# Algebraic Thinking In Kindergarten

I work all year to teach my kids that learning through exploring is valued and appreciated in my class. I think that is important for all academic areas but especially for math. Kids seem to want to know the answer or mathematical process to use before they are willing to try a problem. Getting kids to buy into that philosophy is important for the success of higher level thinking activities. The math equation you see above is very challenging for most kindergarten kids because there is no obvious “starting point.” More than likely their first idea will be wrong and who likes to play a game knowing that? Well, my class loves this game and they ask play over and over, regardless of their mathematical ability.

This game starts in the beginning of the year with me simply writing a number on each table. The kids work to build that number with different manipulatives. My question to them is “What does the number 8 look like?” I highlight how some kids make a row, some kids group four and four, etc. The next step is moving to a story problem. “Sally had three toys, then she got three more. How many does she have now?” I write ___ + ___ = ____ on each table and the kids show the word problem using manipulatives. Then over time we move through different types of word problems that get increasingly difficult. I use the different CGI problem types (more info here) as a guide. **The key to this process is getting kids to share their thinking, not to focus on correct answers.** We applaud the process and cheer for kids willing to share how they worked on the problem and avoid worrying about their answer. Side note: as a teacher I am always making mental notes of who is solving the problem correctly and I use that as a guide for what to work on in small group.

After many months of building our understanding of math concepts, as well as learning that the process is the goal, we are able to really push our thinking. I start with __+__+__=__ and we move on to more challenging problems like the one in this post. When we get to this point I feel the kids are truly building a mathematical foundation as they explore how numbers can be manipulated to achieve and answer. Differentiation is simple as I can easily write any number I want on each table and by changing how I group the students.

If you like this type of activity check out Starting With the Answer. This is another game we play that I feel is very valuable.

You are awesome! Any interest in moving to NJ? Our school is looking for a new K teacher!!!!

Love this! I am a big fan of open-ended problem solving and this kind of attitude towards math- I use it all the time with our math journals! I wrote about them here: http://luckeyfrogslilypad.blogspot.com/2013/06/math-journal-throwback-thursday.html We do number tile puzzles to encourage similar thinking to this, but I love how you’ve made it more accessible to kindergartners by using the cubes.

One thought- do you ever put the “answer” first so students really understand the meaning of the equals sign? That always throws my kids off, even in 2nd and 3rd grade!

Thanks for the comment and sharing your blog Jenny! I agree open-ended thinking is valuable for math. I have written about “Starting with the Answer” here http://mattbgomez.com/math-challenge-for-young-kids-starting-with-the-answer/

That’s definitely another great activity (and one I love to do even with my older kids!) but I’m talking more about in your equations. Do you ever put something like 8 = ___ – ____ + ____ so that the operations come AFTER the equals sign? :)

Oh I see, sorry I misunderstood Jenny. We do switch the equals sign around in different spots and I work hard to get across the point that equals means “balanced” and not the answer. I don’t know that I have done what you show in your example though. Thanks! Going to make sure that happens this year!

I love the math!!! Great idea writing on the tables but are you using dry erase markers and if so what kind of surface do your tables have?

Great activity, engagement, and mathematical thinking happening here. It’s also important to give students problems like __+__+__= 6 + 2 so they understand that the ‘=’ symbol communicates “equivalence” instead of “the answer is coming.”

I love how the kids are adding and subtracting using unifix cubes in different configurations (in rows are scattered).

For me I would say that equals means “the same as”. or “is the same value as”.

sorry, “is the same as”