## Saturday, January 17, 2015

### Discovering Efficiency

We use the word "efficient" in math a lot.  I want my mathematicians to know that math isn't about shortcuts, but it is about efficiency.  Setting them up to discover efficient strategies is what I'm striving for.  I could simply show them, but if they take responsibility for the learning, we're all better off in the end.

One day I handed out addition boards (see below) and counters.  I told them to put counters on their board but one of the parts had to be zero.  The other part was up to them (within reason - they were encouraged to keep the number small and different than their neighbors).  They left their addition boards on their desks and traveled around, collecting as many equations on their whiteboard as they could.  In other words, they wrote the equations they saw on other addition boards.  5+0=5, 0+7=7, 0+9=9, and so on.

(Imagine one part with 0 counters and the other part with a small amount of counters.)

After about five minutes of collecting equations, they brought their whiteboards to our living room.  They saw the chart below, although at the time it was blank except for the +0 at the top.  I asked volunteers for equations from their whiteboards.  I then wrote on the chart.  Then I asked them to discuss in partners what they noticed.  A few people shared with the group as we acknowledged their thoughts.  It only took a few comments to get to the person who noticed a strategy for adding zero.  I got out my highlighter, drew some arrows, and wrote down the person's strategy.

Imagine the above lesson repeated for +1 the following day.

When it came to +2, we didn't get out addition boards and counters.  We looked at our +0 and +1 charts.  "How can +0 and +1 help you know +2?"  We made some discoveries and then practiced using an efficient +2 strategy with their foreheads.  Each child had a +2 equation on their head.  They walked around and collected as many equations as they could.

Given the opportunity, they can make discoveries about efficient strategies.  They just need the right conditions.

1. Love! I used to talk about efficiency starting in grade 4. What was I thinking? I now talk about efficiency a lot and it is definitely a word I use multiple times per day.

Tara
The Math Maniac

1. Tara, it's a very popular word in my room too!

2. Love this ... and wondering about Saturday Sayings ... did I miss the part where you told us all good things must come to an end?

Happy new year!

Barbara

1. Barbara, thank you for asking about Saturday Sayings. I'm giving myself and my readers a short break. :)

3. Thank you! When we're debriefing in class, I always tell the students that any strategy that gives us the right answer is a good strategy, but then I want the students to notice that some strategies are a bit more ... I'm always at a loss for precisely the right word. That word is efficient! Yay!

1. Lee, efficient is a great word and even better when the kids start using it. :)

4. Wonderful! I will have to try this with my kiddos next week. Your math tips are very inspirational to me-it's something I am really trying to do better this year. You've helped me get closer to that goal! :)
Not Just Child's Play

1. Miss Trayers, thank you for saying that. I'm honored to help.

5. You make me want to teach math again! Your first graders are so blessed to have you teaching them in a way that makes math make sense to them. You are building their understanding and strategies, not just working on memorization. :)
Lori
Conversations in Literacy

1. Lori, that is definitely my goal. I've got lots to learn, but at least I'm moving in the right direction.

6. I love how you laid this out. I think it would be beneficial to some of my 2nd graders that aren't making those connections yet. Thanks for sharing your math thinking! Sara

1. Sara, I hope this helps your little kiddos!

7. You always do such a great job of allowing your students to discover strategies on their own. You really value their thinking and you let them know it. You are such an inspiration to me, Tammy. You always make me think about how I can be a better teacher. Thank you!!
Connie Anderson