Transcript Draw a Diagram and Solve a Simpler Problem

COURSE 2 LESSON 5-3
Draw a Diagram and Solve a Simpler Problem
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.
5-3
COURSE 2 LESSON 5-3
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.
5-3
COURSE 2 LESSON 5-3
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.
5-3
COURSE 2 LESSON 5-3
Draw a Diagram and Solve a Simpler Problem
(continued)
2 in.  6 in.
Number of Candles
1
3 in.  7 in.
Number of Candles
1
Short Side
1
2
Second Corner
1
1
Long Side
5
6
Third Corner
1
1
Short Side
1
2
Fourth Corner
1
1
Long Side
5
6
Total
16
20
Part of Cake
First Corner
5-3
COURSE 2 LESSON 5-3
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.
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
10 + 10 + 14 + 14 = 48 candles. Each side, however, shares each corner with
another side, so you need 9 + 9 + 13 + 13 = 44 candles.
5-3
COURSE 2 LESSON 5-3
Draw a Diagram and Solve a Simpler Problem
1. What is the sum of the first fifty odd numbers?
2,500
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?
20 min
5-3