## How Many Steps?

- Lesson

In this lesson, students participate in activities to develop concepts of measurement and statistics. Students are asked to measure distances using non-standard units and to record their measurement in a bar graph. Then they are asked to make comparisons using the bar graph.

Begin the lesson by having students take a "walk" around the classroom. As they are walking, have them notice the kinds of steps their classmates take. Remind students that this is not a race.

Call the students together to discuss what they observed. They may describe the steps as:

- big steps
- little steps
- normal steps

Next, distribute the How Many Steps? Activity Sheet to each student.

How Many Steps? Activity Sheet

Have each student model and clearly understand the meaning of each type of step listed on the activity sheet. For some of the steps, you may wish to demonstrate; for others, have a student demonstrate.

For example, you may wish to have one student demonstrate a "regular" step:

And another student could demonstrate a baby step:

And yet another student could demonstrate a giant step:

Tell students that they will be using one of their baby steps to measure the length of their other steps. That is, they will answer the question, "How many baby steps are equal to 1 _____ step?" To make the comparison easy, have each student cut several copies of their baby-step unit from newspaper. (This can be done most easily by having one student stand with their heels at the edge of the newspaper. Then, as he or she takes a baby step forward, a partner can mark just in front of the toe of their front foot with a crayon or pencil.)

Guide the pupils to measure and record the number of baby steps that equals each of the other steps. A student can take each of the indicated steps, and a partner can help to measure the length using the cut-outs of the baby steps.

Be sure that students measure the distances from the heel of the starting foot to the toe of the ending foot, just as was done with the baby step.

Students should fill in a box on the graph for each baby step. For instance, if one giant step is equal to five baby steps, the student should fill in five boxes. When completed, this graph will form a horizontal bar graph.

Ask students to look at their own graphs, and answer the **Questions for Students**. Then, students should find a partner and compare graphs. What do
their graphs have in common? What is different about their graphs?
These, as well as the **Questions for Students**, can all be discussion points for the comparison of two students' graphs.

### Reference

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

- How Many Steps? Activity Sheet
- Newspaper
- Scissors

**Extensions**

- Organize the pupils into small groups. Help them to compare their graphs by making such statements as
- "My umbrella step was six baby steps long; everyone else's umbrella step was equal to more of their baby steps than mine."
- "George's giant step was ten of his baby step long."
- "Andy's was twelve of his baby step long."
- "Paulette's longest step was the umbrella step; mine was the giant step."

- Encourage the pupils to look up and play variations of the game (see Games Bibliography),
as well as to make up additional steps and to measure the distances of
these steps in "baby steps," adding the data to their graphs.
Games Bibliography

**Questions for Students**

1. Which of the steps was equal to the most baby steps? Which was equal to the least baby steps?

[Student responses will depend upon the sizes of their steps.]

2. Which was equal to more baby steps—the umbrella step, or the giant step?

[Student responses will depend upon the sizes of their steps.]

### Learning Objectives

Students will:

- Measure distance in nonstandard units.
- Record measurement.
- Construct a bar graph of the measurements.
- Make comparisons using the bar graph.

### NCTM Standards and Expectations

- Develop common referents for measures to make comparisons and estimates.

- Represent data using concrete objects, pictures, and graphs.

### Common Core State Standards – Mathematics

-Kindergarten, Measurement & Data

- CCSS.Math.Content.K.MD.A.1

Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

-Kindergarten, Measurement & Data

- CCSS.Math.Content.K.MD.A.2

Directly compare two objects with a measurable attribute in common, to see which object has ''more of''/''less of'' the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Grade 1, Measurement & Data

- CCSS.Math.Content.1.MD.A.1

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Grade 1, Measurement & Data

- CCSS.Math.Content.1.MD.A.2

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.A.1

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.A.4

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.D.9

Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.D.10

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.