How early should we teach words like half, thirds, and fourths to children? I know that I have often heard that we give young children things they are not developmentally ready for, and I agree. But when it comes to having language identify a concrete experience, I think children can handle it. I was measuring lace and ribbon for a project, and my youngest daughter, Lilly, wanted to help. I gave her my measuring tape, and she proceeded to take it and “measure things.” I recognized words like two, half, five, and more in the midst of her conversation. She is only two and a half years old. She longs to be just like her brother and sister, so she loves to use words she hears them say. I’m not intentionally trying to teach her these concepts, just exposing her to a lot of language. The concept of “half” will come. Click here to check out a previous post about Bethany’s experience (my 1st grade daughter) with words like half and a fantastic book that helped her explore fractions.
The geometry domain for K-2 teachers uses the language and develops a foundation for the concepts of fractions. In those clusters students are going to partition shapes, decompose/compose shapes, and reason with shapes.
I’ve typed up the geometry standards that are foundational to fractions. Click on the image to download it. It is interesting to me that the writers continue to label the cluster “Reason with shapes and their attributes.” So what does reasoning look like for students? This is where the mathematical practices are found. When you reason you are “making sense,” moving from “quantitative” (concrete) to the “abstract,” “constructing viable arguments and critiquing the reasoning of others,” and “looking for structure.” Since students need to be communicating about this, I’m working on some sentence frames that I’ll blog about soon.
I was training some fantastic teachers at Kepler Neighborhood School in downtown Fresno, and we composed shapes using pipe cleaners and wikki sticks and then partitioned them.
The wikki sticks are preferred because they can stick to the table, and they are easy to cut when you need to make a partition.
You can also fold or build a half to make a visual that proves it is one-half of the whole. Geoboards are another tool students could use to compose shapes and partition them.
As students manipulate and explore these shapes, they are preparing for fraction concepts. Students need to build an expertise in partitioning shapes and communicating about them using the language of fractions. These experiences of decomposing/composing and partitioning with shapes will support students’ development of fractions in the future and are highly engaging and hands-on. So lets keep student’s hands and minds engaged in mathematics.