In our school, students are grouped during math across the entire grade. This means that students are moved into the right math class for their needs. I teach third grade math to students on grade level. Several of my students attend a third grade teacher's class who uses the fourth grade standards. On this particular day, we are not switching classes due to testing, so I need to do a project all of my students can participate in despite the different levels. I chose adding, multiplying, or simply naming fractions. This lesson does require some preparation of fraction strips. I made mine from brightly colored construction paper, using the same color consistently to represent specific unit fractions.
To begin the lesson, I show three photos of quilts (included here in resources). I ask the students to discuss with their shoulder partner if they see any fractional pieces in the photos and to be specific and name what fractional units they think they are seeing.
In one of the examples, the students did not see any fractional pieces, and they defend by saying nothing "equaled" anything else.
In the two other examples, they found many fractions, and I am sure we could have come up with more if given the time.
Next, I tell students we would be using fractions to create our own "paper" quilt. The quilt squares will also be labeled to show their fractional value as related to the whole (8 x 8 square).
In order to have the students create their own quilt square, I put out several size pieces of construction paper that I pre-cut. I begin with an 8 x 8 square. I also place out pieces cut into 4 x 4, 2 x 2, 2 x 4, and 1 x 1. I tell the students they can design any pattern they want, but can only use these fractional parts, which I did not name.
I listen in as students design, to determine if they are using the mathematical language of fractions. The design of this square is relatively easy and fun. The next step is when I begin watching for problem solving strategies and concrete knowledge of naming fractions.
As the students design, I begin asking them to name the colors represented on their whole. Below is one of the students doing so. As she was speaking with me, she ran into a problem.
In this clip, she figures out a way to solve the problem and name her fractional piece.
I am very impressed with this student's response regarding his design efforts. He obviously began with an outcome in mind, which he explains in this video.
Following the design and naming session, I ask the students to turn their squares over and begin writing equations to represent their work.
This was telling, as all students were able to list each fractional piece and add them together. However, some saw that they could add like fractions together and even write multiplication problems for like fractions.
As a challenge later this week, I will have the group write about the fractions they see on our whole quilt!