“Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.”
―
Over the past few weeks, we have been doing some incredible thinking during a structure we call Number of the Day. Typically in elementary school classrooms, the class will take the number of the day that they are on in school and deconstruct it using the different operations they know. So, say we were beginning the 18th day of school, we would see how many ways we could find to represent that quantity of 18. We might discuss how 6x3, 17+1, 20-2, or ((100-80)-2) could all give us 18. However, I've taken a different approach this year. I've decided to choose our number of the day from the content that we have studied. As we started studying multiplication, using the array cards that we played with during Curriculum Night, we took numbers that we discovered fit that category of number that we uncovered in our classwork called a composite number. I chose numbers that had lots of different factor pairs or dimensions to their array. We looked at numbers like 24, 36, 48, etc. You might also remember that we uncovered the numbers that had square arrays. As mathematicians we call those square numbers, and we are learning that those numbers along with prime numbers are really special because of how they can be used. 
Lately, we have been learning more about how square numbers can be related to one another during our Number of the Day sessions. Starting with squaring 5 to result in 25, we thought first on our own for a minute, then discussed our thinking in our learning partner pairs and built some ideas together in those discussions, then we shared our thinking together as a community of mathematicians. Each day we have squared the number further to increase toward larger and larger amounts using the same process. We uncover cool patterns with our numbers each and every day. And all we are really doing are using the operations we already know well.
Digging deeply into numbers in discussion aloud and in writing helps us to think about multiple ways to see and construct quantities. We might imagine the number as representing money, square feet, linear measurement, time, or other units in order to see the number differently. We might discuss the number in words, consider its factors or addends, or consider multiplying another number by 10 to get the target number. We might see how many times we can add a simple fraction to create the number (1/2 + 1/2 + 1/2 + 1/2....until we get to 18). This practice each day allows me to introduce or reinforce concepts that are different from our main focus in math that day, but connected and really cool to consider. Lately, I've demonstrated during this time how to find the Prime Factorization of some of these square numbers, uncovering some of the ways to use exponents to represent multiple multiplications of the same number.
I share this with you to remind you way to support your child as a mathematician at home. Taking a simple number and thinking about it deeply together, seeing how many different ways you and your family can consider that number and find ways to represent it allows for creativity in mathematical thinking -- something that for me as a math student, my math classes were sorely lacking.
See what happens when you and your family start considering numbers deeply together. If you do, I'd love for you to share some cool things you find out about numbers below in the comments of this blog.
