Math Tip Monday- Operations & Algebraic Thinking in Primary Grades

Hi there! I am so excited to expand on last month's topic of addition and subtraction. For tons of center and lesson ideas, be sure to check out that post. I also included movement and repetition :) (PS. How is it already November???)

Once we have the basics down in first grade, we start looking at some of the more complicated aspects of the Operations and Algebraic standards. First, we need to truly understand what equal means.
We have a little chant that says:
We do a lot of practice just determining what equal and unequal means. I relate it to a balance and we want both sides of the equal sign to show the same amount. By "chopping" equations at the equal sign it helps students to see the two parts rather than learning numbers are added or subtracted and then the answer appears (ex. 8 + 1 = __ and __= 8 + 1).

We also learn that our goal is to make our equations true and how simple it can be to identify some false equations by just looking at the numbers. This is a hard concept for many of my kids to understand. However, it is something I stress. If we see 7 + 1 = 5, then right away we know it can't be true because if I was adding my sum would be larger than 7, not smaller. Here is a FREEBIE to practice true and false equations.
We also spend a lot of time solving for unknown addends, in all positions. Again, I have students "chop" the equation at the equal sign. We know that both sides of our equation need to have the same amount. This year the idea of a party came about and the kids are eating it up!
 First we look at our equation. We read it as "6 plus some number is the same amount as 9". This helps us visualize what the problem is really asking us to do.
 Next we chop it at the equal sign. This visual helps us separate our information.
Now we draw in the parts that we know. We know we have 9 total on this side. We also write it at the bottom to remind us.
My goal is to have my left side match the right...both sides need 9. We draw the 6 dots that the problem gives us so far. We ask ourselves, "If number 6 wants to go to 9's party we need to give him some help. Right now, he's not cool enough to go to a 9 party. "
We get poor little 6 some help. We start by thinking if he could invite his friend 1 to go with him. Nope. Now we only have 7 dots. Still not cool enough to go. Good bye 1! (As we say goodbye to the numbers the kids get really dramatic which makes it even more fun.)
We continue to add dots to our mystery box to see which "number friend" can help 6 be cool enough to go to 9's party. In other words, how many more do we need to add to 6 so it is equivalent to 9? A lot of times my students want to count the 6 and 9 dots together and write 15 in the mystery box. The friend analogy helps because I can point out that we can't call 3 dots by any other name than Three.
We repeat this process many times. Eventually we switch to the blank first ( __ + 6 = 9) and the sum first (9 = 6 + __). Although very similar, each type needs explicit modeling and practice. We typically do a lot of work on white boards to solve these equations.

Another way we work on this skill is by using manipulatives. We use partitioned paper plates, counters, and cards for this one game. Simply place a card in the "whole" section. You can decompose the number into two smaller parts, or you can give students one of the numbers and allow them to find the missing addend.

 If you don't have paper plates you can use plain counters. I like to read word problems and guide my students through the process. A ten's frame definitely helps.
For a seasonal twist I used ice cube trays from Dollar Tree and plastic eyeballs. Oh my goodness did the kids freak out (in a good way of course!). We could see the two sides needing to be equal. I also had them flip the eyeballs they were adding upside down so we could tell the two numbers apart. Only as a teacher do you get to say that counting eyeballs taught your kids math :)

 Sidenote- I have this Dry Erase tape on my table which is AMAZING! I can quickly write a word or number and not worry about getting a whole white board out. I bought it at Office Max but you can get it from many different stores.
 Lastly I am adding in one more FREEBIE for you today!! Continuing with the part-part-whole relationships and missing addends, this puzzle has been tons of fun for my kiddos. I hope you enjoy it too. I find that I need to sit down in small groups with this game at first, especially with my struggling students. Having conversations about which piece fits and why has been a great help!

I hope you found some new ideas for teaching Operations and Algebraic thinking in the primary grades. If you have a blog post on the topic please feel free to link up with us. Don't forget to check out all of the other great ideas and check back next month for seasonal (engaging/rigorous) activities!


  1. Love these ideas, although the "scary eyes" is probably my favorite! (I'm a sucky for all things Halloween!) Thank you for linking up with my Teaching Tuesday blog post. I hope to see you back again next week!
    ~Heather aka HoJo!

  2. This comment has been removed by a blog administrator.

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