# Combining Like Terms

Since being back in the classroom, I find myself doing activities with my lessons and thinking “I gotta blog about that.”  These ideas may not be profound, but you never know if there’s some teacher out there in the universe that could use this cool thing.

One of my goals every year is for my students to make sense of math.  And recently, one of our units (6th grade) was on equations and expressions.  One of the topics was combining like terms.

I first pass out playing cards (poker cards) to each student.  I made sure to use numbers 1 through 10.  I also make sure I pass out a variety of clubs, diamonds, spades and hearts usually just the numbers 2-10.

Then I instruct the students to “combine like terms”.  Now this is usually when they give me the most quizzical look.  Then they try to ask a million questions, but I find myself just repeating myself with those 3 words.  “Combine Like Terms!”

When it looks like the students have settled down and found their partner, I take a survey of what cards they put together.  Here’s what they come up with.

Without even looking, I can predict this every year.  And without any direction, I ask the students what their thinking was in pairing up.  The answers I get are usually 1. The 2 cards are the same color.  2. the numbers are the same.  3. The numbers are even or 4. they cards are sequential.

After this initial pre-assessment, I show them examples of like terms and unlike terms.  Usually I have at least one student who will connect the lesson with the card activity.

“Hey Mrs. A, what if we matched up the cards by the symbols?”

Bingo!  Now we are onto something.

I proceeded to turning the  playing cards into algebraic expressions.  We used variables like D to represent for the diamond and H to represent the heart.  Those can’t be combined because they don’t have the same variable.   If you check back on the above picture…the only two cards that could be combined are the 7 of clubs and the 8 of clubs.  Those students partnered up because the cards were “in order,” however they realized during our post-lesson discussion that they were the only pair that could be considered the same terms.

By using manipulatives and contextualizing an abstract algebra topic, it makes it a little easier for the students to grasp.

Until next time,

Kristen

# 12 Ways to Get 11

As I have said countless times in previous posts, my 6th graders have been math buddies with a kindergarten class.  The other kinder teacher and I spend numerous hours trying to create and plan different activities for both classes to do.  One of the books I came across on Twitter was 12 Ways to Get 11 by Eve Merriam.

While planning, we purposely waited to do this activity when kindergarten was much more in tune with their addition facts and when 6th grade needed a break from testing.

I let my collaborative partner perform and read the book.  She’s so expressive with her reading.  The kinder students involved themselves at counting everything to 11.  After the book was read, we counted things around the room to 11.  For instance, students noticed that there were exactly 11 clouds hanging from the ceiling (complete coincidence!).  Students also noticed 11 months that were listed next to the calendar (May was being used on the calendar).

Next, we let both sets of students explore combinations of 11.  We explained that more than 2 numbers could add up to 11. My students love working with cuisenaire rods (their manipulative of choice).

This is what they came up with.  I loved seeing how each set of students would represent the combinations.  Kindergarten mostly just used the rods, where as my students had to represent the combinations with drawings, sketches, or some sort of visual representation.

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Here’s some footage of what we observed.

We wish we had more time to do more with this activity.  We meant to go back to it, but other things get thrown at us at the end of the school year.

Until next time,

Kristen

For the past few months, I’ve been completely sidelined with another project that required my full attention and writing skills.  Luckily, the project is finished and now it’s the waiting game.  SO my apologies for my disappearance.  However, I have a few blog posts that I’m going to catch up on in the next few weeks.

As most of you know, I’m a clothesline math enthusiast.  Love the routine.  Love the conversation surrounding it.  Love that it creates student engagement.  As a matter of fact, some of you might have seen this.  Chris Shore wrote a full book about it and gave me and my school an acknowledgement.  Super cool.

When it was time for my fractions, decimals, and percent unit, I was thrilled to use the clothesline.  I wanted my students to see the interconnectedness between each of the concepts.   After I taught them the skills needed (how to convert fractions to decimals, decimals to percents and fractions to percents), I broke out the clothesline.  This time, instead of pre-designated cards, I had my students design their own.  With the use of a hundreds grid, my kids got to design color in as many squares as they wanted.  From there, they collaborated with their table groups and figured out the fraction, decimal and percent of the grids colored in compared to 100.

