Division in 4th grade

We have been on spring break this past week, however I had a hankering to write about other previous experiences in classrooms. Back in January, I had been asked to help with division  in a 4th grade classroom.  She wanted a fun activity to help the students.

I introduced the class to a game I called Division War.  With the help of Uno cards, the students had the opportunity to create their own division problems.   The student who had the largest quotient wins the round.  The concept is similar to what I had heard from Robert Kaplinsky in a session on Open Middle.  However, unlike just challenging students with an Open Middle concept, I like to rev up the engagement a notch with a little friendly competition.  The students don’t know that they are working on a DOK level 2 or 3.  They think they’re just playing cards.

To get the students started, Mrs. P and I played one round on the whiteboard.  I chose the numbers 8, 7, 7, and 2.   I asked the students where I should put my numbers.  They were pretty random with where to put them and this is what it looked like.  What I also liked about this part is that they had to identify which part was what.  We used our math vocabulary to make sure we were all talking about the same parts of the problem.

IMG_5937

Then Mrs. P went with her green cards.  She chose 4 cards which were 4, 4, 5, 2.  The students helped her put the numbers in some sort of arrangement.  She happened to get a bigger quotient than I did.  Mrs. P won that round.

IMG_5938

Now rather than just letting them start to play, I wanted to push their thinking a bit more.  I asked them if there was any way that I could win that round. Could I switch any numbers around so that my quotient beats Mrs. P’s quotient.   Some suggested to just rearrange the numbers in any order and hope for the best. However, one student finally came through.  “You put the 2 in the divisor and make the largest number possible in the dividend”  Bingo!  There’s the lightbulb going on!

IMG_5939

The kiddos started playing.  It was great to see them having so much fun with a simple rendition of war but with Uno cards. I guess the novelty of having me help out and a competitive spirit really got the best of them.

Just as I was musing on the high level of engagement, Mrs. P came to chat with me.  “We have an issue. One of the groups has figured out how to get the highest quotient without doing any of the math.”    Well…now you have my attention.   We marched over to the group and I asked them to explain what they were doing.   One student told me that he didn’t need to solve the rest of the problem because he pulled a one and put it as the divisor.  He knew he had won.

Then I heard this from a boy at the same table…”That’s cheating–he’s using one in the divisor.”  The boy sat there smugly like he had figured out my secret.  (I was laughing on the inside–loved it!)

As I walked away to check on other groups, I overheard Mrs. P trying to get the students to show their work.  She then threw them another challenge.  Mrs. P asked them to play another few rounds but with finding the smallest quotient.

Mrs. P ran over to me and told me about her discussion.  I looked at her wide-eyed and gave her a high-five.  That was actually a brilliant twist to my plan.

In our debrief, we encountered one hiccup.  How do we get the students to show all their work?  The group that figured out the “secret” would just choose 4 cards, look at them, and declare a winner without actually doing any of the calculations.  I consider that a good problem to have.

Kristen

Clothesline Fractions

Fractions is one of the “F” words in math.  (The other is functions, but I’m not working with that grade level).   Whenever these two words are said, teachers usually groan with frustration (that other F word). Understood because both can be hard to understand for students.  Part of my job is to turn that frustration into FUN!

Third grade has been working on their fractions for the past 4 weeks. This week I went in to work with them.

First I started off my visit with a number talk using a picture that has been floating around Facebook.  This picture had the potential to initiate lots of discussion and it surely didn’t disappoint.

watermelons
5 watermelons

I let the students just stare at it awhile. Rather than taking observations and questions right away, I like my students to just have quiet time to internalize what they’re seeing. Next, they shared with their elbow partners their thoughts and questions. Then, I let them share their thoughts with me.  Watermelons provoke lots of discussion (who knew?).  Lastly, I asked them what possible question I could ask of them.  One of the teachers rose her hand and said, “how many watermelons are there?”  Being picky about words and vocabulary, I politely added to her question.  I asked the students “how many WHOLE watermelons are there?”

Here are some of the highlights of the three classes’ discussions….

  • I see eight pieces of watermelon.
  • They are in a square.
  • It looks like an optical illusion. It’s kind of like the 4 outside melons are the frame and the half melons are the picture.
  • Some of them look like Pac-Man
  • How are they standing up like that?
  • Finally, the quietest girl explained how she saw 5 watermelons.

Onto the class activity.  The third grade knows I come with something different, innovative, and unique.  I like to surprise them.  I didn’t invent this idea.  As a matter of fact, my inspiration was from a workshop I had attended given by Andrew Stadel.  He introduced me to Clothesline Math.   I wanted to use this idea of an interactive number line with fractions.   I envisioned a single clothesline with students approximating where to place certain fractions between 0 and 1.  However, one question lingered.  How can I maximize the engagement with the whole class in this activity?  Print out 30 fraction cards?  With my active imagination, I saw kids running for the number line, tripping over each other, and ending up in one gigantic entangled web of limbs, fraction cards, and rope.  Yeah…that wasn’t happening.

After a trial run in my office, one of my colleagues suggested that I put up two clothes lines.   LIGHT BULB!!!  That was it!  Split the class up.  13-15 kids working on a number line was a much better option than 30 kids per one number line.

So happily, I strung up two number lines in the classrooms (one in the front and one in the back).  I printed out about 20 fraction cards on colored cardstock.  I not only used unit fractions, but also chose equivalent fractions, and pictorial fractions.

The students were stoked and excited.  I promised them that they weren’t being timed (don’t like to pressure students with that element) but emphasized that they needed to work as a team.  Off they went.

One of the teams decided to analyze and read all the cards first.  Good strategy.  Other teams just started grabbing cards and ran for the line.  One of the teachers approached me and asked if the kids could use their fraction bars.  My compromise was to let them work for 10-15 minutes first before using their fractions bars.  They ended up only using their fraction bars to check their work after their number lines were completed.  Very resourceful.

Here’s something I found intriguing.  One of the kids clipped together these two cards as equivalent fractions (see below).  He saw the picture as 1/5.  I intended for the answer to be 4/5, but could a student validate this as equivalent fractions?  I asked one team this question and none of the kids wanted to take ownership of it.  I think they were embarrassed to admit to it in fear that they would be wrong.

IMG_6332
4/5 or 1/5?

As a closing activity, we did a “would you rather” question.  Would they rather eat 2/3 box of cookies or 4/5 box of cookies?  They could write out their reasoning on the paper.  They were allowed to use whatever strategy they could to validate their reasoning.   I didn’t get to see how these turned out as my time ran out with each class, but my hope is that it was worthwhile.

After the excitement of the day, my mind is reeling with other concepts that could be used on the number line.  The third grade teachers also want to use the clothesline concept for other topics.  This especially excited me because it means I’m empowering my teachers to try new things in their classroom.

Kristen