A list of strategies that is ordered from the most simplistic strategy to more complex strategies. Within each category (counting, addition, subtraction, multiplication, and division) the strategies are separated into three categories: concrete, pictoral, and abstract. Teachers have to bridge the learning from when students use manipulatives and then try to apply that knowledge to abstract word problems. This document assists in bridging that gap. Teachers can utilize this list to know how to question students to the next level of learning and also assist students in what strategies to fall back on if they are struggling. One example is when a student is having a difficult time on solving a word problem you would look back at the strategies they can use when drawing a picture. another example is if students understand how to solve a problem using manipulatives, you bring them to the next step by representing the manipulatives with a drawing. Some of the strategies include decomposition, decomposition, and compensation. This document could also assist parents in understanding more conceptual strategies for solving problems instead of relying on the standard algorithm.