Understanding Area and Shape Decomposition

This lesson for grade six focuses on understanding area through decomposition and rearrangement. Students begin with a warm-up activity to identify figures that can be used to find area. The main activity involves using GeoGebra to manipulate shapes and explore how rearranging parts of a shape does not change its area. An optional activity is provided for further exploration. The lesson concludes with practice problems to reinforce the concept that rearranging a shape's parts maintains its area.

What is the main focus of this lesson?

• Understanding volume and its properties

• Finding and understanding area, including decomposing and rearranging shapes

• Learning about different types of angles

• Exploring the concept of symmetry

In the warm-up activity, what are students asked to identify?

• Which figures have rectangles that can be used to find the area

• Which figures have triangles that can be used to find the area

• Which figures have squares that can be used to find the area

• Which figures have circles that can be used to find the area

What tool is introduced for the main activity to help students understand area?

• GeoGebra, a digital tool for manipulating shapes

• A protractor

• A calculator

• A physical ruler

What is the purpose of using GeoGebra in this lesson?

• To calculate the perimeter of shapes

• To draw perfect circles

• To measure angles accurately

• To manipulate shapes digitally and understand area

How can two small triangles be used in the shape exploration activity?

• To create a circle

• To form a square

• To make a rectangle

• To build a hexagon

What is the key takeaway from the lesson summary?

• Perimeter is the same regardless of shape arrangement

• Area changes when shapes are rearranged

• Area remains the same when shapes are rearranged

• Volume is affected by rearranging shapes

In the practice problems, what is the task involving a rectangle?

• To find the perimeter of the rectangle

• To decompose the rectangle along the diagonal and recompose it

• To calculate the volume of the rectangle

• To measure the angles of the rectangle

What is the width of a rectangle if its area is 78 square meters and its length is 13 meters?

• 5 meters

• 7 meters

• 8 meters

• 6 meters

Why is the student's statement about not finding the area of a complex shape incorrect?

• Because complex shapes cannot be measured

• Because the area can be found by decomposing the shape into smaller, manageable parts

• Because only simple shapes have measurable areas

• Because the shape is too large to measure