Triangle Area = Half of Corresponding Rectangle (Prime and Composite Areas) (K-2nd Grade)(Tuesday-Friday only; not Monday classes)

Last week we explored the area of rectangles by looking at the multiplication of dimensions. It is only logical to extend this lesson to looking at the area of each rectangles corresponding triangle as exactly one half. For example, if a rectangle of dimension 2 x 5 has an area of 10, then a right triangle with the same perpendicular dimensions has an area of half of 2 x 5 which is 5 square units.

The children first indicated next to each of the first 25 whole numbers whether it was prime (P) or composite (C) (has more than one rectangle or said another way, factors other than one and itself). If the rectangle area had more than one rectangle representing the number such as 12 which has 3 rectangles (1 by 12, 2 by 6, and 4 by 3), then it is composite.

Then, I had the children draw diagonals from vertex to opposite vertex in each rectangle to create triangles which area are exactly half that of the corresponding rectangle. The children were challenged to write the area of the triangle even for the odd numbered areas. The way I taught them to think of half of an odd number is to first break the odd number up into 1 and the highest even number (for example, 9 = 8 + 1) so if we take half of the even number 8 (which is 4) and half of the number 1 (which is 1/2), we then need only to add the two halves together so 4 plus 1/2 is 4 1/2.

The children were given ample graph paper to create their own rectangles to cut in half.