Open Problems on Whiteboards

 

Today, my first grader and I grabbed a whiteboard pen and headed to the the carpet.  I drew the problem on the board and she got exploring.  In big black letters, I wrote all the numbers down....

1, 2, 3, 4, 5, 6, 7, 8, 9

Then I wrote _____  _____ + _____ _____ = 100

I said, "You may only use each numeral once to make the statement true."  

She looked at me and batted her beautiful long eyelashes and away she went.  She first wanted to try a one digit number by a two digit number to make 100 and soon realized that it didn't work because both addends needed to be two digit numbers. 

 She frowned a little, scratched her head, and began exploring some more.  

As she wiped off the board, a huge grin spread across her face. "I know!" she shrieked. She proudly wrote 21+79=100.  I gave her a huge high five and we kept exploring.

She wrote the following numbers:

When she was done, I asked her if she saw any patterns.  She noticed that a lot of her numbers had one and nine in the ones place, or two and eight.  I tried to help her make the connection that she made 10 in the ones place and 90 in the tens place.

Next week, I will work on drawing visual models with her to represent how bundling works and why we can group ten ones and make a ten to ensure her understanding of place value and number sense.  We will solve one problem that equals 100 in various ways and see how they connect, and commonalities and differences. 

If you want to try a similar problem, you can find it here.