Department of Mathematics and Science Education

Do It Session

August 23, 2005

Jim Wilson

## http://www.intermath-uga.gatech.edu/topics/algebra/functns/r13.htm

Hansel has goldfish that quadruple, or become four times as many, every month. Gretel has goldfish that increase by 20 every month. Right now, Hansel has 4 goldfish and Gretel has 128 goldfish. In how many months will they have the same number of goldfish? Show how you arrived at your answer.

(Source: Adapted from Mathematics Teaching in the Middle School, Nov-Dec 1995).

This is an investigation from Project InterMath from the Algebra topics.

## How does the ratio AD:DB compare with the ratio area of triangle ADC:area of triangle DCB ? Explain.

3. 6th grade GPS task:  Similar Figures (with added questions involving the ratios of perimeter and area)

a) Triangle ECD is similar to triangle EAB. What is the scale factor for the two triangles? Explain how you found the scale factor. Find side AB.  Find the perimeters of triangle ECD and triangle EAB.  What is the ratio of the perimeters?  Is it the same or different from the scale factor?  Why do you think it is the same or different?

4. 6th grade GPS task:  Similar Figures (with added questions involving the ratios of perimeter and area)

Gregory is in the sixth grade and is working on a project having to do with agricultural use of land in South Georgia. He has a small copy of a map of a farm in his area but needs to make a much larger version on which he can record all accumulated data. The map he wants to enlarge is shown below.

He has decided that he wants the length of the northern boundary of the farm for the larger version to be 24 inches. How would you explain to him what he should do to find the lengths of the other sides so that the enlarged map is a scale drawing of the smaller one?

Find the area and perimeter of the original map of the farm and the larger map. Find the ratios of the areas and of the perimeters. How do these ratios relate to the scale factor of the maps? Are they the same ratios or different? Why do you think they are the same or different?