A cake is shaped like a rectangle that is 13 in. long and 9 in. wide. There is one candle at each corner of the cake, and there are candles at one-inch intervals along the edges of the cake. How many candles are there in all? The length of the cake is 13 in. long, and it is 9 in. wide. There is a candle in each corner, and at one-inch intervals along the edges. The goal is to find out how many candles are on the cake. COURSE 2 LESSON Draw a Diagram and Solve a Simpler Problem

(continued) Method 1 Draw a Diagram Draw a diagram, such as the one at the right, that allows you to see where the candles are placed. There are 44 candles along the edges of the cake. COURSE 2 LESSON Draw a Diagram and Solve a Simpler Problem

(continued) Method 2 Solve a Simpler Problem Instead of solving the problem for a 9-in. by 13-in. cake, change the problem to a simpler one based on a 2-in. by 6-in. cake, and then on a 3-in. by 7-in. cake. COURSE 2 LESSON Draw a Diagram and Solve a Simpler Problem

(continued) Part of Cake First Corner Short Side Second Corner Long Side Third Corner Short Side Fourth Corner Long Side Total 2 in.  6 in. Number of Candles in.  7 in. Number of Candles COURSE 2 LESSON Draw a Diagram and Solve a Simpler Problem

(continued) There are 16 candles on a 2-in.  6-in. cake and 20 candles on a 3-in.  7-in. cake. You add 4 candles for each inch added to the length and width of the cake. So there are 44 candles on a 9-in.  13-in. cake. COURSE 2 LESSON Your first thought might have been that there are 10 candles on each short side of the cake and 14 candles on each long side, and therefore you need = 48 candles. Each side, however, shares each corner with another side, so you need = 44 candles. Draw a Diagram and Solve a Simpler Problem

1.What is the sum of the first fifty odd numbers? 2.Alan cut a log into 4 pieces in 12 minutes. How long would it take him to cut a log of the same size into 6 pieces? 2, min COURSE 2 LESSON Draw a Diagram and Solve a Simpler Problem