Expanding Learning Time in After-School and Summer
Enrichment Programs: Science, Math, and Integrated STEM
Activities for Middle and High School Students
Edited By
Drs. Babette M. Benken and Laura Henriques
with
Ms. Andrea Johnson
California State University, Long Beach
Expanding Learning Time in AfterSchool and Summer Enrichment
Programs: Science, Math, and
Integrated STEM Activities for
Middle and High School Students
Expanding Learning Time in After-School and Summer Enrichment Programs:
Science, Math, and Integrated STEM Activities for Middle and High School
Students
Spring 2011 saw large numbers of elementary teachers being laid off due to state and district
budget cuts. In an effort to help experienced teachers gain skills and new certifications, a
program was developed by California State University, Long Beach faculty to help laid-off
elementary teachers earn a middle school mathematics or science teaching credential.
Generously funded by the S.D. Bechtel Jr. Foundation, the David and Lucille Packard
Foundation, and the Southbay Workforce Initiative Board, this project (Fall 2011–Summer 2012)
provided content courses and a secondary mathematics or science methodology course for
approximately 50 laid-off elementary teachers from the Long Beach Unified School District
(Southern California).
As part of this program, teacher-participants developed and field-tested math, science, and
integrated STEM lessons. While most of these lessons would work well in a traditional
classroom setting, participants developed them for the after-school setting. Most of these lessons
explore content relative to, and could be adapted for, multiple grades in middle school through
high school. Post development, the activities were taught to middle school children in afterschool settings in Norwalk-La Mirada, CA. After field-testing, the activities were further revised
numerous times. In some cases, the lessons were implemented yet again. In the final step of the
process, we (the three editors for this project) made further additions, edits and revisions to the
activities. This compilation of STEM activities is the result of that effort.
Each activity has a 1-2 page cover sheet, which includes an overview of the activity, suggested
grade ranges, approximate time to complete the activity, relevant mathematics and/or science
standards, lesson objectives, a materials list, safety considerations (if any), and the list of
contributing authors. In some cases multiple teacher-participants taught an early version of the
lesson and provided lesson plans and field testing notes. For each activity, there is a detailed
summary for implementation that includes assumed prior knowledge, relevant facilitator
questions, and recommendations for how to assess understanding and scaffold students’
independent practice. Lessons also include suggestions for differentiation and/or extension
activities. Where appropriate, we have added additional STEM connections so that you and your
students are able to see how science, technology, engineering and mathematics intertwine.
We hope that you find these lessons useful, engaging and thought provoking.
Drs. Babette Benken & Laura Henriques, Co-Editors & Directors of the FLM/FLGS Programs
CSU Long Beach
Table of Contents
1. Use Your Shoe!
 Mean, median, and mode
2. Transformations and Illusions
 Rotations, translations, and reflections of figures
3. The Soundinator
 Sound waves
4. Drop of Doom!
 Quantitative and graphical representations of functions
 Velocity
5. Reflections on Light
 Properties and reflections of light
 Geometric angle constructions
6. How Much Water Fits on a Penny?
 Properties of water
 Mean, median, and mode
7. Snack Time!
 Representing data in bar graphs, pie charts, and box and whisker plots
8. Stretching It
 Hooke’s Law
 Linear relationships
9. Run!
 Distance versus time graphs
 Rates of change and slope
10. Peas in a Pod
 Collecting and analyzing data
 Scatterplot graphs
 Modeling with functions
11. Happy Birthday to You!
 Number patterns and number sense
Use Your Shoe!1
Each student will contribute to the class shoe size data, collect data for the entire class, and
analyze the data by determining the mean, median and mode. Students will use their analyses to
make inferences about the average shoe size of larger populations.
Suggested Grade Range: 6-8
Approximate Time: 2 hours
State of California Content Standards:
Mathematics Content Standards Grade 8: Probability and Statistics
10.0 Students know the definitions of the mean, median, and mode of distribution of data
and can compute each of them in particular situations.
Science Content Standards Grades 6-8: Investigation and Experimentation
7. b. Students will use appropriate tools and technology to perform tests, collect data,
and display data.
9. b. Students will evaluate the reproducibility of data.
