Summary:

At the Helmwood Heights Elementary School in Elizabethtown, Kentucky, Kathy Doolittle's students use array structures to reason and conjecture about relationships between sums and products of number added and multiplied to themselves. Patterns and relationships are sought when numbers are added to themselves and when multiplied by each other. Groups are assigned one number and told to create a model of its sum and product. (If N is the assigned number, then an N x 2 array will represent its sum and an N x N array its product.) Students place their arrays on grid paper, and label each one with the symbolic solutions to the addition and multiplication problems. Each group then posts its models and solutions around the classroom so students can detect patterns, seek relationships, and discuss findings.

Standard Connection:

(Practice Standard)—Common Core Practice Standard #7—Look for and make use of structures—is evident in this fourth grade class. Here students are looking for patterns using concrete and/or pictorial models. Array structures made on grid paper helps students in their search for the patterns and relationships between sums and products found when a number is added to itself and multiplied by itself. The students see interesting connections in the array structures they create, but without access to a well-ordered collection of examples, their conjectures lack in richness. At the conclusion of the class, the students realize that they did not have enough "structure" and "order" in the arrangement of the examples for them to fully detect patterns.

(Content Standard)—The domain that best encompasses the content of this clip is Operations and Algebraic Thinking—4. OA. These fourth graders are getting experience in learning to generate and analyze patterns using array structures. They see some indications that patterns exist but sense the examples are not arranged in any kind of order, and this limits their pattern detection ability.

Questions to Consider:

What value is there to the study of patterns in arithmetic, geometry, algebra, measurement, and data analysis and probability? Why did the teacher have students create both array structures and symbolic representations for the sums and products for numbers assigned?

7. Look for and make use of structures

4.OA Operations and Algebraic Thinking