Formative Assessment 133

Assessment Problem: 

Problem 1: Grandmother Rachel mixed 20 kilograms of jam containing 15% sugar with 15 kilograms of jam containing 40% sugar. How many kilograms of
sugar should be added to the new mixture in order to obtain jam that contains 35% sugar?

Common Responses: 

Many students’ difficulties stem from being unable to chunk and label information. When presenting these problems, asks students to first translate the information into a table with labeled columns/rows. Common difficulties with this task include:
-Being too vague with labels (e.g. labeling a column “amount")
-Mislabeling (e.g. labeling a column “mixture” but filling in values that correspond to kilograms of sugar)

Mathematical Issues: 

Students who are able to make categorical self-explanations while translating an algebra word problem into a table are more successful at finding a correct solution to the problem. A categorical self-explanation for this type of problem is the act of naming the rows and/or columns in a table. These problems can be used to assess how students are categorizing and processing information from word problems.

Modeling & Word Problems
Common Core Standards: 
7.RP: Ratios and Proportional Relationships
Research References: 
Neuman, Y., & Schwarz, B. (2000). Substituting one mystery for another: the role of self-explanations in solving algebra word-problems. Learning and Instruction, 10(3), 203-220.