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GRED 505 (Topics in mathematics for elementary teachers)
Assignment 5: Geometrical applications of operations on fractions
Brain Teaser. On an electronic (computational) geoboard, find all rectangles
with area numerically equal to perimeter.
Alternative Problem 1. In how many ways can one cover completely (i.e.,
without gaps or overlaps) fraction circle 1/2 using two other fraction circles?
Represent your finding both through fractions and fraction circles. Provide a
mathematical proof (formal demonstration) of your finding. Use algebra (i.e.,
equations) to show the relationship between this problem and Brain Teaser.
Alternative Problem 2. In how many ways can one cover completely (i.e.,
without gaps or overlaps) fraction circle 1/3 using two other fraction circles?
Represent your finding both through fractions and fraction circles. Provide a
mathematical proof (formal demonstration) of your finding.
Alternative Problem 3. In how many ways can one cover completely (i.e.,
without gaps or overlaps) fraction circle 1/4 using two other fraction circles?
Represent your finding both through fractions and fraction circles. Provide a
mathematical proof (formal demonstration) of your finding.
Task 1. The sum of two adjacent sides of a rectangle is called the semi-perimeter.
On a geoboard, find all rectangles with area and semi-perimeter being numerically
in the ratio of a) 3:1; b) 4 :1. How are Task 1 and the last two problems related?
Use algebra (i.e., equations) to show the relationship between: (i) case a) and
Alternative Problem 2; (ii) case b) and Alternative Problem 3.
Instructor Sergei Abramovich
