Groups randomly draw a number (8 - 17) from a bag. Using Color Tiles or orange Pattern Blocks, students make as many filled-in rectangles (squares are rectangles) as they can using that number of squares indicated by the number they drew. They recorded their rectangles on 1" grid paper, cut them out, and glue or tape them on a chart.
Students then discuss the patterns and here's what they observed...
| Shared by Marengo Elementary School | |
| Ben: | The area is the same as the number of blocks used. |
| Dashiell and Ben: | In the single row rectangles, the perimeter always goes up 2. Each time you add the additional block the inside (common sides) are not counted in the perimeter. |
| Ben: | In the single row rectangles, if you subtract the area from the perimeter for the first rectangle the answer is 3 (P - A = 3 or 4 - 1 = 3). As you do the same for each additional rectangle in sequence, the answer goes up by 1 each time. (example: 6 - 2 = 4 for the second rectangle and 8 - 3 = 5 for the third rectangle). |
| Dashiell: | When finding the perimeter for the single row of rectangles, double the long side and add 2 (P = 2s +2) To find the perimeter for the double row of rectangles, double the long side and add 4 (P=2s +4) To find the perimeter for the triple row of rectangles, double the long side and add 6 (P = 2s +6) |
| Nikolai and Wayne: | In the double row rectangles the difference between the perimeter and area is always 4. (P - A = 4) |
| Wayne: | Only the even numbers can make rectangles in the double row rectangles. |