Thursday Tool School: Math Tools for Computational Fluency

Today's tools are Base 10 blocks. I can remember when I first started teaching, the tool we had the most of was Base 10 blocks. We had an abundance of them! Each teacher had a large classroom set or a tub of random ones; however, I did not know what to do with them as an upper elementary school teacher. Over the years though, I have discovered some essential uses that I will share with you over the next few weeks.

Both as a teacher and as a math coach, I see students struggling with understanding basic operations. Specifically, I see students struggle to demonstrate true understanding of subtraction with zeros. Typically, I see students slashing zeros and adding numbers above them with no meaning whatsoever-- a meaningless process because it is not tied to a conceptual understanding. I feel like that is one of the best uses for Base 10 blocks, to truly illustrate this concept in a more meaningful and concrete way.

Modeling addition and subtraction with Base 10 blocks is a great way to get students to "see" a model and connect it to the algorithm at the same time. In the picture below, I have modeled how Base 10 blocks can be used side-by-side with the subtraction algorithm to illustrate the connection between real-life "borrowing" (regrouping) and the slashing and changing quantities students do.

When connected to a model, students are more easily able to see why the zero in the tens place eventually becomes nine tens and the zero in the ones place becomes ten ones. This is often hard for students to see as they do not understand that the zero in the tens place first became ten tens after regrouping the hundred into tens and that the second zero became ten after regrouping one of the tens into ten ones.

Below, I have included some games to practice using a model and accompanying algorithm to understand regrouping with addition and subtraction.

• Race to a Flat- Students roll two dice (6- or 10-sided), add the numbers on the dice together, take that many units, or rods and units, to add to their total, and regroup their quantity until they have achieved a flat (100). (Variation-- Play "Race to a Cube (1,000)" following the same directions but using one die as the tens place and the other die as the ones place. (Two different colored die work great here.)
• Race to Zero- Beginning with a flat, students roll two dice (6- or 10-sided), add the numbers on the dice together, subtract that many units from their collection, and  regroup as needed until they reach zero. (Variation-- Play "Race to Zero" from a cube (1,000) following the same directions but using one die as the tens place and the other die as the ones place. (Two different colored die work great here.)

Sound Off! How do you use Base 10 blocks in the classroom?