What is Number Sense?

We throw the term around but rarely define it.  I had two experiences this week that help bring the concept into sharper focus.

I was fortunate enough to work with second graders on Oahu, in a Hawai’ian language school.   I had beansticks and bundles and leftovers with me.  After the keiki (children) became familiar with beansticks, I posed this question to them; “Build the number that is 1 beanstick and 15 beans.” 

All children were able to figure out it equaled 25.   But some children built it with two beansticks and 5 loose beans and some did exactly what I’d asked.  Then we had to discuss if both answers were correct and equal.  It led to a lively discussion and some very strong opinions!

It was developmentally interesting to see the children struggle when we moved to bundles and leftovers.  Since they couldn’t see the 10s as clearly, building one bundle with 20 ones was much more problematic.  The children spent a great deal of time taking the bundles apart, counting 10s, and putting them back together.  Obviously, they didn't trust my bundling skills!!

My second experience was sitting in a workshop with Dr. Yeap Ban Har, our favorite expert from Singapore.   He talked about number sense as a complete understanding of number bonds.  Our children need to understand 25 is 20 + 5, but also 10 + 15.  Without this understanding, they won’t be prepared for regrouping.  As they get older, that understanding needs to generalize.  3/5 is 2/5 + 1/5.  If one dividing 351 by 3, it doesn’t help much to break the number into 300 + 50 + 1.  Number sense means the child understands that 300 + 30 + 21 is a much more logical way to decompose the number.  Ban Har will be joining us at our National Conference for Singapore Math on July 9-10. http://sde.com/nationals/2014/

Try posing some number sense questions to your students and then give them some time to struggle with the concepts.  Don’t jump in and help too soon!

Come See Me!

I have an exciting Spring planned.  Besides all my regular fun things, March 15 will be my first time presenting at ASCD in Los Angeles.  March 22-29 is my trip to Singapore!  I'm beyond excited.  I promise to post everyday about what I see and what I learn.  I already have two days scheduled in classrooms, thanks to Char Forsten.  Eliza Thomas, another fabulous SDE presenter will be joining me.

Shortly after my return,  I'll be presenting a session on Fraction Games at NCTM in New Orleans in April.  NCTM is always an exciting time to learn, shop, and see what's coming.  I know Kristin Hilty is also presenting there this year.

July is the National Conference on Singapore Math.  I'm so excited about this year's conference.  Dr. Yeap Ban Har is doing a full day on whole numbers this year.  Marcy Cook is presenting sessions on critical thinking and reasoning (all aligned to CCSS!), and Jasmine Kho is coming from Singapore to teach us about lesson planning and algebraic thinking.  For more information about the conference, visit the SDE website

http://sde.com/singapore-math2014/Presenters.asp 

Singapore Math and Flipped Learning

Theresa and Stacye approached me and asked how I felt about flipped learning.  I love the idea in principle but wasn't sure about how it would work with second graders.  Especially since they're also adopting Math in Focus this year.  It seems like a lot to tackle all at once.  But if they were game, so was I, and I agreed to help them on their journey.  Now, we're four months into the experiment and things seem to be going really well.  I've talked to parents, other teachers, the principal and everyone is enthusiastic.  I've even heard from other schools that they're using the videos in class for their students and to train teachers.

What really blew me away was when I went to do some model drawing in another second grade class, who are also part of the journey.  We'd drawn a model and were ready to subtract 179 from 603.  Buck raised his hand and asked if they should use compensation subtraction, open number line, or traditional algorithm.  Whoa!  Turns out an unexpected side benefit is children learn more vocabulary from watching the videos repeated times.  I asked Buck which method made more sense to him.  He said, "I like traditional, but compensation makes more sense because there's a zero."

Theresa and Stacye will be presenting a session on Flipped Learning at our National Conference on Singapore Math this summer.  Registration is now open.  http://sde.com/singapore-math2014/  I can't wait to see what they have to say.

Another Great Singapore Math Problem

Marilyn from NJ sent me this 4th grade problem.  First, I made a video using my smart recorder.  In my defense, I got in VERY late last night and woke up VERY early this morning, so thinking wasn't very high on my list.  This problem is a great platform for having students visualize the problem before they start to solve it.  Lots of ways to incorporate the CCS PRACTICE standards here!

Priscilla was making gift baskets. Each basket would contain three soaps and two bottles of lotion. Priscilla had 293 soaps and 167 bottles of lotion. How many gift baskets could Priscilla complete?

If I think about it, I realize I don't have to do all the division.  I can just estimate first.  I can make just under 30 baskets using the soaps and just over 80 baskets using the lotion.  Since I only want complete baskets, I need to figure out the exact number of baskets using lotion. Wish I'd thought of that before I did all this work.

This problem also highlights the issue of remainders in division.  Do I round up?  Do I discard?  Do I make it a fraction or decimal?  It makes this problem really interesting.  

All in all, a great problem.  Wish I'd thought about it before I solved it.   But isn't that what your students would do?  

Singapore Math--Model Drawing vs. Algebra

I was lucky enough to watch Kim Bell present at NCCTM a bit ago.  Kim is another wonderful SDE presenter.  She showed this wonderful comparison of model drawing to algebra.  I'm using this here with her permission.

Mrs. Grant made 300 cookies. She sold  3/4  of them and gave  1/3  of the remainder to her neighbor. How many cookies were left?

¾ * (y )+ 1/3 (1/4 * y) + x= y
Let y=300 (total cookies)

¾ * 300 + 1/3 (1/4 * 300) + x=300

225 + 1/3 (1/4*300) + x=300

225 + 1/3 (75) + x=300

225 + 25 + x=300

250+x=300

250-250 + x=300 – 250

x=50

Watch to video to see how much easier it is with model drawing!!

A Great Problem for Mathspot.Net

I found this problem on Mathspot.net, a great blog by Lisa Englard and really liked it.  It was co-written by Lisa and first appeared in Teaching Children Mathematics, Math by the Month column, October 2013.  It is here with Lisa's permission.  

Jared’s mom works for a company that publishes books. When he visits her office, he likes to watch the machine that binds the books. Mr. Green, who runs the machine, told Jared that the machine can bind 12,000 books in 1 hour and 20 minutes and that the machine runs steadily for 10 hours every day. He also found out from Mr. Lee in marketing that last month, the company printed fiction and non-fiction books in the ratio of 4:1, with 540,000 more fiction books printed than non-fiction. Jared’s mom asked him if he could use all the information he learned to figure out how many days it took last month to bind all the fiction and non-fiction books that were printed. Does he have enough information? If so, how many days did it take? If not, what other information does he need? 

There's a Sale! What Percent are you Saving?

I was sitting at the airport, one of my favorite places to find math problems. I'm also an accomplished eavesdropped.  An commercial played on TV, touting a huge savings of $10 off every $25 spent.  The woman behind me turned to her friend and asked, "What percent savings is that?"  I thought it would make an interesting question to ask our students, since they might have lots of different ways to show their number sense as they solve it.