## Developing Multidigit Number Sense

Students in primary grades have developed a notion of counting but have a difficult time studying subject matter that contains large numbers, such as the population of a country, distances to the planets and stars, and the cost of running a space mission. Although they are fascinated by large quantities, they have a limited understanding of them and often express exaggerated amounts in their conversation as in, “There were thousands of people at my birthday party.” When students lack an understanding of large numbers, they cannot reason effectively with the information they are given. In this situation, teachers need to develop the students’ ability to process large numbers, that is, develop their multidigit number sense.

The concept of multidigit number sense refers to the students’ understanding of, and flexibility in, using numbers of more than one

digit. It includes intuitive feelings for large numbers and their uses as well as the ability to make judgments about the reasonableness of multidigit numbers in different problem situations (Jones, Thornton, & Putt, 1994). Because of the complexity of this topic, teachers should select meaningful activities that help students make sense of how large numbers are used in context.

Diezmann and English (2001) have found success working with students in the primary grades by selecting activities that help the students read large numbers, develop meaningful examples for large numbers, and understand large numbers that represent quantity, distance, and money.

**Reading large numbers**. In this activity, students are introduced to the pattern in reading large numbers. Numbers of increasing magnitude are displayed for the students, starting with the ones column, progressing to the thousands column, and finally, the millions column. The name of each column is added to facilitate students’ reading.

**Developing physical examples of large numbers.** Concrete examples help students understand the nature of ever-increasing numbers. One activity to show visually the quantities 1, 10, 100 and 1,000 is to use colored sprinkles (confectionery decoration) on buttered bread that is cut into four pieces. The students add 1 sprinkle on the first piece of bread, 10 sprinkles on the second piece, approximately 100 sprinkles on the third piece (by estimating groups of 10), and approximately 1,000 sprinkles on the final piece (by estimating groups of 100).

The sprinkles activity provides a meaningful example for the students’ understanding of the relative magnitude of numbers to a thousand. Some students may extrapolate beyond the physical examples, and observe that you probably cannot fit one million sprinkles on one piece of bread.

**Appreciating large numbers in money**. What sized container would be needed to carry a million dollars? Before solving this problem, the students should complete two tasks. The first involves making posters that are labeled with the amounts $1, $10, $100, $1,000, $10,000, $100,000 and $1,000,000. The students identify items in magazine and newspaper advertisements that approximately cost each of these amounts, and glue the pictures of items under the corresponding amounts. This activity raises students’ awareness of the monetary value of expensive items. In the second task, the students calculate how much money is in a Monopoly game.

After completing these tasks, the students tackle the main problem of determining the container size needed to hold a million dollars. The students should use the Monopoly money to help them solve this problem. No containers are provided as the students are encouraged to model different container sizes with their hands. Through discussion, the students should realize that there is more than one answer to the problem. For instance, the size of the container is dependent on the denomination of the notes that are used to make one million dollars. Some students may observe that a larger-sized container would be required if notes of low value are used and vice versa.

**Appreciating large numbers in distance**. How far away are the brightest stars? The purpose of this activity is to develop the students’ understanding of large distances within the context of space travel. One approach is to have the students make 10 paper stars and label them with the names of the 10 brightest stars in the sky, their brightness, and their distance from Earth. The stars can be fastened onto upturned paper cups for ease of mobility. The students initially arrange the stars by order of brightness, beginning with the brightest star.

Next, consideration is given to the stars’ distances from Earth. After the students discuss the notion of measuring stellar distances in light years, they rearrange the stars in order from the closest to Earth to the most distant. Extend the activity by asking the students to discuss whether there is a relationship between the brightness of a star and its distance from Earth.

To represent the stars’ relative distances from Earth in light years, draw a time line and mark it in 100s from 0 to 1,000. Ask the students to position each star at the correct number of light years from Earth. Then they can discuss the fact that when we see a star today, the light from that star was actually emitted many years ago. Older students may be able to connect the year when light was emitted from particular stars to significant historic events on Earth. In this way, students make links between their mathematical understanding and their scientific knowledge.

### References

Diezmann, C. M., & English, L. D. (2001, Fall). Developing young children’s multidigit number sense. Roeper Review, 24, 11–13.

Jones, G., Thornton, C., & Putt, I. (1994). A model for nurturing and assessing multidigit number sense among first grade children. Educational Studies in Mathematics, 27, 117–143.