  We did go over the answer the next day.  My students worked on the problem for an entire class period and most spent additional time on it at home, and around 5 students had a solution, yet I gave the entire class the solution.  Was this there right thing to do?  Probably not.  Should I have had students work on it again that night?  I don’t know.  When a problem like this is more of a struggle for students than I anticipated, I don’t know the right balance between giving them enough time to wrestle with the problem and burning them out/frustrating them too much with one task.

BUT I do know that because I, as the teacher, persisted through the lesson rather than giving up and moving on, I gave myself experience in this situation that I can use in future lessons that don’t go as planned and because of that, I don’t consider the lesson a complete fail.

And in case you’re interested, here is a solution to the problem.