Once they put them on the clothesline, we had a discussion about percentages less than 1% (and what they would look like).  We also had a discussion on 200% and where that would go in comparison to 100%.  Big math argument.  One student put 200% to the right of 100%.  Other students were arguing that it should be equally spaced compared to where 0-100% was placed.  100%-200% should be the same distance.

The lesson was a success.  But I had a revelation about clothesline.  Rather than me choosing with fraction, percents, decimals to, did I increase student engagement with having students create their own?  Is there more ownership with student-created clotheslines?  More importantly, how could other grade levels create their own clotheslines?

This sparked a new category of clotheslines.  I tried out my idea with a kindergarten intervention group.  The students were enthusiastic about it.  They liked seeing how many different ways we could create a certain number.  I saw the potential of using blank tens frames.  Kindergarten also creates their own with the use of the names. (see here)

Here are my latest additions to the clothesline world.  I’ve created blank templates in hopes that our students can take ownership of their own clotheslines.

10frame

double10frame

decimal

Fraction Decimal Percent

Until next time,

Kristen

# Making sense of conversions

My son, Jared, is in 6th grade.  He has told me he thinks it’s “cool” that I’m teaching 6th grade too.  According to him, we have stuff to talk about.  I can finally help him with his homework.  (Really?  Like I’ve never been able to help you with any of your other homework?!?  What the what?!?!?).  Of course I left that last editorial in my head, but I think I knew what he was talking about.   I think he meant that we are finally at the same grade level as teacher (me) and student.

On one evening, he was having trouble with conversions of measurements. This was his homework.

And this is what he showed me.

I was not thrilled to see “memorize” on my son’s notes.  It dawned on my husband and I that our son’s teacher has only been teaching a few years.  He’s probably used to just memorizing steps and procedures.  I don’t like to teach that way.  I like to teach for understanding.  I like to teach more conceptually.  I like to have my students make sense of a problem rather than “memorize” steps.

Just for kicks and giggles, I went to page 290 to see what is said.  This is what I found.

I sat and stared at his paper and at the “steps.” If my son didn’t understand and remember the steps, how could I get him to comprehend what they were asking?

I looked at the 1st question again.  “If 16 C = 1 gallon, then 8 gallons = ________?”  Rather than doing a fancy algorithm or proportion (which he hadn’t done in the curriculum–my husband had an issue with that.), I went back to the basics.  Let’s draw a picture.

16 cups are in one gallon (rectangles).  8 gallons with 16 cups in each.   Once I sat and explained the situation to my son, the lightbulb went off in his head.  “Oh mom, all you have to do is multiply 16 times 8 to get the number of cups.”  BINGO!

And the rest of the hour, we drew pictures, diagrams, and whatever else helped him make sense of the conversions.  And each time we drew a new picture, the lightbulb kept going off in his head.  (Proud Math teacher and Mom!)

The next day after school, I asked my son if his teacher said anything about the homework we did.   My son told me that his teacher said,you should have done it the way I told you too.”   ARE YOU KIDDING ME?!?!?

MATH RANT – –   After close to twenty years of teaching math, this just blew me out of the water.  It is no secret that there are many ways to get answers to math problems.  I usually give the anecdote that there are many ways to get from here to New York.  Some ways are faster, some ways are slower, some ways are more expensive and that’s ok.  Pick which way works best for you…..as long as you get to NY.  Same goes for math.  It is our job and soul purpose to teach our students.  It is well known that one size doesn’t fit all.  One approach to solving conversions doesn’t work for everyone.  Why are we still having students memorize procedures if they don’t understand the problem?  What happened to making sense of things? It only happens to be the first standard of math practice!!!    It baffles me that this is from a newer teacher who hasn’t done any conceptual lessons and/or applications.   The whole thing blows my mind! Maybe it’s also the realization that not every math teacher thinks or teaches like me.

So what do we do?  Do we challenge teachers like this?  Is it worth the fight when they may not understand the importance themselves?

My son’s situation just proves that there’s more work to be done out there.  Teachers still need training.  And just because we, in our youth, learned to memorize procedures, doesn’t mean we actually made sense of things.

Math rant over. Disengaging.

Until next time,

Kristen

# Mills, Bills, and Trill

The first week of school lesson plans usually consist of getting-to-know-you type activities.  In planning, I figured it would be a great time for exploring in math.  I hemmed and hawed about it.  At first I thought I’d do a 3 act lesson.  They are always exciting and engaging, but I couldn’t think or find one that these kids hadn’t seen in 5th grade.

