# LessonMeasuring and Graphing: How Tall Are We?

### Quick Look

Time Required: 45 minutes

Lesson Dependency: None

Subject Areas: Life Science, Measurement, Number and Operations

### Summary

Kindergartners measure each others' heights using large building blocks as the unit of measure. For their measurement technique, they tally how many blocks high each student is. Then they display the collected data in bar graphs made from from paper cut-outs of miniature building blocks glued on paper, which helps them see how bar graphs look like the various student heights they observe. Doing this establishes an important foundation for both creating and interpreting graphs in future years, as well as prepares students for the associated activity when they visit a second- and a fourth-grade class to measure those older students' heights. They also measure adults in the school community. Creating bar graphs from this additional data enables students to compare the different age groups to foresee how they may grow taller. Through this introduction to graphing lesson and its associated activity, students develop the concepts and vocabulary to describe, in a non-ambiguous way, how height changes as children age.
This engineering curriculum aligns to Next Generation Science Standards (NGSS).

### Engineering Connection

Measuring and graphing are important skills used by engineers of all disciplines.

### Learning Objectives

After this lesson, students should be able to:

• Measure the heights of their classmates using a non-standard method (building blocks instead of rulers).
• Record collected data in an organized fashion.

### Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

###### NGSS: Next Generation Science Standards - Science
• Make observations (firsthand or from media) to collect data that can be used to make comparisons. (Grades K - 1) More Details

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• Analyzing data in K–2 builds on prior experiences and progresses to collecting, recording, and sharing observations. (Grades K - 2) More Details

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###### Common Core State Standards - Math
• Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. (Grade K) More Details

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• 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. (Grade K) More Details

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• Understand the relationship between numbers and quantities; connect counting to cardinality. (Grade K) More Details

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• Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. (Grade K) More Details

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• Compare two numbers between 1 and 10 presented as written numerals. (Grade K) More Details

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• Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. (Grade 1) More Details

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• Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. (Grade 2) More Details

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• 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) More Details

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• 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. (Grade 2) More Details

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###### International Technology and Engineering Educators Association - Technology
• Safely use tools to complete tasks. (Grades Pre-K - 2) More Details

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• Information is data that has been organized. (Grades K - 2) More Details

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###### North Carolina - Math
• Compare two numbers between 1 and 10 presented as written numerals. (Grade K) More Details

Do you agree with this alignment?

• Understand the relationship between numbers and quantities; connect counting to cardinality. (Grade K) More Details

Do you agree with this alignment?

• Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. (Grade K) More Details

Do you agree with this alignment?

• 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. (Grade K) More Details

Do you agree with this alignment?

• Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. (Grade K) More Details

Do you agree with this alignment?

• Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. (Grade 1) More Details

Do you agree with this alignment?

• 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) More Details

Do you agree with this alignment?

• 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. (Grade 2) More Details

Do you agree with this alignment?

• Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. (Grade 2) More Details

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Suggest an alignment not listed above

### Introduction/Motivation

(By the time they are in kindergarten, most children are well aware of the size differences, most notably in height, between babies, young children, older children and adults. Furthermore, adults frequently comment on how much children have grown, and from the tone of voice used, children understand that this is a good thing. These comments make a good way to open this lesson.)

Have grownups ever told you how big you are getting or how much you've grown since the last time they saw you? (Let some students share their stories.)

Have you ever had your height measured, maybe at a doctor's office? How were you measured? (Listen to a few student descriptions.) Why is it important to have your height measured. (Listen to student ideas.) Growth is an indication of the health of a body. If a child isn't growing as expected, it can be a sign of an underlying health problem that needs attention.

Well, we don't have the same equipment that is in doctors' offices. But we can measure your heights in a different way, by measuring each other with building blocks. Let's get started.

### Lesson Background and Concepts for Teachers

Lesson Procedure

Estimation: With the class still gathered together, ask one student to come to the front and stand against the wall. Then place a building block on end next to the student. Ask if the student is taller than the block. Then ask how many blocks tall they think the student is, that is, how many blocks need to be stacked up to reach the top of the child's head. Let students share their guesses. Record their guesses on chart paper or the classroom board.

Measurement Technique: Then ask another student to come help you measure the first student. Ask this helper to hold a finger at the top of the block. Then show how you can pick up the block, and move it to a position right on top of where the block was originally. At this point, count aloud and say something like, "One, two, it takes two blocks to go part way up Ben's leg." Ask a third student to make two tally marks on the chart paper or board, to show how to keep track of how many blocks tall the first student is.

With your helpers, continue to use the block to measure the first student. Ask the rest of the class to help the tally-marking student keep count. When you get to the first student's head, it is unlikely that the student will be exactly as tall as a full block. So show the class how to decide if the student's height is closer to the height obtained by adding a half-block, or if it is closer to that by adding a whole block. Once the determination has been made, ask the class to help you count the tally marks, and then write down the final measurement. Compare this to the guesses students made earlier .

Students might have trouble with the last part of the measuring technique, in which a half-block or whole-block decision must be made. As you deem necessary, repeat the measurement demonstration using a different student and two other helpers.

Data Recording: Divide the class into groups of three students each and give each student a data sheet. The data sheet should be divided into three sections. Each section is identical and contains a space for recording the tally marks and a space for recording the final height measurement (see the Example Data Sheet). Direct students to use the three different sections to record the names and data for each of the three students in the group. Make sure everyone understands what needs to be written on the data sheet. Then, provide each group with a measuring block and have the group members work together to measure and record the heights of all three students in the group. Following the lesson, students can then follow the associated activity As We Grow: Measuring Heights and Graphing Data to take their new skills outside of the classroom to measure the heights of older students, and display the results in bar graphs.

### Lesson Closure

(Gather the class together and hold a brief discussion of the in-team measurements that just took place.) How did it go? Was there anything particularly difficult about making the measurements? (If you noticed any problems students were having, bring these up and ask how students solved them.)

(Ask each child what his or her height was, and make a list on the chart paper or classroom board.) Let's look at our collected measurements. Which student in our class is the tallest? Which is the shortest?

(Direct all the students stand up and arrange themselves in order by height. Give them time to sort this out for themselves; try to avoid intervening.) Look at the numbers again. Do your measurments, the data you recorded, match your line-up? In other words, are the students at each end of the line the same students that were measured to be the tallest and shortest? (If there are any discrepancies, discuss how these may have come about. These are most likely to occur due to differences in the ways students decide whether the last block added is closer to a whole block, half block or no additional block. In other words, they are due to differences in the ways students "round" their measurements.This is a fairly sophisticated concept, however, which is beyond the grasp of most kindergartners. Therefore, it is fine to mention it, but do not imply that students made poor measurements or got wrong answers if their line-up does not match the recorded measurements. Instead, simply point out that it can be hard to make these sorts of judgments sometimes.)

### Assessment

Measurement Technique: Observe students as they manipulate the blocks to make sure they are able to obtain reasonable height measurements and record the measurement data accurately. Observations of students as they complete the lesson should be adequate for assessment purposes at this stage. Identify and assist students who have difficulty in either the measurement or data recording aspects of the lesson, since these skills are needed for the associated activity.

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### Contributors

Mary R. Hebrank, project and lesson/activity consultant

### Supporting Program

Engineering K-PhD Program, Pratt School of Engineering, Duke University

### Acknowledgements

This content was developed by the MUSIC (Math Understanding through Science Integrated with Curriculum) Program in the Pratt School of Engineering at Duke University under National Science Foundation GK-12 grant no. DGE 0338262. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.