Early Algebra in Investigations
One goal of the Investigations curriculum is “to make the foundations of algebra … more visible to teachers and students, to expand this work in the context of students’ study of number and operations, and to deepen the focus on patterns, functions, and change.” (Algebra in the Revision)
In addition to a unit per grade level focused on patterns, functions, and change, work on early algebraic ideas is embedded in the number and operations units at each grade. This work focuses on using models, representations, and contexts to investigate and justify general claims about the properties of numbers and operations. For example, does order matter when you count? When you add? What about the other operations?
How does the curriculum help teachers identify and explore generalizations that arise in the course of students’ study of number and operations? How do students learn to describe such generalizations and consider questions like: Does this generalization apply to all numbers (that I know about)? Why does it work? How do I know? The curriculum supports teachers with this in a variety of ways.
At the Unit Level
- Algebra Connections in This Unit. These essays, which appear in every unit focused on number and operations or patterns, functions, and change, explain “how the activities and ideas of the curriculum unit are laying a foundation for students’ later work with algebra.” (p. 8 of Implementing Investigations at Grade X) For example, it might “highlight several generalizations and include examples of how students think about and represent them.” (Algebra in the Revision)
Read a Kindergarten example.
- Algebra Notes. These notes, located in the margins of Sessions, alert the teacher to activities and discussions in which algebraic ideas are likely to arise. “For example, in Grade 2, students consider whether the order of terms affects the sum in addition problems or the difference in subtraction. In Grade 3, students discuss the generalization underlying the equivalence of subtraction expressions as in the equation, 104 – 78 = 106 – 80. In Grade 5, students justify why halving one factor and doubling the other in multiplication results in the same product (e.g., 65 x 24 = 130 x 12 = 1560).” (Algebra in the Revision)
- Teacher Note: Reasoning and Proof in Mathematics. Two versions of this Teacher Note appear in grades 2-5, providing images of what “proof” looks like in the elementary grades. For example, in Grade 2, these Teacher Notes focus on equivalent problems in addition (2U6, p. 153) and adding even and odd numbers (2U8, p. 153).
- Content-related Teacher Notes (e.g. Repeating Patterns and Counting Numbers) and Dialogue Boxes (e.g. Does the Order Matter? in KU2).
At the Curriculum Level
Implementing Investigations at Grade X includes two kinds of support:
- K-5 Teacher Note: Foundations of Algebra in the Elementary Grades.
- Classroom cases that deal with algebra ideas. (Read a Grade 1 example.)
What does early algebra look and sound like in K-5?
Explore examples of students making, using, and proving generalizations they have made about number and operations in the course of their work.