Calculating the Area of Rectangles

Ms. Bradbury's third grade class has been learning multiplication facts and how to use them to solve problems. Today they are learning how to calculate area by working on finding the size of a two-dimensional flat surface. Ms. Bradbury begins with a hands-on activity that is easy for them to visualize and remember. She gives each student diagrams of squares or rectangles and a bag of square crackers. They fill each square or rectangle with the crackers and count the number of crackers they use to come up with a measurement. They label the size of each shape as the number of square crackers.

Next Ms. Bradbury uses her laptop and a projector to show the students how to do a similar activity on the computer. Using Cacoo, a collaborative diagramming tool, she draws a large rectangle on the screen and drags enough squares on top of the rectangle to fill it. There are 2 rows of 3 squares. The students then count the squares and label the area of this as 6 square Cacoos, an invented unit of measurement.

Ms. Bradbury then uses the group function to connect the 3 squares in a row so that they can be moved as a unit. The class discusses that the rows are equal and that 2 rows of 3 squares equals 6. Next, she shows them several ways to write this as a formula: 3 + 3 = 6 or 3 x 2 = 6. She shows them that if they know the number of squares in a row and the number of rows, they can calculate the area without filling in all the squares. Finally, she has the students work in pairs using Cacoo and a laptop. One student draws a rectangle on the screen and the other drags squares into the rectangle. Together, the students count, add, or multiply to calculate the area.

Ms. Bradbury understands that the physical arrangement of the classroom needs to support this type of interaction. Before she begins this activity she helps the students arrange their desks so that each pair of students can easily see and access the laptop.

Ms. Bradbury asks the students who are having difficulty with the concept of area to study a learning object on the Internet. The learning object is found at a site called TV411. It provides a short digital lesson with content, practice problems, and assessments. They use their tablets or smartphones for this activity.

When students understand the concept of area, but need to build fluency with multiplication facts, Ms. Bradbury gives them time to do skill building exercises using an application such as Math Magician or IXL Math on their tablets. The exercises present students with 10 multiplication problems and give them feedback on their accuracy and the time required to solve the problems. The goal is to complete 10 problems in under a minute. Several times a week Ms. Bradbury writes a goal on the whiteboard for learning multiplication facts to 12. For example, on Monday, she may challenge the students to learn the multiplication facts for 5 and Wednesday for 7. She asks the students to show her the screen of their tablet when they have achieved 100% for that multiplication fact.

Finally, Ms. Bradbury wants to assess how well the students understand the concept of area and their multiplication facts. She uses an online assessment tool Quia Web to create a quiz. The tool allows her to create multiple choice, matching, short answer, and many other types of questions. Using their laptops, the students take the quiz. Ms. Bradbury uses the automatic grading to identify the problems a student missed and the answers they chose.

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