This lesson's activity has students model square numbers using arrays. An array is a grouping of objects that makes equal rows. They can visually see that the array makes a square.
Additional Resources
Books
When a number is multiplied by itself, the product is called a square number. Example: 3 x 3 equals 9. When students model square numbers using arrays they can visually see that the array makes a square. An array is a grouping of objects that makes equal rows. It is important to teach students to read arrays by rows first, and then columns.
2. Become effective problem solvers by selecting appropriate methods, employing a variety of strategies, and exploring alternative approaches to solve problems.
Invitation to Learn
Pass out a small bag of centimeter cubes to each student. Explain that the students are going to make arrays using the cubes. An array is a grouping of objects in equal rows. Ask the students to count out nine cubes. Have students share their arrays as they make them and then model them on the overhead. Students should come up with 1 x 9, 9 x 1, and 3 x 3. These numbers represent the factors of nine. Ask the students if they notice anything about the 3x3 array? Explain that nine is a square number. Can anyone tell why it is called a square number? Are there more square numbers?
Instructional Procedure
Family Connections
Research Basis
Jensen, E. (2000). Moving with the brain in mind. Educational Leadership, 58 (3), 34-37. Retrieved January 18, 2007 from from http://www.newsletteronline.com
Brain research has shown that physical movement -- moving, stretching, and acting out concepts, can increase the learning process. Active learners remember the information longer and better than sedentary learners. Teachers should have students: engage in a variety of postures throughout the day, engage in movement during class, use their bodies to demonstrate concepts, role play and include a variety of physical activities to help students learn and if these ideas are not possible then students should at least stop and stretch every 20 minutes.
Marzano, R.J., Pickering, D.J., & Pollock, J.E. (2001). Nonlinguistic Representations. In classroom instruction that works, (72-83). Alexandria, Virginia: ASCD.
Researchers believe that students learn and store information in two different ways. The first form is a linguistic form where the learner either listens to the information or reads it in a book. In the second form, non-linguistic, the learner forms a mental image or a physical sensation by touching, smelling, listening, tasting, or kinesthetic association. Research has shown that when students learn using both forms their achievement improves greatly. After a non-linguistic form of learning has taken place students should be asked to explain and justify what they have learned. When students are able to explain their thinking and reasoning to others their knowledge increases and they are able to recall it easier. Non-linguistic representations include: making physical models, using manipulatives, drawing pictures, graphic organizers, or engaging in kinesthetic activities.