But then I found this……

This was a picture I found a long while ago and kept it in my files, never knowing what to do with it.  I saw the math in it, but didn’t have a solid idea.  However, over the summer, inspiration struck and I got to work.

Have you ever asked your students about millions, billions, or trillions?  Do they truly understand the magnitude of these ginormous numbers?  It was worth a conversations.

Part one of our investigation was showing the above picture and simply asking “what do you notice and what you wonder?”

My students recognized notice/wonder which thrilled me.  Some perked right up when they saw those questions (which made me smile).  I noticed that my students focussed on the picture itself.  Some of my higher thinkers started pondering the saying.  Finally, we got to the question I was looking for….which was how many pictures are in a video.

Here’s the information we were looking for…

We decided we needed to figure out how many pictures were in a second, then a minute, and so on.  They determined that one second of video would be worth 2400 words.  And the video would have to be less than 1 minute.  One minute of video would be 1,440,000 words.   Not bad for my 6th graders.  They were getting the hang out this.

Then I asked them how long it would take them to draw a billion circles.  Saw this at a workshop given by Graham Fletcher back in January and I finally found a use for it. The students were thrilled to investigate this for sure.

With much enthusiasm, the students were jumping with energy on this one.   One girl raised her hand and asked, “are were really doing a billion?”  I looked at the clock and responded, “we got a few hours left so I don’t see why not.”  Their eyes got bigger.

First we took guesses.  I felt like I was on the Price is Right.  “I’ll say 7 hours…I’ll say 7 hours and 15 minutes.”  One group kept whispering about the question and concluded that it should take about 1 second per circle.  I loved this observation because I could tell they were not only thinking, but trying to make sense of the problem.   The class concluded that we should just try it for a minute.    Before we got started though, there was more discussion on how big of a circle they should draw.  Wouldn’t that be a factor in how many they could draw in a minute?

I started the timer and the students worked vigorously on their circles.  The looks on their faces was priceless.  They focussed, they concentrated, they were super-serious about getting this done.

When the timer went off, they counted up their circles.  We took a poll to see how many circles were drawn and the range was between 80 to 120.  For our purposes, we kept using 100.  Next, we figured out how many circles in an hour, a day, and then a year.  Finding out how many circles in a year was a bit of a doozy for them, but they persevered.  I was also happy to report that they knew how to read their place value very well.  Whew!

We even discussed what would 2 years looked like, and they told me it would only be one hundred  million circles.  “That’s not enough.”

I revealed the answer and they were floored.  I’m not going to reveal the answer in this post because I want to leave a little mystery to the question.  Go ahead…do the math yourselves.  (Answer is in the lesson PDF below).

We weren’t done yet.  For the last piece to this investigation,  I remembered this Twitter pic from Mark Chubb.   And I also saw a ripe opportunity to break out the clothesline.  I asked my students “Where would 1 million go?  Where would 1 billion go?”

After much debate and moving cards back and forth, this is what they agreed upon.  I was puzzled because they didn’t really know the relationship between billion and trillion.  I let them watch a video I found on Youtube and some referenced that when they were validating their answers.

However, I wanted to push them further.  I inquired why each of the cards was equally spaced.   Were there an equal amount of numbers between each number?  Some answered yes.  Some were completely puzzled.  Rather than beat the horse to death, I wrote a few new numbers on cards to see if they could show me the relationship.  I wrote 0, 10, 100, 1000.     The conversation got a little more exciting because my students were dealing with numbers they could relate to a bit more.  Unfortunately I forgot to take a picture of the final clothesline and specifically where they moved the cards.

Final thoughts…

• We hear how the US and other countries have trillion dollar debts, but how many people truly know the size of that number.  It’s quite “ginormous” but how does it relate to millions and billions?
• The students loved that they got to “investigate” something tangible.  They could all draw circles.  It was an easy task that they all handled.  It was hilarious to see them take it so seriously.
• The idea of the trillion clothesline was spot on with the investigation, but I saw many blank stares because the students couldn’t really fathom a trillion.  Instead of beating the idea to a pulp, we went with something they were familiar with based on their discussion and reasoning.
• This showed their lack of knowledge in how 10 related to 100 and so on.
• Considering this was the 2nd day of school, this showed that we will be making math fun, accessible, and worthy of their attention.   Many of my students said this was their favorite thing of the day.

