# 3.3: Activities and Answer Keys

**At Grade**Created by: CK-12

## Activity 2-1: How Tall?

### PLAN

** Summary** In this activity students use graphs to compare the rate of growth and the average height of males and females between the ages of 1 and 19. They also identify when rapid spurts of growth are likely to take place.

*Objectives*

Students:

\begin{align*}\checkmark\end{align*} examine average heights and average rates of growth.

\begin{align*}\checkmark\end{align*} interpret a graph.

\begin{align*}\checkmark\end{align*} compute percentage.

*Student Materials*

- Activity Report
- 1 ruler per student if possible, or per group (pairs are suggested)

*Teacher Materials*

- Activity Report Answer Key

*Advance Preparation*

Gather rulers.

Make a transparency of the two graphs in the exercise to make explanation and discussion easier. (Optional)

*Estimated Time*

This activity should take 30-45 minutes, depending on students' familiarity with graphing.

*Interdisciplinary Connections*

This activity has **Math** and **Science** connections because it involves graphing and calculating. It can be extended to include:

**Physical Education/Health** Have students take their height measurements. Ask them to bring that information to their math classes.

**Math** Use the height measurements taken in PE or Health class to graph the heights of males and females in the class. Discuss the difference between a straight-line graph and a bell curve, which should roughly be the result of the height measurements. If your class is able, go one step further and calculate the average height within the class for males, and the average height for females. Stress that average is not the same as normal, and that there is a very wide range of normal for each age and grade level.

*Prerequisites and Background Information*

If students are not familiar with graphs, time should be taken before the exercise to explain terms such as *plot line,* \begin{align*}x\end{align*}- and \begin{align*}y\end{align*}*-axis*, and *average*. Learning how to read the graph is part of the exercise itself. The exercise also involves determining percentage.

### IMPLEMENT

** Introduce Activity 2-1** by asking students if all 4-year-olds are the same height. Are all 8-year-olds? Are all adults? Explain that in this activity they will see how wide the range of normal height is at all ages. If students are unfamiliar with graphing, take time to go over what a graph is, types of graphs, and what the parts of a graph are. Do not let their lack of graphing skills stop you from doing the activity. It is a good time for them to learn. An alternative approach is to conduct the graphing as a demonstration.

** Steps 1-5** Based on your assessment of the classes' skill level in math, you can have them work independently, in groups, or lead them step-by-step. Distribute a ruler and Activity Report to each student (or pair of students).

Read the directions with the students, answer questions about procedure, then give the class time to make their calculations.

** Conclude Activity 2-1** by discussing their findings. Lead them to the conclusion that there is a wide range of normal in height, particularly during adolescence.

### ASSESS

Use the Activity Report responses to assess if students can

\begin{align*}\checkmark\end{align*} read a graph.

\begin{align*}\checkmark\end{align*} calculate percentages.

\begin{align*}\checkmark\end{align*} define the terms average and normal and explain the difference between these terms.

## Activity 2-1: How Tall? – Activity Report Answer Key

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

Look at the graph in Figure 2.3 Average Heights for Boys and Girls on p. 11 of your textbook. Follow the steps below to figure out how tall the average boy or girl would be at age 10.

- Place the edge of your ruler at age 10, then, keeping it straight up, see where it crosses the two plot lines for boys and girls. Since they are so close together at this point, we will treat them as one.
- Mark with your pencil the point on the plot line that your ruler is touching.
- Now place the ruler horizontally from that point until it reaches the vertical line. It will intersect a little below the \begin{align*}140-cm\end{align*} mark. This is the average height a boy or girl will be at age 10. Now that you know how to read the graph with your ruler, find out the average height of boys and girls your own age and mark it below. Remember, you may be taller or shorter than the average height for your age, but still be perfectly normal. My age is
- As you can see from studying the graph, the average heights of boys and girls are almost exactly the same for many years, with the line for girls falling only a tiny bit below the line for boys. Then the pattern begins to change. a. At what age do average heights for boys and girls first seem to meet at the same point on the graph? b. Between what ages is the average height for girls taller than the average height for boys? c. At what point do the average heights for boys and girls meet for the second time? d. After that point, are males or females taller on average? e. When plot lines level off, or become horizontal, they then show that height remains constant. What is the difference in height, on average, between boys and girls once their growth levels off?
- The next measurement you make might surprise you. Using the same graph, use your ruler to find out the average height of girls at age 2 and write it down. Do the same for age 19. a. average height of girls at age 2 b. average height of girls at age 19 c. How do these figures compare? At age 19, females are about twice as tall as when they are 2 years old. That means that by age 2, girls have already reached half, or 50%, of their adult height. The same would be true for boys at age 3.
- Now do the same calculations for boys at age 11 and at age 19. a. average height of boys at age 11 b. average height of boys at age 19 c. What percentage of their adult height have males reached at age 11?
- Go back to your textbook and look at the graph labeled Figure 1.4, Growth Spurts. a. During what three-year period is growth the greatest for both boys and girls? b. On average, during what three-year period is the growth spurt greatest for girls? Which year is the peak year? c. On average, what three-year period shows the most rapid growth for boys? What is the peak year?
- Read the final paragraph of this activity in your textbook.

