Early success in basic fact retrieval may be due to memorization rather than conceptual development. Telling stories about adding and subtracting enhances conceptual development because students see the story outcomes based on the operations. For example, adding stories should start with smaller quantities joined to make a larger quantity, while subtraction stories should start with larger quantities that are "taken away," resulting in smaller quantities. Drawing pictures to illustrate a story will make the abstract concepts more concrete because students can see what happens to the quantities. Conceptual understanding is more beneficial than procedural mastery in developing numerical reasoning.
While multiplication and division are usually not introduced until the third or fourth grade, students can begin to see the power of multiplication through repeated addition. Start with a quantity such as four. Depict four tires on a car, and then have the students add on additional cars to see that each car increases the number of tires by four. By displaying the total number of tires on a chart next to the number of cars, the students will begin to relate the multiples to the factors.
Repeated subtraction can be used to preview division. Start with a higher quantity such as 40, and then continue to subtract four from that number. Students will see how many times the number four can be subtracted from 40 until zero is reached.
By observing basic geometric shapes such as rectangles, squares and triangles, concepts such as parallel and perpendicular, similar and congruent, and polygon classification can be introduced. Students can determine how shapes are alike and different and begin to develop an understanding of vocabulary words used in geometry classes. Besides identifying a shape, describing a shape's properties helps promote reasoning and reflection of geometric features while developing spatial reasoning skills.
Students begin to compare sizes of various objects as early as preschool. Measurement tools such as meter sticks provide students with concrete representations of size in units of measurement. Students can begin to estimate the length of various objects as larger than or smaller than a meter. From there, students can progress to making estimations of how many meters or centimeters an object is. Another option is to display two different measurements such as 50 and 75 centimeters and direct students to find an object that is in between both measurements.
Another option is to use a customary ruler for the same activities. In addition to developing measurement and estimation skills, the use of the inch measurement also leads to the introduction of fractions.