Relevant National Content Standards:
Mathematics Common Core State Standard: 7.SP
2. Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated samples) of
the same size to gauge the variation in estimates or predictions. Gauge how far off the
estimate or prediction might be.
Lesson Content Objectives:
 Distinguish among and calculate the mean, median and mode of a data set.
 Collect and organize data from the group.
 Calculate the mean, median and mode of the group data.
 Draw inferences about a population after examining the group’s sample.
 Practice calculating the mean, median and mode for data from different contexts.
Materials Needed:
 One copy per student of the “Mean, Median, and Mode” notes sheet, “Use Your
Shoe!” activity sheet, and “Independent Practice” sheet (included)
 One shoe card per student to record their shoe size (included)
 Tape
1
An early version of this lesson was adapted and field-tested by Alex Chao and Thy Pech, participants in
the California State University, Long Beach Foundational Level Mathematics/General Science Credential
Program.
STEM Activities for Middle and High School Students
Use Your Shoe!
1-1
Summary of Lesson Sequence
 Provide the “Warm Up” activity sheet (included) for students to practice using the
correct order of operations to evaluate multi-step expressions.
 Introduce the lesson by allowing students to find out the shoe size of five other
students in the class and discussing how that data could be used to make a guess
about the shoe size for the whole class.
 Lead students through the “Mean, Median, and Mode: Guided Notes” (included) by
modeling how to find these measures of central tendency.
 Allow all students to contribute their shoe sizes by taping each student’s shoe card to
the board on a frequency chart. Guide students through their own practice of finding
the mean, median and mode for the entire class using the data on the board and the
“Use Your Shoe!: Guided Practice” activity sheet (included).
 Check for students’ understanding by asking the key questions provided while
students are working on the guided practice.
 Close the lesson with a discussion of their findings and how their findings could be
extended to larger populations.
 Provide the “Independent Practice” sheet for students to practice finding the mean,
median and mode for data in different contexts.
Assumed Prior Knowledge
Prior to this lesson students should be able to use the correct order of operations to
evaluate multi-step expressions.
Classroom Set Up
Students will be asked to participate in discussions and work in small groups for portions
of this lesson.
Lesson Description
Introduction
Provide students with the “Warm Up” activity, allowing them time to practice using the
correct order of operations to evaluate multi-step expressions. Students should be able to
complete the warm up on their own.
Provide every student with a pre-cut square with a picture of a shoe on it. Students should
write their shoe size on the square. Allow students a couple of minutes to move around
the room and share shoe sizes with four other students, (each student write down their
own size and the shoe size of four peers so all will have 5 data points). They can record
the other students’ shoe sizes on the back of their own shoe card. After about two
minutes, ask students to find their seats again to begin a brief discussion. Ask:
Based on the data you collected from four other students and yourself, what do you think
is the most common shoe size in the classroom?
What shoe size do you think is right in the middle of the biggest and smallest?
STEM Activities for Middle and High School Students
Use Your Shoe!
1-2
Can you hypothesize from the five shoe sizes that you know what the average shoe size
for the whole class might be?
Tell students that they will be learning how to analyze data using three measures of
central tendency: mean, median and mode. Make sure your discussion arrives at
classroom understanding of working definitions for these terms.
Input and Model
Provide students with the “Mean, Median, and Mode: Guided Notes” sheet and review
the definitions for mean, median and mode:
Mean: average
The mean is the sum of all values
divided by the number of values in
the data set.
Median: middle
The median is the middle value of
the data set when the data set is
ordered least to greatest.
Mode: most
The mode is the most frequently
occurring value of the data set.
Demonstrate for students the method
for calculating the mean by adding
up all the shoe sizes of the sample
set and dividing by the number of
students in the sample set.
Encourage students to find the mean
of their sample of five students’ shoe
sizes that they collected. Allow
students to notice that their answers
may vary because they collected
data from different students. This
can lead to a conversation about
larger sample sizes being more
representative of the entire group.
Model for students the method for
finding the median of the sample
data by organizing the sample set as
a list from least to greatest and
finding the middle shoe size.
