# Focus on Math

## Helping children become mathematicians!

### Ten Frames for Solving ProblemsSeptember 14, 2011

Earlier I wrote about using 10 frames to help students learn basic facts. Using those pre-made ten frames, students used strategies to help them solve equations such as 9 + 7 = ?

Blank ten frames can also be useful in solving problems, those which involve numbers in the “basic facts” category as well as those which involve larger numbers. In the first case, students might use large blank ten frames and put blocks or other counters on them to work out the problem. Egg cartons can also be cut down to replicate a 10 frame and used with blocks or counters.

When students do problem solving with me, and am usually interested in having them document their thinking using pictures, numbers, and/or words. I want students of any age to learn how to record the mathematical thinking they used in solving a problem.

One of the ways I facilitate this recording is to provide mini versions of visual tools we use in the classroom. These sit in small baskets in the room available for students to come and take and to then glue into their exercise book. Mini blank 10 frames (27 per page)  (40 per page) are useful in such situations, particularly for primary students. If a student has used larger 10 frames (or egg cartons) with blocks, he can record what he has done by gluing on however many little blank ten frames he needs, and then drawing circles on them (or colouring in the squares) to record the solutions. Some students are happy to not use the larger version of the 10 frames, and just use the mini version to work out the solution to the problem.

I use mini 100 dot arrays and mini 100 charts in this same way. Baskets of each of these sit at the back of the classroom (cut apart and ready for the student to “grab and glue”). Students who have solved a particular problem in more than one way may have used several of these tools (or the same tool but with different thinking strategies shown).

Thanks to Charlene K. for sharing these mini 10 frames with me. She made the original sheet and has allowed me to share it with others.

Remember, students even in Kindergarten and grade 1 can learn to represent their mathematical thinking, and providing tools for them can make it easier.

Mathematically yours,
Carollee

### 100 Chart Tic-Tac-ToeJune 9, 2011

One of my favorite activities with young mathematicians is to explore the 100 chart and all of its patterns. It is something I do with every class, not just the early learners! There is power in really knowing and seeing the patterns that are there, and they are many!

With young learners, one of the things I like to do is 100-chart tic-tac-toe. Now, I must confess that it is not really a game as is suggested by the name (although one could make a version of the game– feel free to adapt this!) I use the name because of the grid set-up. Practically every child knows how to draw the two vertical and two horizontal lines to set up the game of tic-tac-toe, and that is what starts us off, too.

Once kids draw the grid, I always begin by choosing a number to place in the middle. In the example shown you see the number 28 as the start number. We work together to place the other numbers. “What number is one less/one more than 28?” or “What number comes right before/after 28?” are the kinds of prompts to use. During the first number of times I use this with a class, I only go on to the numbers immediately above and below the centre number. Again, the questioning/talking is important as it is not the positional relationship we want to emphasize, but rather the 10 more/10 less relationships of those other numbers. Once students are familiar with this (and we keep looking at an actual 100 chart during this process), it is fine to extend the +10/-10 relationships to the “one before” and “one after” numbers on the sides.

The illustration also show two things that can be done to allow students, even the weakest ones, to fill in their grids independently. One way is to use a cut-out that fits the particular 100 chart the students are working with. By cutting a 5 x 5 square grid, and then removing the 3 x 3 centre, a window is created for showcasing the particular 3×3 section of the 100 chart that the students are trying to fill in on their grids. If you are doing this, it is best to use cardstock for durability. The second way is to have the students use a highlighter on the 100 chart (or a washable marker on a laminated 100 chart) to mark off the 3 x 3 grid.

You will notice that in two of the tic-tac-toe grids in the illustration that the starter number is not in the centre of the grid. This is where I go with students once they are successful completing the grids from a centre start. Of course, the starter number can be placed in any of the outside blocks, and the students enjoy the challenge a new spot gives.

A further extension is to start with a three-digit number, say 128, in the centre. For students dealing with numbers 100-999, this is a way to help them understand the one more/one less and ten more/ten less relationships.

Once students know how to do this, it can be done quickly as a warm-up/refresher. At this point a 100 chart on the classroom wall is often the only visual needed as a reference.

Give it a try with your students and let me know how it goes!
Mathematically yours,
Carollee