Here’s the lesson if you’d like to try it out for yourself.

Until next time,

Kristen

Welcome back to a whole new school year!  I’ve spent the whole summer steadily preparing for my new assignment and it’s one that I’m embracing.

Here is it…the night before my first day at a new school, new routines, new students, new colleagues—actually, they aren’t that new to me.  I’m supposed to be trying to rest up and review my plans for tomorrow and all I can think about is “I have to blog about this!”

To catch you all up….I used to be a middle school math teacher for 16 years.  The last 2 years, I was a elementary math coach.  Now I’m going to conquer teaching 6th grade, but at an elementary school.    I get to be with little kiddos again.  Ok…my kiddos won’t be so little, but I get to experience the joy, the smiles, the high-five moments, and the celebrations that come with learning.

This transition was tough at first.  In the months following my decision, I had weeks where I was raring to go and then weeks when I was doubting myself.  I kept asking myself if I made the right decision by heading to an elementary school.  My 6th grade buddies at the other elementary schools were cheering me on every step of the way.  And with positive mindset, much support from the other 6th grade teachers, and lots of studying over the summer, I’m ready for my challenge.  This is going to be an awesome year.

In diving into this new experience, my inner elementary teacher started coming out.  I spent a good 2 months planning for decorating my classroom.  One of the kindergarten teachers at my site asked me back in March, “what’s your theme going to be?”  My reaction was “Theme?!?!?  Middle schools teachers never did a theme!?!?!?”  I go home and tell my husband about the conversation and he starts looking up things on Pinterest (he is totally a teacher’s husband!).  Low and behold, he holds up this picture….

My classroom is completely decked out with college stuff for my theme.  I created something from nothing.  All of what I’m about to show you is because of this single picture.    As a matter of fact, I’m calling it Acosta Academy.  I’ve had colleagues come in to see my progress and were completely floored with what I had done.

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I also had a revelation.  I put more energy into putting together this elementary classroom than I had in all my 18 years of teaching.  I embraced the belief “Go big or go home!”  More is more in elementary.

And in the little time that I’ve been in the elementary community, I’ve learned so much.  For instance, who knew that you could buy Walmart flat bed sheets for \$5.00 and they were big enough for your bulletin boards/walls?  And I’ve discovered the joys of lamination.  It’s such a magical treat.  I can’t get enough.

And I’ve created some goals for myself for this year….

1. Integrate 3 Acts, Which One Doesn’t Belong, Estimation,  Clotheslines, Open Middle, Numberless Word Problems, number talks and engaging math activities/stations into my math curriculum.
2. Learn and implement Google classroom as well as other Google tech with my students (Recently took a Google Cue Launch workshop and will be taking the first test soon)
3. Conquer my fear of teaching English/Language Arts.  It’s a monster.
4. Find creative activities for partnering my kids with kindergarteners.  The kinder teacher and I have a few great math ideas/activities.
5. Use my time in the classroom to embrace the joy, to foster curiosity, and to give my students the best for their last year at elementary school.

On a side note, I’m proud to announce that my kindergarten collaborator and I have been asked to speak at 2 conferences.  One of them will be at Calif. Math Council’s northern conference in Asilomar.  The other is at the Southern California Kindergarten Conference in February in Pasadena.

I’ve also been asked the speak at my alma mater, Frostburg State University.  Sloop Institute on Leadership & Excellence has asked me to present on “Empowering Others.”  I love the topic choice and have already outlined what I’d present.  Even though the conference isn’t until March, it’s never to early to brainstorm.

There’s more exciting plans coming in the 2018-2019 year, but I’ll wait to report on that when things are more finalized.

Until next time,

Kristen

# Kinder clothesline with 6th grade

Some of my 6th graders went back to kindergarten.  They didn’t know it and we didn’t tell them till the end of the activity.  The teachers and I just wanted to do it out of sheer curiosity.   And it turned out to be a curiosity that was worth exploring.

Let me back up a bit.  Just last week, I led a workshop on the clothesline activity.  I like starting off with the teachers trying one out on their own.  I pulled out my weight cards that were used for kindergarten.  These cards are filled with colorful pictures of a bike, building, tree, a leaf, and other objects.  Students are asked to order the objects by weight (the lightest being on the left and the heaviest objects toward the right).

