Most of us are familiar with ten-frames as a structure for making sense of numbers in the primary grades. Students use it to learn facts, to represent numbers, and to help them think through problems.
This is a ten frame representing the number 4. It also could be used to represent a variety of facts including 10 - 6 = 4. These ten frames make sense to our little kiddos. They are prevalent throughout our classrooms. They are the concrete representation of numbers when students use the manipulatives to build the numbers and the pictorial representation when put onto paper. The concrete and representational stages are very important to conceptual understanding before our students move into the abstract stage which just uses numbers and symbols.
But what if we tried to bridge the gap by using ten frames with our older students in grades 3, 4, and 5? Certainly, there might be some of our students who still need this ten frame to help them make sense of some basic number problems, but what if we looked at it differently? What if the frame represents 100 and the counters are each worth 10? This ten frame could help our kiddos make to see that 40 is closer to 0 than to 100. It might help them to better conceptualize our base ten system. Similarly, the counters could represent 100 and the frame could be worth 1000...
Having some manipulatives and visuals that are common with our students from K-5 should lead to a stronger conceptual understanding of numbers. Our students use base ten blocks well, but I believe this would be a next step to help them build their deep understanding of our numbers and how they work. Besides, a ten frame is often easier for a student to draw independently to represent their thinking than base ten blocks or a 100 grid. To show ones in the grid above, students could break one of the ten squares into a smaller ten frame as shown below.
This ten frame could represent 43. It could represent 430. Using these frames in a variety of contexts will help our students to better understand how numbers work.
Whole numbers in ten frames are great, but what if we used the above ten frame to show 4.3? Students can easily visualize the 4 ones and then the next one has been decomposed into 10 parts/tenths. Using these visuals would help adding, subtracting, and rounding easier.
Similarly, the above ten frame could represent o.43 with each counter being worth a tenth and each of the little counters representing a hundredth.
Using these ten frames in a variety of ways will help our students to gain a stronger foundation of place value. By changing the whole of the ten frame, the number being represented inside changes. For some of our kids, it will provide them with an easier way to record numbers. For others who struggle with place value, it might offer them a familiar format that they can understand.
Do you have other ideas for using ten frames throughout grade school? Please feel free to share in the comments below.
