Addition and Subtraction Work Mats

I hope everyone is having a wonderful start to the new year, and that you are getting back into the swing of things. The break is always very much needed and well appreciated, but it can be tricky making up for any holiday regression!

The Common Core places a lot of emphasis on using models in mathematics. In fact, it is listed as one of the mathematical practice standards for all grade levels. 

CCSS.Math.Practice.MP4 Model with mathematics.

Some of the mathematical models I am focusing on with my second graders are the number line, ten frames, and the hundreds chart. Many of my students are still struggling with their addition and subtraction facts. The models provide them with the extra support they need.

When introducing the mats, I have my students solve a variety of different addition and subtraction problems using all of the model types. As time goes on, I allow my students to use the model that best meets their particular needs. Different models appeal to different students. I believe that it is my job to expose students to all of the types of models and make sure they understand how to use each model. Once students are familiar with each model, they are able to choose whichever one appeals to them. They need to be able to make choices and take ownership. Also, different types of addition and subtraction problems will work well with different models. Students need to be able to recognize this on their own in time.

For the mats, I printed a copy for each student and laminated the copy. Students then write on the mats with dry erase markers. There is something about dry erase markers that students love. The same activity with paper and pencil just wouldn't be the same. 

If you would like a copy of the work mat, click here, or on the image above.

How do you teach your students to use models in mathematics?

Subtracting Halves

In afterschool tutoring, my second graders had been working hard on learning their doubles addition facts. I felt they had developed a pretty good understanding of these facts. Now, they were ready to move on to subtraction. I really wanted to make sure that my students understood that addition and subtraction are inverse operations.

We began by using manipulatives and our "Part-Part-Whole" Mat. I gave students an amount to make in the "whole" section. Then, students counted out the cubes evenly into each "Part" section. The "Part" sections had to have equal amounts of cubes. We came up with the subtraction number sentence to represent our problem. (Click the picture for a copy of the mat.)

Students were still able to use the manipulatives and mats to complete the next activity. Students picked a number, and together we determined what would be half of that total amount. Then, we came up with the corresponding number sentence.

To continue practicing, students played a game called "Halves Race." Students spun the spinner to get a subtraction half fact. Students solved the fact and then moved their game piece to the corresponding answer on the board.

This game is extremely simple, but the kids loved it. They said it was one of their favorite games, which really surprised me. Sometimes, it's the simple things! If you would like a blank copy of the board game and the spinner click here. (If you have a current, up-to-date Adobe Acrobat, you should be able to edit the template right on the computer. Otherwise, you can just print it out and write on it.)

What is one of your favorite math games to play with your students?

Let's Make Ten!

We survived another week! I cannot believe that it will be November next week! As if running intervention groups was not enough, I am also tutoring after-school in second grade for both reading and math. So far, I really like having the chance to work with students, uninterrupted, for an entire hour. I never get that kind of time with my reading groups! Anyways, my second graders and I started right at the beginning, with addition and subtraction strategies. Currently we are working on making ten.

To begin the lesson, we started with a simple addition problem about apples. There were ten apples total. Some of the apples were red and some of the apples were yellow. Students had to use manipulatives and ten frames to find out all of the different combinations to make ten.

(I didn't quite have enough green cubes, so a blue one snuck in!)

I love using manipulatives with my students. I think they are so helpful in establishing student's conceptual understandings.  Often times I think teachers take the manipulatives away too soon. I know my struggling students benefit greatly from using the manipulatives.

After working through the apple addition problem together, we did a similar problem using subtraction. I really wanted my students to understand that addition and subtraction are inverse operations. Once again, students used the ten frame and manipulatives to find the different combinations to make ten, but this time using subtraction sentences.

Then, students had a chance to practice making ten on their own using problems similar to the apple problems, but about cupcakes. They continued to use manipulatives and the ten frame. For a copy of the cupcake and apple problems click here.

I believe games make for very meaningful practice in math. To continue working on making ten, students played a game similar to Go Fish. This game is called Make Ten. Students have five cards to begin with. Then, students take turns asking each other for cards to make a match, and make ten. When the student makes ten with two cards (ex. 8 and 2), he or she can lay down her match. The first player to match all of their cards wins!

For the last activity, students played Fill Ten. In this game, students draw number cards, (or you can use playing cards). Students fill in the number they drew on their ten frame. Then, students take turns drawing cards. The goal is to make matches and fill all of the ten frames first. (Note: It is best to have a small deck, or else kids will be drawing cards all day!)

What sort of games do you play to work on addition and subtraction strategies?