Formative Assessment 78

Assessment Problem: 

Jason uses a simple method to work out problems like 27 + 15 and 34 + 19 in his head.
                    Jason’s calculation (Picture)
1) Show how to use Jason’s method to work out 298 + 57
2) Show how to use Jason’s method to work out 35.7 + 9.8
3) Use Jason’s method to work out what goes in the space: 58 + n = 60 + _______
4) Use Jason’s method to work out what goes in the space: 9.9 + k = 10 + _______
5) Use Jason’s method to work out what goes in the space: a + b = (a + c) + ______

Common Responses: 

1) 300 + 55
2) 10 + 35.5
3) 58 + n = 60 + n - 2
4) 9.9 + k = 10 + k - 0.1
5) a + b = (a + c) + (b - c)

Mathematical Issues: 

This assessment may be good for exploring students’ ability to generalize based on the structure of equations and expressions. Students found to be most able to generalize a pattern (identify the constant and the rule for any term of the sequence) were those with advanced mental strategies for additive, multiplicative, and proportional operations. Taking students from their use of strategies for numerical calculation into the generalities that could be expressed algebraically needs to be purposeful.

Domain: 
Variables & Expressions
Theme: 
Arithmetic Compensation
Common Core Standards: 
7.EE: Expressions and Equations
Research References: 
Britt, M. and K. Irwin (2008). "Algebraic thinking with and without algebraic representation: a three-year longitudinal study." ZDM 40(1): 39-53.