Encourage students to find the
median of their sample of five
students’ shoe sizes that they
collected. Discuss how they would
find the median if their data had an
even number of data points (e.g., 6
shoe sizes).
Model for students the method for
finding the mode of the sample data
by observing which shoe size occurs
most frequently in the sample set.
Explain that data sets might not have
a mode or might have more than one
mode; ask volunteers to provide
examples of data sets that have no or
multiple modes. Students should
recognize whether there is a mode
for the sample of five shoe sizes and
identify the mode if there is one.
Show students how to create a frequency chart for the sample set of data.
Model for students the second sample set of data for the number of text messages sent.
STEM Activities for Middle and High School Students
Use Your Shoe!
1-3
Guide Students Through Their Practice
Draw an outline of a frequency chart on the board for the whole class’ shoe size data; an
example frequency chart outline is on the students’ “Guided Notes.” Allow students to
come to the board and tape their shoe card above the number value for their shoe size,
vertically stacking repeated values to create a bar graph.
Students should use the data on the board to complete the “Use Your Shoe!: Guided
Practice” activity sheet.
Students may work together to complete the guided practice.
Check for Understanding
Check for students’ understanding while they are working on the guided practice by
asking the following key questions:
Are the mean, median and mode for the whole class different from the mean median and
mode you found from the set of five that you collected?
Why might they be the same or different?
Each measure of central tendency tells us something different about the data. What does
the mean tell us? The median? Mode?
Which measure of central tendency do you think is helpful for understanding this
particular shoe data? Why?
Independent Practice
Provide students with the “Independent Practice” sheet to complete on their own.
Closure
To close the lesson, allow students to share their findings about the mean, median, and
mode for the whole class. Ask students:
Was the sample of five shoe sizes helpful for guessing the mean, median, and mode for
the whole class?
Do you think we could use our findings for the whole class to guess the shoe size of a
larger population? [Other classes of the same age, the whole school, all children of the
same age around the world, all Americans, etc.]
To what extent is the data we collected today reproducible by another class here at our
school?
STEM Activities for Middle and High School Students
Use Your Shoe!
1-4
Suggestions for Differentiation and Extension
 This activity may be extended by allowing students to develop their own survey, collect
data outside of the classroom, and summarize and analyze the data using the measures of
central tendency they learned in this lesson.
 If working with the same group of students over a period of time, students could be asked
to explain what they learned in the days following the activity in a journal, or as a warmup.
 Students may conduct research using the Internet to determine whether the shoe size data
for the classroom is representative of larger populations.
 Depending on the class, students’ heights may be collected instead of shoe size to provide
more variability.
 Students may use graphing calculators to calculate the mean, median and mode for the
shoe size data, as well as for the independent practice problems. Students may also use
graphing calculators to create frequency tables for the sets of data.
STEM Activities for Middle and High School Students
Use Your Shoe!
1-5
Use Your Shoe!
Warm Up
1. Simplify:
2+3+4+5+6+7=
6
2. Simplify:
2(4) + 4(3) + 2(7) =
3. (4 x 6) + (2 x 3) =
9
4. 11 x 6 + 6 x 3 + 2 x 2 =
5. 4567 ÷ 22 =
STEM Activities for Middle and High School Students
Use Your Shoe!
1-6
Mean, Median, and Mode
Guided Notes
1. Create a frequency chart for this sample set of shoes sizes: 6, 10, 9, 8, 8, 6, 12, 14, 9, and 8.
Student #
A
B
C
D
E
F
G
H
I
J
Shoe Size
6
10
9
8
8
6
12
14
9
8
___________________________________________
Shoe Size
Find:
A.
Mean: add all shoe sizes and divide by total number of students.
_ Sum of all shoe sizes__
Total number of students
=
= ________________
=
B. Median: write all shoe sizes in order from least to greatest and find the middle shoe size.
If there are two middle shoe sizes, add those two sizes and divide by 2
+
2
=
C. Mode: find the shoe size that occurs the most.
STEM Activities for Middle and High School Students
Use Your Shoe!
1-7
2. Second sample: Last week, Jane sent 34 text messages, John sent 25, Sofia sent 41, Priscilla
sent 12, Cisco sent 33, Fred sent 24, and Riley sent 25.
