by Len Sparrow and Paul Swan

The following lesson is from Len Sparrow and Paul Swan’s Learning Math with Calculators (Math Solutions Publications, 2001). The book is organized into two sections: the first addresses a broad range of teachers’ questions and concerns about using calculators for teaching math; the second is a collection of classroom-tested activities using calculators, all chosen for the purpose of developing children’s number sense and problem-solving ability. In this lesson, children reflect on the idea that when a number less than one is multiplied by a whole number, the answer will be smaller than the starting number. This fact conflicts with the belief of many students that multiplying a number always makes it larger.

### Materials

• calculators, 1 for each pair of students
• pencil and paper for recording

## Activity

Ask each pair of students to generate a list of numbers; for example:

65     72     187     23     5     689     1,234

One of the students then multiplies each of the numbers by a number slightly less than 1 (for example, 0.9), while the other student multiplies the same numbers by a number slightly more than 1 (for example, 1.1). These multipliers will produce answers slightly smaller and slightly larger than the original numbers. Both partners keep a written record of the number, the multiplier, and the answer, using a chart like the one shown below. Partners compare their answers and discuss the relationships that are revealed. ### Extension

Students can check other multipliers that are close together and near to one to confirm their ideas.

### Teaching Notes

This exercise can be effectively partnered with the activity Closest to One Thousand.

From Online Newsletter Issue Number 6, Summer 2002

Related Publication:
Learning Math with Calculators: Activities for Grades 3–8
by Len Sparrow and Paul Swan