Objects-Drawings-Symbols

Strategy 2: Objects - Drawings - Symbols
Young children solve well-structured problems by using objects – counters – to model the action in the problem. For the Jennie problem, a child will count out 5 shells, and then bring forward 3 more. At first, many children re-count them all. Over time, they develop more efficient strategies, like counting on from the first number, or counting on from the larger number. The next step in children’s strategies is to abstract the action in the problem into a simple picture.  And from here, students learn to write the action in mathematical symbols: 3 + 5 = 8

This object – drawing – symbols progression works for learning all kinds of mathematics, including fractions, decimals and percents. When older students struggle with setting up a problem symbolically, have them back up and use a drawing first to represent the situation. The drawing gives you good insight into their thinking.

Try it: Use fraction bars or fraction circles to model 1/4 + 3/8. Then make a drawing to show how to add them. Using the process involved in the drawing, develop an algorithm that can be used with the symbolic expression. The use of objects gets children to "trade" the 1/4 piece for 2 1/8 pieces, which translated into "finding common denomintors" in the drawing and symbolic expression. 2/8 + 3/8 = 5/8