Oh My! The Progression of Multiplication

Well, I’ve watched this video three times now and I think I need to watch it at least five more times. I love, love, love how this presented to the audience.

 

My take aways for when I am teaching multiplication:

  1. I need to stop stealing the opportunity to let my students use concrete tools! They should be available every SINGLE DAY.
  2. Rushing to the traditional algorithm is a huge mistake. I am thinking we need to have some serious conversations about when to introduce this.
  3. I need to let the students explore. Let me say that one again, I need to let the students EXPLORE. So many times when they hit a struggling point I feel this need to jump in and tell…I need a muzzle for my mouth!

What did you take away from this?

Math is Messy!

Today I filled in for a teacher who had to be out suddenly. It was so exciting! I’ve been coaching now for several months and I was anxious to slip back into teacher mode.

These were fourth graders who had been introduced to the distributive property the day before. The teacher was looking for something to both review and solidify their knowledge. I decided to try to connect their past experiences with multiplication to their new thinking from the day before. I wanted it to be a little messy!

The learning target:

I can solve multiplication sentences in more than one way.

I had the students rate themselves based on this success criteria:

0: “What is multiplication?”
1: “I’ve heard the word multiplication before but I do not have any strategies to solve it without help.”
2: “I can memorize facts, but I still don’t know what multiplication really looks like.”
3:  “I have more than one strategy to solve a multiplication sentence like 6 x 8: number lines, equal groups, repeated addition, etc.”
4:  “I can apply what I know for strategies to harder problems, like 16 x 8.”

Then, I put them in groups to solve the following two facts as many ways as they could on giant paper…6×8 and 17×5. The results were remarkable, AND messy!

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Math is messy!

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One student wanted a new paper, but I explained that mistakes feel kind of awesome. We should expect to make mistakes and try again, it is all about perseverance.

This messiness reflected the thinking of the students. I had to suppress the urge to organize their thinking into my own pretty little anchor chart. I had to remind myself that this wasn’t about an anchor chart, it was about letting the students know that math is messy and that they could learn from each other’s thinking.

After giving them about 10 minutes, it was time to share. We rated ourselves against the success criteria to see where each group was. Then, I asked them to think about which strategy was most efficient on their poster.  They laughed pretty hard about the inefficiency of drawing 85 circles/tallies.

Here were some of the favorite efficient strategies that students shared:

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A nice notation of the distributive property, where the student broke the 17 into 10 and 7.

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Classic repeated addition (bottom), and another way to note the distributive property on the top.

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This person used the distributive property, but broke the 17 into 8 and 9! Very cool. I also appreciated how they showed their thinking below the number sentence.

My personal favorite was this one:

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He broke the 10 into two fives! That is someone who really understands what he is doing.

It was wonderful to get them talking and sharing.  The person doing the talking is the person doing the learning!

 

A Team Approach to Learning Math Facts

(I wanted to title this post Ugh! %#$*% Math Facts, but somehow that didn’t seem very appropriate!) Sometimes I feel as though I am banging my head against the wall in an effort to help students learn math facts. There are many ways to practice in our room with a weekly set of facts (differentiated to their needs): building them, arrays, number lines, fact families, strategy work, drill, flashcards…

But we’ve hit a point in the school year where the students are less than happy to practice.  Whenever I mention math fact practice, I hear groans and moans about it.  IT IS DRIVING ME CRAZY. I started to look at their behaviors, noticing that when it was time to practice math facts, their efforts were half hearted as if they were on auto-pilot. I was having to track down who was practicing and who wasn’t.

On April 4th, I noticed only 7 people out of 25 students got 100% (10 out of 10) on their weekly math fact quick check.  I was completely at a loss because this number had been falling every week. My students know that I hold very high expectations, which means that somehow we were failing each other.

So I really started pushing them to practice at school, even twice a day at times for the next week.  I rewarded and recognized students who had completed their wok, and took photos of really cool strategies to put up on the interactive white board.

One week later right before we were about to start our quick check, I wrote this on the board:

Tips for Learning Math Facts

I explained that only seven people had gotten 100% last week.  I told the class that today I would keep track of the number of students who received 100%, and the difference between the two would be the number of extra minutes of recess given next Monday.  Here is what happened:

Tips for Learning Math Facts

 

We had a quick class chat after it was over. I offered this deal to them each week, April 4th was the baseline, the number of minutes of recess was up to them. I asked them if they could work together as a team to meet their goals. Here were the agreements that they came up with together after I told them it was a standing offer:

  1. Practice every morning when you get to school.
  2. Add 5 minutes of math fact practice at home.
  3. Practice when we finish our math assignment during math class
  4. Quiz each other on our math facts throughout the day

We will see how they do this coming Friday.  I am really interested in rewarding their hard work, and if it is a few extra minutes of recess, so be it!

Let THEM Make Those Math Connections!

One of my favorite parts about teaching math (and multiplication specifically) is all of the amazing patterns and connections from one thing to the next.  When I first started teaching I would to preach these patterns to my students.  They thought they were cool, but that was about all.  One day a student in my class saw a pattern I hadn’t seen before, and I realized that it has WAY more meaning if they discover the connections themselves.  Now, when THEY discover the patterns/connections it feels even more amazing, not to mention the fact that it sticks in their minds.

My students finally connected with a multiplication concept today.  We are at the beginning stages of teaching multiplication, so the whole thing is a little mind blowing to them.  They learned to multiply with repeated addition, equal groups, arrays, and with using a number line.  I noticed that they didn’t seem to understand how they were all related.

So I sat them down with a blank piece of paper with the words: “Multiplication: It’s all related!” I asked them to see if they could find how each thing I put on the chart was related.  I didn’t speak as I put up each one, one at a time.

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The moment came when I got to the third one…arrays…and placed each square up (in rows of 5).  I heard a few “oh’s!” and hands flew up in the air.  Then they started to predict what my number line was going to do (I drew it out first before the hops-again not even saying a word!).  Seeing them predict meant that many of them were catching on to how they are all connected.  At the end I asked them what they thought the multiplication fact was, and the answer was shouted to me by 26 children.

“5 times 3!”