## Spinning Tops

Students measure distances using standard and nonstandard units and record their measurement in various tables. Then they are asked to use descriptive statistics to report the results. During a top-spinning contest, students measure the distance along a curve using indirect measurement. They record the data for their group in a chart, and compute their individual median and the group median.

Guide the students as they decorate tops made by pushing a writing pen through a plastic cover, such as those from yogurt and margarine containers.

Distribute a large sheet of white paper to each group, and demonstrate a spin on the top and how to "measure" the distance—with yarn or string, follow the path of the pen, and then measure the string with a centimeter ruler.

Distribute the Spinning Tops Activity Sheet to each student.

Guide the students as they record the data in their charts and compute the medians. Students should remember that the median is found by placing the data in order (from least to greatest, for example) and identifying the middle number. If there are two middle numbers, the median is the average of the two.

Encourage discussion of the tables created.

### Reference

Silverman, Helene. "IDEAS: Games, Measurement, and Statistics." The Arithmetic Teacher. April, 1990, pp. 27-32.

- Spinning Tops Activity Sheet
- Small Circular Plastic Tops (1 per student)
- Felt tip pens
- Large Sheets of White Paper
- Skeins of Yarn (1 per group)
- Scissors

**Extension**

Demonstrate how to make a stem-and-leaf plot with the data from all the groups. Guide the students as they display and analyze their position within the table, as well as the general tendency of their group.

### The Celebrated Jumping Frog

### Learning Objectives

Students will:

- Measure the distance along a curve using indirect measurement.
- Record data in chart form.
- Compute individual and group medians.
- Analyze data.

### NCTM Standards and Expectations

- Use common benchmarks to select appropriate methods for estimating measurements.

- Find, use, and interpret measures of center and spread, including mean and interquartile range.

### Common Core State Standards – Mathematics

Grade 6, Stats & Probability

- CCSS.Math.Content.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Grade 6, Stats & Probability

- CCSS.Math.Content.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.