A suggested response will be provided upon request. **Please send an email to teachers-requests@ck12.org.**

Look at the table above showing Olympic performances in the long-jump event. At what rate are the men's and women's records changing?

What Do You Think?On average, since adult males have the potential to develop stronger muscles than adult females, should adult females be excluded from jobs that involve heavy physical labor (for example, fire fighting)?

What are some ways you mark your growth and development? Do your friends or family celebrate or recognize milestones (accomplishments, growth) in any way? How? How might you recognize those milestones important to you, but not currently celebrated, and share them with someone?

## Review Questions/Answers

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

- What factors influence how tall you will be?
- What factors affect your weight?
- How does puberty affect exercise and endurance?
- What causes acne, and what can you do about it?
- Name three other health concerns common to adolescents, and describe them.

## Activity 2-1 Report: How Tall? (Student Reproducible)

Look at the graph in Figure 2.3, Average Heights for Boys and Girls, on p. 11 of your textbook. Follow the steps below to figure out how tall the average boy or girl would be at age 10.

1. Place the edge of your ruler at age 10, then, keeping it straight up, see where it crosses the two plot lines for boys and girls. Since they are so close together at this point, we will treat them as one.

2. Mark with your pencil the point on the plot line that your ruler is touching.

3. Now place the ruler horizontally from that point until it reaches the vertical line. It will intersect a little below the \begin{align*}140-cm\end{align*} mark. This is the average height a boy or girl will be at age 10. Now that you know how to read the graph with your ruler, find out the average height of boys and girls your own age and mark it below. Remember, you may be taller or shorter than the average height for your age, but still be perfectly normal.

My age is _________.

The average height of boys my age is ____________________.

The average height of girls my age is ____________________.

4. As you can see from studying the graph, the average heights of boys and girls are almost exactly the same for many years, with the line for girls falling only a tiny bit below the line for boys. Then the pattern begins to change.

a. At what age do average heights for boys and girls first seem to meet at the same point on the graph?

_____________________________________________

b. Between what ages is the average height for girls taller than the average height for boys?

_____________________________________________

c. At what point do the average heights for boys and girls meet for the second time?

_____________________________________________

d. After that point, are males or females taller on average? __________________

e. When plot lines level off, or become horizontal, they then show that height remains constant. What is the difference in height, on average, between boys and girls once their growth levels off?

_____________________________________________

5. The next measurement you make might surprise you. Using the same graph, use your ruler to find out the average height of girls at age 2 and write it down. Do the same for age 19.

a. average height of girls at age 2 _______________________

b. average height of girls at age 19 ______________________

c. How do these figures compare? __________________________

6. Now do the same calculations for boys at age 11 and at age 19.

a. average height of boys at age 11 ______________________

b. average height of boys at age 19 ______________________

c. What percentage of their adult height have males reached at age 11 ? ______

7. Go back to your textbook and look at the graph labeled Figure 1.4 Growth Spurts.

a. During what three-year period is growth the greatest for both boys and girls?

_____________________________________________

b. On average, during what three-year period is the growth spurt greatest for girls?

_____________________________________________

Which year is the peak year? ________________________

c. On average, what three-year period shows the most rapid growth for boys?

_____________________________________________

What is the peak year? ________________________

8. Read the final paragraph of this activity in your textbook.

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