Discovering a Formula to Calculate Area

Unit of Study 15: Understand AreaGlobal Concept Guide: 2 of 3

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

make problems relevant to students and deepen their understanding.

In this GCG students should begin to abstract the idea of area by representing it symbolically using a formula.

Concrete Pictorial Abstract

Do not rush to reveal the formula prematurely. It should be DISCOVERED by students through continued exploration.

Day 1 The focus of day 1 is generating a formula to calculate area.

Avoid beginning by introducing students to the formula (l x w). Let them discover it. Instead, have students practice calculating the areas of various rectangles and generate a common rule for doing so.

Sample Task: Provide each student with a bag of 10 color tiles. Have them try and cover a rectangle where they will not have enough tiles to finish. Students will have to grapple with how to find the area, or fully cover the inside of the rectangle. They should come to realize that they are building an array when they are tiling, and that arrays are made of equal groups. Ask questions about the operations used when working with equal groups only. Then have students come up with an expression that represents how they calculated the area of the rectangle. Have them test the expression on many rectangles. Does it always work? How come?

Example:

Day 2 The focus of day 2 is using an array to find the area of a rectangle.

Sample Task: “Mowing for Money.” Students roll dice to determine lawn dimensions and use grid paper to compute areas to find the amount of money they will receive for mowing that lawn.

Students will share their strategies for finding the areas of the lawn. Some students will choose to use repeated addition of the length of one side of the rectangle, some students will count each square unit n the rectangle, and other students may multiply the dimensions to find the area. This activity further reinforces the concept of building and using arrays to find the area of a rectangle.

“By having students share their strategies, more students can be exposed to the use of multiplication in this context.” –Van De Walle

Enrich/Reteach/Intervention Reteach

Have students work with a partner to make an array that has 3 rows with 4 tiles, no spaces. Write a number sentence for the array. Explain that each tile is a square unit, remind them that area is the number of square units that cover a shape. Ask: How can you use multiplication to find the area of a rectangle? Repeat using rectangles of different dimensions.

Enrich: Students will find the area for each room of a given floor plan.

Mystery Mansion Measure