When I tried this out in kindergarten, we had the students put their cards in 3 basic categories—-light weight, medium weight, and heaviest weight.  We were not looking for precision.   However, 6th grade brought in the precision aspect.  Because they have more background knowledge, they were not only integrating math, but science, social studies, and language arts.  The 6th grade teacher also told me that this was great because the students were persuading their peers as to which order the cards should go.  They had been working on argumentative statements in the weeks prior to this activity.  (Gotta love when you can bring more than one curriculum into an activity—I call it “more bang for your buck!”)

Let me give you a visual…

Kindergartenput these in the “light category”.  No arguments from them.

6th gradeargued whether the leaf or the feathers should be switched.  One student brought up the fact that the leaf was made of water and the stem makes it heavier.  Another student claimed that there were 2 feathers compared to just one leaf.

Kindergartenput the train in the heavy category although some questioned whether it was a toy train or a real train.

6th grade put it in the heavy category althought argued whether it was a toy or real.  One student said it was a toy because of the multi-colors.  Another student argued back that it was real because of the smoke coming out of the smoke stack.  Another student questioned whether it was made of wood or metal.

Kindergarten put this card in the heavy side.  No questions/arguments.

6th grade put this card on the heavy side, however others had issues with it.  One student wondered if it was a toy plane.  Another students said there was blue sky behind it and so it was real.  Another student said the weight might vary because we don’t know if it’s full of people.

Kindergartenput this on the heavy side.  They said they have seen these trucks on the roads and highways.

6th grade – put it on the heavy side.  Questions of whether or not it was a toy were brought up.  Another student asked it if was filled with anything because that would make a difference.  For instance, the weight would vary if it were filled with feathers versus bricks.

Kindergartenput this in the middle category.  They did wonder if it was filled with anything.

6th grade Wondered if it were filled with anything.  One student said that when she bought a new backpack it was filled with paper to make it look full.  Another student said it could be filled with books.

One last thing.  We did not say a word about this being a kindergarten activity to the 6th graders.  We just told them to put the cards in order from least to greatest. At one point, an exasperated student exclaimed “THIS IS SO COMPLICATED!”

Below is the final clothesline that the 6th graders “settled” on.  (There were some that were still not happy with the outcome.)

Until next time….

Kristen

# New Routines for 6th grade

In my district, there are several 6th grade teams at three separate elementary schools. They are an anomaly in that they are invited to secondary professional developments & textbook trainings with other middle school teachers, but yet they are their own special group.  It’s not easy to have secondary expectations, all the while being at a site with kindergarteners passing by your window.  With all these new expectations, new standards, and a new curriculum guide, I saw the need for help.  Me –being a middle school teacher turned math coach–jumped right in.

Our latest venture at one site has been to start math talks.  I introduced them to Which One Doesn’t Belong, Estimation 180 and Would You Rather. They were excited by these routines because they are engaging for the students.  It’s not their usual math.  It’s different.  The teachers are now sparking conversations with the pictures and questions.  It’s been incredible for them.  I recently took their principal on a math walk into the three 6th grade classrooms so she could observe their new routines.  The principal was supremely happy.

One popular thought that came up during our work last year and this year was a simple question….how do you review previous units?  How do we keep information that we did at the beginning of the year fresh?  For instance, 6th grade began the year introducing rates and ratios.  Part of their “Would you rather” routine reviews rates.  For instance…would you rather buy a Starbucks Venti for \$3.59 or a Starbucks Grande for \$2.99.  Essentially we are asking which is a better buy. We are starting a math argument.

So how do you bring fractions, decimals, percents, and ratios to life?  How do you make that lively and different from what they see in their textbooks?   Well…let’s first look at this pic….

What do you see? What do you notice?  What math questions could we ask?

What fraction of the donuts have green icing?  What’s the ratio between sprinkled donuts to stripped donuts?  What percentage of donuts have chocolate icing? What fraction of the donuts have purple icing?  Can you turn that into a decimal?

A simple routine comprised of many pictures of donuts, cupcakes, legos, or any variety of objects.  I’ve seen many math educators use pictures like this to start a visual routine/number talk.  Pictures are an amazing way to wake the students up and look at things differently.  I might bring this routine to my kindergarten teachers as a sorting activity.

So many donuts…..so many possibilities.

Until next time,

Kristen