Arrays Make Math Easy to Visualize

As young mathematicians, we are exploring the use of arrays to help us with multiplication. It is imperative that we develop strong visual images of multiplication to develop conceptual strategies for solving multiplication problems. When we can clearly visualize how the numbers being multiplied are related, we can develop flexible, efficient, and accurate strategies for solving any multiplication problems.

One way we are learning to visualize these relationships is through the use of arrays. An array is a rectangular arrangement of an equal number of items in rows and columns. Arrays can be helpful when solving more “difficult” multiplication situations. Being able to visualize how to break multiplication problems into parts becomes even more important when we begin to solve multi-digit problems.

The following is an example of how we can split an array into smaller arrays making it easier to find the product.

Another way we can lay a strong foundation for multiplication is to practice skip counting by multiples of numbers 2-12. The goal is to skip count fluently (within 3 seconds) from one multiple to the next.This task can be practiced at home, between commercial breaks, or even in the car. Being able to skip count fluently will undoubtedly help us in our work with multiplication and division. Check out this website that helps with skip counting.

Comparing Arrays

Last week in Math Workshop, our young mathematicians spent time arranging different amounts of chairs into rows and columns (arrays). We looked first at ways to arrange 12 chairs. Then, during Work Session students paired up to explore with two other arrangements. Exploring with the numbers 9, 15-21, 23-25, 27, and 30 helped us to see how differently numbers can be arranged, and gave us the opportunity to discuss the similarities and differences among the varying arrays.  

For example, look at the arrangement of 16 and 17 chairs below:

What do you notice about these arrays? Do any of the arrays have a special or unique shape? What do you notice about the number of arrays that can be made with 16 chairs compared to 17 chairs?

Hopefully, you notice that 16 chairs can be arranged in several different arrays. That is because it has many factors: 1, 2, 4, 8, 16. A number that has more than two factors is called a composite number. You probably noticed that 17 only has two arrays. This is because 17 is a prime number. Any number that has only two factors, one and itself, is a prime number. The factors of 17 are 17 and 1.Also, you may have noticed that 16 can be arranged into a perfect square with 4 rows and 4 columns. Any number that has an array that is a square is a square number.  Our young mathematicians talked about square numbers when we analyzed the arrays for 9 (3x3) and 25 (5x5).

Students also realized that you could skip count by either the column or the row to get the product. Sixteen, for example, has an array that is a 2x8. You can count by 2's eight times... 2, 4, 6, 8, 10, 12, 14, 16 or you can count by 8's two times... 8, 16.

Stay tuned this week as our young mathematicians learn how to decompose an array to make a more difficult multiplication equation simpler.

What is a Gizmo?

Gizmos are online simulations that power inquiry and understanding. Gizmos is one of the programs we will be using to explore on the laptop.

Your child has a log-in and password for Gizmos (as of 9-19-11) in the back of his/her planner. We have selected several introductory math simulations for students to use. These include:

1. Cannonball Clowns (estimation)

2. Rounding Whole Numbers

3. Target Sum Card Game (Close to 100)

4. Number Line Frog Hop (Addition and Subtraction)

We have also selected several science simulations that align with our current unit of study, Plants. These include:
1. Growing Plants (students are able to change variables in order to test how plants grow best)

2. Germination

As we explore more Gizmos in class, we will make them available on your child's account. In order to access your child's account, use the navigation bar on the right side of this blog. Under the heading "Our Favorite Math Sites," choose Gizmos. This will be available for the remainder of this school year.

What is your favorite Gizmos so far? :)