## Summer Math:Counting and Subitizing

I’ve been in a “blogging about math” funk for a few months.  One of my summer goals is to write more, so I thought I’d start a series of blog posts about the math that I am doing with my children at home this summer.  To be clear, this is not a series that is planned.  Instead, I am going to try to be very mindful of the times we do math together formally or informally.  My children, who just finished grade 1 and 2, are probably involved in informal math conversations about the same as many children of teachers. Both of them are pretty good mathematicians, and by that I mean they use flexible strategies to do mental math calculations, they notice math in the world around them, and come up with strategies for solving math problems that naturally occur around them.  I’m a firm believer that this happened because I am intentional about helping them mathematize their world, just as I am intentional about making sure they learned to read by reading to them at least every night before bed (and usually more often!)

Earlier in the week I received an e-mail about the latest Mathies resources.  This morning we finally had time to sit down and explore a bit.  I picked a game for my 6 year old called “Representation Match” and if it wasn’t for his Minecraft addiction I think we’d still be playing it (he only gets to play on Saturdays and when he sneaks my phone into his closet unnoticed so it’s tough competition!)

I chose the numbers 0-20 for him, and I chose all the representations of those numbers.  He had to find matches – two ways to make 14, or 19, or 17, or any number between 0-20. These are all the choices available.

He had to work at this!  He was not able to subitize all the numbers so we had a few conversations about how to figure out the number represented.  For example,  there were 3 dice, two showing 6 and one showing 5. I prompted him to think about 6+6 which he knows is 12.  Then I pointed to the 5. He counted on by 1’s to get to 17, then chose the numeral 17 as it’s match. Sometimes he had to match two picture representations.

When he played again, he chose 2 or 3 representations for himself, always a different combination.  My daughter did the same.  She played with the 0-20 cards, even though she is in grade 2.  She likes to get answers fast, so this appealed to her. She was also playing with the cards hidden, more like a traditional memory game and said she had a lot to keep track of in her mind if she was playing with the higher numbers.

We use Dreambox a lot at school.  I love it!  But I also like to have students doing some targeted math activities that keep them immersed in a specific skill for a while.  Dream box allows them to pause a game and move on to something else, which is fine, but also lets them give up too easily sometimes.  I think this Mathies game would make a great supplemental activity for us during the first month or more of school when we are talking about counting strategies, as well as for practice throughout the year.  Did I tell you I’m scheduled to teach a grade 1, 2, 3 split next year? I haven’t taught grade 1 before so I am anticipating how that will look.  The “Representation Match” game will let me set them up to match numbers 0-5, 0-10, 0-20 and 20-50, I think it will be good for the whole class.

## Slice of Life: Multiply the Money

I wrote yesterday about a Number Talk I had worked on with my class.

Today I extended that activity by making an array using money.  I used the Mathies money tool to display an array made of nickels, then I asked, “What do you see?”

We built this display of our thinking a bit at a time, so I am sure it made more sense to us than it might to you!  Someone saw 45 cents.  Then someone else saw 15 cents (3x5cents) and then 3 groups of 15 = 45.  Some saw the array 3 x 3 = 9 nickels all together. I pointed out 3 x 15 and 9 x 5.  Thanks to our work with fact families, a few realized 45 “shared by” 3 people means they get 15 cents each.  Seriously!  They didn’t just point out that 3×15=45 so 45 divided by 3 = 15.  They actually explained what was happening! (Full disclosure: not all of them.)

After this conversation, I cleared the board and made an array using toonies. Now, you might have been expecting me to use dimes, but I thought the \$2 coin was better considering that we haven’t talked about multiplying by 10 and my grade 2s would get a lot more out of the conversation if we were thinking about multiples of 2 rather than 10. I will probably give 10s a try tomorrow on their own.  After our success today it seems like a good way to get everyone to start thinking about multiples of 10. I’m looking forward to it!