Estimating and Exploring Area

Unit of Study 15: Understand AreaGlobal Concept Guide: 1of 3

Content Development Make sure to provide real world applications when working with area to

make problems relevant to students and deepen their understanding.

Many students have difficulty distinguishing between the area and the perimeter of figures. Provide opportunities for students to make connections to perimeter and area. Make sure students know the difference between both.

We want students to move from modeling area concretely to pictorially by the end of this Unit of Study. However during this GCG, using manipulatives to tile figures when finding their area is encouraged.

Tiling develops the idea that the area of a figure is measured by covering its inside entirely with the same unit, without overlapping.

The formula for finding the area of a rectangle will be covered in the next GCG and should not be introduced at this time.

Day 1 The focus of day 1 is estimating the area of plane shapes. Make sure to

provide students with shapes that are not all polygons.

Example:

When introducing area, begin by using the attributes of plane figures to estimate their areas. Then have students use manipulatives and tiling to find the actual areas. Students should constantly be comparing their estimates to actual measures and evaluating for reasonableness.

Sample Task: Students can estimate the area of classroom surfaces and then use post it notes to compare their estimate to the actual area found.

Day 2 The focus of day 2 is calculating the area of plane shapes.

Students can use a variety of strategies to calculate area. Tiling and grid paper are appropriate at this stage. If students are ready, they can begin to use the attributes of shapes (side lengths) to calculate area through pictorial tiling. • Example: If a student is given Figure 1, they can draw auxiliary lines to

subdivide it into an array based on the length of the figure’s sides (Figure 2). They can then count the tiles to find the area.

Figure 1: Figure 2:

They should begin to compare the areas of different shapes as well as create multiple shapes with the same area and different perimeters.

Enrich/Reteach/Intervention Reteach:

The intervention activity listed within the lesson “Cover Me” located on the GCG under Lesson Ideas can be utilized. Students can use outlined shapes and cover them with tangram pieces to reinforce the concept of the conservation of area.

Students can also engage in more practice using tiling to find the area of plane figures.

Enrich : You can utilize “Fill ‘Er Up” located on the GCG under Lesson Ideas.

Students find the area of large spaces using at least two different units. During the Extension activity on the lesson “Changing Areas” students

will build two color tile shapes, one with a perimeter of 20 units and having the least possible area and the other with the same perimeter and having the greatest possible area.

Literature Connection