Geometry in First and Fourth Grades

In math, topics often cycle from grade to grade and the students delve deeper and deeper into important concepts.  I was recently able to see how the concepts taught in one grade stick with students as they continue on with math from year to year.  In both first grade and fourth grades, we have been working on geometry.  In first grade, this meant that were identifying features of shapes, such as number of sides and corners, and working on learning the names for shapes.  The kids were really proud of themselves for remembering tricky words like hexagon and trapezoid, and for remembering that a “diamond” is not a shape, but a rhombus is.  First graders applied their knowledge of shapes by using iPads to take photos of shapes throughout the lower school.  They eagerly looked for circles, squares, rectangles, triangles, trapezoids, rhombuses and hexagons.

In fourth grade, we have been studying a related geometry concept of area and perimeter.  The students began this study by using 8 squares and seeing how many possible perimeters there were for shapes made with this number of cubes.  They then tried the same thing with an odd number of squares (11 squares) and they quickly realized that all of the possible perimeters found with both 8 and 11 squares were even numbers.  As we ended the class, I asked the question, “Is there a formula for finding the greatest possible perimeter for any number of squares?”  The students have been thinking about it, and we will soon be discovering that by doubling the number and adding two, you can find the greatest possible perimeter.  They have also been looking for the shape that consistently creates this perimeter, and when they figure out the configuration of squares the formula will soon become evident.