What is Number Sense?
Number sense is a broad term that reflects a deep understanding of numbers – what they represent and how they behave. The Curriculum and Evaluation Standards (NCTM, 1989) describe five key elements of number sense:
- Number meaning,
- Number relationships,
- Number magnitude,
- Operations involving numbers, and
- Referents for numbers and quantities.
One of the primary goals of mathematics education in the elementary grades is to build number sense. Manipulatives are a key tool and there are two important attributes to consider. These models can be proportional or non-proportional. They can also be groupable or pre-grouped. Developmentally, proportional models help students understand number magnitude and groupable models help them see number relationships. Over the course of instruction, students should have experience with a wide range of models.
This webinar features Cuisenaire Rods, Rekenreks, and Place Value Chips. We cannot share all the uses of these tools in a single session; the webinar shares examples of activities that are most closely related to number sense.
Cuisenaire Rods include rods of 10 different colors, each corresponding to a specific length. White rods, the shortest, are 1 cm long. Orange rods, the longest, are 10 cm long. Rods allow students to explore all fundamental math concepts, including addition and patterning, multiplication, division, fractions and decimals, and data analysis. Learn more...
Uses of Cuisenaire Rods modeled in the webinar
- Counting – 1:1 correspondence, one more/one less
- Subitizing – seeing a number as a whole entity, not a collection of single items
- Fact Families – how many ways can you make a train of a given length/value?
- Modeling Operations
The Rekenrek, or arithmetic rack, was developed by Adrian Treffers, a researcher at the Freudenthal Institute in Holland. A common version consists of twenty beads on a frame. The beads are organized in two rows of ten, where five are red and five are white on each row.
Uses of the Rekenrek modeled in the webinar
- Representing Numbers
- Addition & Subtraction - counting on/counting back
- Benchmark Numbers - 5 and 10
Place Value Chips
Place Value Chips are colored counters where each color is labeled with a different place value amount. Green chips represent hundreds while pink chips represent tens, for example. They are used to model numbers and operations, especially with large numbers, where base ten blocks and other proportional tools are not practical.
Uses of Place Value Chips modeled in the webinar
- Division - whole numbers
National Council of Teachers of Mathematics (NCTM). Curriculum and Evaluation
Standards for School Mathematics. Reston, Va.: NCTM, 1989.