# Growing and Graphing

## Learning Objectives

Students will be able to measure heights in a non-standard, age-appropriate way (using building blocks instead of rulers), and display data in the form of pictorial bar graphs. They will also demonstrate ability to interpret these bar graphs, and describe how the heights of children change as they get older.

### Materials List

• long building blocks, about 10 inches long; one for every two students in the class
•  medium building blocks, half as long as the long blocks above; one for every two students
• 15-30 sheets of construction paper (preferably all one color)
•  glue for students to use
•  several sheets of poster board (all one color, or you can use four different colors, one for each age group)

### Materials prepared by the teacher ahead of time:

1. A data sheet that students will use when they go visit the other grades. It should allow them to record the names and heights of a second grader and a fourth grader, and have space for the tally marks students made as they measure the older students (see sample provided).
2. On a sheet of chart paper or poster board, create a large data sheet in which you can record the heights of the adults being measured. This sheet need only be a list of names and heights (in building blocks, of course)..
3. For students to construct bar graphs, you will need to use the construction paper to cut up to 500 rectangles, all the same size. (A paper cutter will make this easier!) A suggested size is 1" x 3". The exact size doesn't matter, but they should be proportioned about like the building blocks being used and should be easy for the students to handle. Since construction paper measures 9" x 12", rectangles that are 1" x 3" are easily marked off and cut. (1½" x 4" rectangles are also easy, but you will need more construction paper.) The actual number of rectangles needed will depend on the number of students in classes at your school. If you are fortunate enough to have small class sizes, you will not need so many.

It will also be easier for students to glue these rectangles more neatly onto the poster board if you first use a meter stick to lightly draw vertical lines about every three to four inches across the poster. (Use the wider spacing if your rectangles are the larger size.) Then when students glue the rectangles down, they can line up their rectangles along the vertical lines to keep their graphs from leaning or going too crooked. Draw one vertical line for each student in the class, and write a different student's name at the bottom of each of the lines.

## Introduction/Motivation

Gather the class together and remind them of the discussion that was held after they measured each other using building blocks. Point out the list of student heights that was obtained during that discussion. Then tell the class that you know a way to show all that information in a special type of picture called a graph. Ask if any of them have ever heard of a graph. If so, ask them where they saw it, and how it was used. Point out that graphs are very useful because they let people share or learn about a lot of information in a quick and easy way. Finally, tell students that they will help you make a large graph of their heights.

## Procedure

Over the course of several days, students will:

• As a whole class activity, create a bar graph that shows all the heights of the students in the class. This is accomplished by gluing pre-cut rectangles, resembling the measuring blocks students used, onto lined chart paper.
• Visit a 2nd grade and a 4th grade class to measure the heights of those students.
• Measure the heights of several adults recruited from the school community.
• As a group activity, create bar graphs that compare the heights of 2nd graders, 4th graders, and adults.

## Body of Activity

### Part 1: Making a Class Graph

Show the class the poster board and rectangles you prepared ahead of time. Place the poster paper on the floor or a table so that it is flat. Then, using the actual data for one student, show how you can line up the rectangles on end, one above the other, to represent the student's height. Do not glue the rectangles down, though. Also point out how you can use the vertical lines drawn on the poster paper to keep the line of rectangles straight, and be sure to show that you placed the rectangles on the line marked with the name of the student whose data you chose.
Explain to the students that you would like each person to glue rectangles on the poster to show his or her own height, using the vertical line corresponding to his or her own name. Then remove the rectangles you used for demonstration, and let students begin creating their own graphs. To avoid congestion, this can be done as a center activity through which the groups of three rotate.

### Part 2: Measuring 2nd and 4th graders

A few days in advance, arrange times when your class can visit a second grade class and a fourth grade class. It would be best if you determine ahead of time which pair of kindergartners will measure the heights of which two older students in each class.
Explain to your students that it might be fun to visit some other classes and see how tall some older students are. Explain that you have arranged visits to a 2nd grade and a 4th grade class. Ask students how they think the heights of these older students will compare to their kindergarten heights. When students say they think the older students will be taller, ask them how much taller. Students may use their arms to demonstrate, but ask them how many blocks taller they think each group will be. Record their guesses on chart paper or the chalkboard.
Next explain that this time, students will work in pairs to measure two 2nd graders and two 4th graders. This way one kindergartner can work as the tally marker and the other does the block measurement. Encourage them to trade jobs every time they measure a new student.

A week or two in advance, recruit a dozen or so adults to visit your class and be measured by your students. These can be parents of students, administrators, librarians, counselors, etc. -- anyone who can spare a few minutes. Try to get both males and females, and be sure to include yourself. Note: it would be best if all the recruited adults can visit the class at the same time, but if not, they can be scheduled over several different days and times.
On the appointed day (or just before the first of the adult visits), ask the class how many blocks tall they think adults in the school community are. As before, record their predictions. As your recruits visit the class to be measured, record their names and heights on the large data sheet prepared ahead of time. As the data comes in, compare the actual adult heights to the heights that students predicted earlier.

### Part 4: Graphing older students and adults

Using the poster boards prepared ahead of time, have students glue on bars for the 2nd graders and 4th graders they measured. These should be made in the same manner as the graphs they made of their own heights. Again, this can be done as a center activity. Likewise, assign individual students to glue bars representing the adults onto the poster board prepared earlier for the adult height graph.

### Part 5: Discussion and Investigating Questions

Display all four completed graphs in a row, in order from the youngest to the oldest age groups. Ask students to comment on what they observe about the graphs. Their first response is most likely that as people get older, they get taller. Then ask questions to narrow their observations, such as:

•  Is there a big difference between the heights of kindergartners and the heights of second graders?
•  Is there a big difference between the heights of kindergartners and the heights of fourth graders?
•  Are all kindergartners the same height? What about second and fourth graders?
•  Is there a difference between the heights of boys and girls in each class? (There shouldn't be much difference, or if anything, girls may be slightly taller on average.)
•  Is there a difference between the heights of men and women in the adults?

Next, explain that there is a more exact way to talk about the differences between the heights of the four age groups. Starting with the kindergartner poster, ask your students who the shortest person in the class is. At the bottom of the chart paper, write down that student's measurement. Then ask who the next taller student is. Write down that student's measurement directly above the first's. Continue putting the student heights in order from shortest to tallest.

Then explain that you are going to start crossing off heights two at a time, by crossing off the shortest and tallest together. Then cross of the second shortest and second tallest together, and continue crossing off pairs of measurements until only one or two measurements in the middle of the list remain. Explain to the class that since you have crossed off all the short and tall students, you now have the middle-sized kindergarten height remaining. (In mathematical terms, you have determined the median height, but avoid using this term with young children. "Middle-sized" is a term they can understand and serves just as well.)

Repeat the same procedure for the second grade class. Point out that you can now easily compare the heights of middle-sized kindergartners to middle-sized second graders: e.g., "A middle-sized kindergartner is 4 blocks tall, and a middle-sized second grader is 4½ blocks tall. So the second grader is one-half of a block taller than the kindergartner."

Do the same for the fourth grade class and the adults. By having them compare the heights of the different age groups using numbers (quantitatively), you are helping your students develop both number sense and an understanding that numbers can be used to help describe and compare things of interest.

## Safety Issues

Students may need to stand on chairs or tables to measure adults, so be sure to monitor this activity closely.