During the warm up of this lesson, I review the difference between perimeter and area. These are different, often confused by students, and math concepts that are likely to occur on the state assessment given later in the year. I choose to highlight the differences through a compare and contrast. This focus is on the difference between perimeter and area. Perimeter is measuring only one direction of length, while area is focused on measuring two directions of length and width.
Using rectangles and polygons, I ask the students to find the area and perimeter. I also ask them to provide an explanation for each of these terms. This explanation is the real focus of my warm-up, rather than on the numeric solution to area and perimeter. That work is intended to stimulate their thinking.
I use graph paper, a basic word - apple, to model how to create letters on the paper. I also draw the letters larger than single squares so that the area increases and challenges students into creating block letters rather than focusing on a single line. Although this is not necessary, it provides some challenge to the students.
Next, I focus on letters with slanted lines including k, m, n, v, w, x, y, and z. These letters will need to have special consideration depending on how the student draws the letters. These letters can individual boxes traced diagonally on the graph paper, or they can draw a straight line diagonally. The second option will result in areas that are more complicated to calculate because the students will need to combine triangular shapes. This is an option for differentiation with students' abilities for area.
During this section of the lesson one of my students commented this activity is just like the game "Minecraft". This real world connection provided the students with another opportunity to engagement with area.
During this section of the lesson the students create their names on grid paper to find the area of their own name. I encourage the students to use pencil to draw the outline, using as many rectangles as possible for each letter. This allows the students to use their skills in finding area of irregular shapes by locating rectangles and adding these areas together.
The challenge for the students exists in the letters with slanted lines such as a w or an x. If students use individual blocks, it will make it easier to calculate area. To challenge students with the connection to fractions required in the Common Core standards, students can draw diagonal lines to create half triangles to calculate area. This will also support the vertical alignment of area of triangles in fourth and fifth grade.
This student explains how he drew his name. He used individual squares to create the slanted lines on the letter K.
When the students had completed finding their area of their names, I had the students partner up with another student who had the same number of letters in their own name. This allowed them to compare how they drew the letters, determining the area, and how they divided each letter into rectangles for multiplying the length x width.
For students with the longest names, I paired them together even if they number of letters in their names did not match. They still had the opportunity to have the math discussion but they just did not have an exact comparison between their names.