Posted in Geometry

Pentagon to Quadrilateral Puzzle

Puzzles involving cutting shapes and forming them into different shapes helps reinforce the idea that area do not necessarily change with change in shape. It is also a good activity for developing visualisation skill and spatial ability.

The puzzle below is from one of the leaflets at the booth of Japan Society of Mathematical Education last ICME 12 in Seoul, Korea. The original puzzle is suited for Grade 4. The instruction was to cut the pentagon along the dotted lines and then form them into the shapes shown. The shapes shown in the leaflet is a parallelogram, a rectangle, an isosceles trapezoid, and a general trapezoid. I modified the puzzle for students in the higher level. I have indicated the measure of the two angles just in case you want your students to justify that the pieces really form into quadrilaterals. This is one way to assess your students knowledge of the properties of these parallelograms, trapezoid and trapezoids as they justify each shape formed.

pentagon puzzle

Here are two solutions – rectangle and isosceles trapezoid. Form the other two shapes.

trapezium and rectangle

Posted in Geometry

Problem Solving Involving Quadrilaterals

‘To understand mathematics is to make connections.’ This is one of the central ideas in current reforms in mathematics teaching. Every question, every task a teacher prepares in his/her math classes should contribute towards strengthening the connections among concepts. There are many ways of doing this. In this post I will share one of the ways this can be done: Use the same context for different problems.

The following are some of the problems that can be formulated based on quadrilateral BADF.  You can pose these problems to your class but the best way is to simply show the diagram to the students then ask them to formulate the problems themselves.

quadrilateral

Problem #1. What is the area of the quadrilateral? Show different methods.

The solution to this question depends on the grade level of students. The one shown below can be done by a Grade 5 or 6 student. Continue reading “Problem Solving Involving Quadrilaterals”