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

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Thanks so much for giving examples for using the 100 dot arrays. I’m going to use this for tomorrow’s class.