Problems and Problem Solving - Ministry of Education
Problems and Problem Solving - Ministry of Education
Problems and Problem Solving - Ministry of Education
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There are three triangles in the diagram below. The diagram has a total <strong>of</strong><br />
seven lines.<br />
Michelle is trying to figure out how many lines would be in diagrams which have<br />
from three up to nine triangles. So far she knows that a diagram with:<br />
• five triangles would have 11 lines; <strong>and</strong><br />
• nine triangles would have 19 lines.<br />
Help her to determine the number <strong>of</strong> lines for the diagrams that she has not drawn<br />
as yet.<br />
Drawing a graph to represent the information known thus far helps (see graph). Even though the<br />
graph shows the number <strong>of</strong> lines for diagrams with 3, 5 <strong>and</strong> 9 triangles, we can also determine<br />
the number <strong>of</strong> lines in diagrams with 1 – 9 triangles. For example, by reading the graph we can<br />
deduce that a diagram having:<br />
•y 4 triangles will have 9 lines; <strong>and</strong><br />
•y 7 triangles will have 15 lines, <strong>and</strong> so on.<br />
48 PROBLEMS AND PROBLEM SOLVING<br />
<strong>Problem</strong><strong>Solving</strong>.indd 48<br />
8/24/12 6:56:01 PM
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