The warm-up for this lesson is to look at and discuss the differences between the three shapes, square, parallelogram, and rhombus, that will be the focus of this lesson. I use math shape blocks for this discussion, and I ask the student groups to create a list or a chart to share with another group. I provide students with the names for each of these shape blocks. I want their focus to be on the attributes of the shape, rather than on searching for the name. Prior to the lesson, I drew samples on the whiteboard, and I will also project an actual piece with the name labeled next to it. Our school also has manipulative resources for each of the students to reference at their desks.
The focus of this lesson is defining the differences between a parallelogram, rhombus, and square. Because these shapes are so similar it is important for students to use manipulatives to explore their differences as well as have written explanations.
The definitions for this lesson include:
I find it is helpful for students to have the definitions built in progression by adding the next attribute. That way they can rely on their prior understanding to build a new understanding. This approach is also well supported by concrete elements, such as visuals or concrete examples.
I display the definitions on the projector and then give students different shape blocks to identify for each term. The students use rulers to measure the lengths of the sides, and index cards to compare the angles. At this time, the students are not familiar with measuring angles with protractors. The use of the index cards provides an exact 90 degree angle that will match only to the square tile.
During this section of the lesson students find different three different shapes, compare these different shapes focusing on the attributes, and identify the shape. I am looking for students to start to make comparisons using observations and patterns (MP7) while not always relying on exact measurements. It is important to change the visual plane their interactions, by making a shift in their perspective from one shape to another, rotating the paper, or visually comparing angles to improve their analysis of a shape.
Each student is given preprinted sheets with the different shapes for this activity. I use a 2-D Shape Resource from the K-5 Math Teaching resources. I cut out just the shapes for this activity, and then manipulated their size using the copy machine to make the shapes proportional in size.
Because I want my students to focus on comparing shapes for this lesson, I asked them to complete a Venn Diagram for the three shapes in this lesson. Illuminations (NCTM) has a Venn Diagram Shape sorting site to engage students in this activity. My students work on this site at the end of this lesson, and again during their technology class later in the day. This creates a cross-curricular lesson experience for both the students and teachers.