Formative Assessment 79

Assessment Problem: 

65 + 49 =
58 + 79 =
126 + 199 =
Tell me how you solved this mentally.

Common Responses: 

65 + 49 = (64 + 1) + (50 - 1) = 64 + 50 = 114.

Mathematical Issues: 

The move from elementary arithmetic to algebra requires students to build on previously acquired knowledge, but to use entirely new types of thinking. Algebra becomes more meaningful as students face problems that cannot be solved with arithmetic. Problems with two unknowns are good examples, but are probably too difficult to use as a beginning point in the teaching of algebra.

Variables & Expressions
Arithmetic Compensation
Common Core Standards: 
6.EE Expressions and Equations
Research References: 
Cortes, A. V., G.; & Kavafian, N. . (1990). From arithmetic to algebra: Negotiating a jump in the learning process. Paper presented at the Psychology of Mathematics Education. Britt, M., & Irwin, K. (2008). Algebraic thinking with and without algebraic representation: a three-year longitudinal study. ZDM, 40(1), 39-53. “The ideas of algebra, K-1; 1988; National Council of Teachers of Mathematics” especially the papers by Carolyn Kieran and by Zalman Usiskyn The ideas of Y. Chevallard and E. Filloy