Name
# Of messages sent
__________________________________________
Total Number of Texts
Find:
A. Mean: add all text messages and divide by the number of students.
Total text messages__
Total number of students
=
= ________________
=
B. Median: write all numbers of messages sent from least amount to greatest and find the
middle data point.
If there are two data points in the middle, add them and divide by 2.
+
2
=
C. Mode: find the amount of messages sent that occurs most frequently.
STEM Activities for Middle and High School Students
Use Your Shoe!
1-8
Use Your Shoe!
Guided Practice
Student
1
Shoe Size
Gender
2
Review vocabulary: mean, median, mode.
A. Mean is the sum of all values divided by the number of values
in the data set. Another term used for mean is average.
B. Median is the middle value in the data set. If there are two
middle values, add them and divide by two.
C. Mode is the most frequently occurring value data point of the
set.
3
4
5
6
7
8
9
10
11
12
13
14
Shoe Size
15
16
Mean (add all shoe sizes / total # of students) = ____________
Add all shoe sizes

Total # of students
=
_____________ =
17
18
19
20
Median (write all shoe sizes in order from least to greatest, find
the middle shoe size. If there are two middle shoe sizes, add them
up and divide by 2) = ____________
21
22
23
24
Mode (find the shoe size that occurs most frequently) = ____________
STEM Activities for Middle and High School Students
Use Your Shoe!
1-9
Mean, Median, and Mode
Independent Practice
Practice finding the mean of a data set by calculating the Grade Point Average (GPA) using the
sample report card provided. First read the “Report Card Information,” then use the data from the
“Sample Student Report Card” to find the GPA.
Report Card Information
Honor Roll
Honor Roll is determined by grade point average (GPA).
Honor Roll:
3.0 -3.5
High Honor Roll:
3.6 -3.9
Highest Honors:
4.0 - 4.3
Grades (with Numerical Value)
High schools use the table below for determining Grade Point Averages and Rank in Class:
A+ = 4.3
B+ = 3.3
C+ = 2.3
A = 4.0
B = 3.0
C = 2.0
D = 1.0
A- = 3.7
B- = 2.7
C- = 1.7
F = 0.0
Grade points corresponding to letter grades for students in AP Courses (who take the AP Exam) are 0.3
units higher.
***For example a student in an AP Course would receive 3.6 points for a B+ instead of 3.3. An F for these
students remains at 0 points.
***When calculating the GPA, the letter grade's numerical value is multiplied by the units to determine the
weighted grade points. These are totaled and divided by the total units in that marking period. The following
example illustrates the calculation of a GPA for a student with no AP Courses using the grade point table
above:
STEM Activities for Middle and High School Students
Use Your Shoe!
1 - 10
Sample Student Report Card
Units
Course
Letter Grade
Numerical Value
Grade Points
1
A.P. English
B+
3.3
3.6
1
Math
A-
3.7
3.7
1
Science
A
4
4
1
Social Studies
C
2
2
1
Computer
D
1
1
*.50
PE
P
0
0
.50
Orchestra
A
4
2
*PE is not counted in the divisor because of the Pass/Fail status of the course. Therefore, you DO NOT
include it in your calculations of GPA.
**All courses that are graded pass/fail are not considered in GPA (ex. College Seminar, Teaching Assistant,
etc.).
1. Use the sample report card above to calculate the weighted GPA.
2. Based on the GPA you calculated, would a student with this report card earn any honors?
STEM Activities for Middle and High School Students
Use Your Shoe!
1 - 11
STEM Activities for Middle and High School Students
Use Your Shoe!
1 - 12
Transformations and Illusions1
Students will have the opportunity to explore geometric transformations in a piece of M.C.
Escher’s artwork after learning to identify and draw reflections, translations, and rotations of
figures.
Suggested Grade Range: 7-12
Approximate Time: 1 hour
State of California Content Standards:
Mathematics Content Standards Grades 8-12: Geometry
2.2 Know the effect of rigid motion on figures in the coordinate plane and space,
including rotations, translations, and reflections.
Relevant National Content Standards:
Mathematics Common Core State Standard: 8.G
1. Verify experimentally the properties of rotations, reflections, and translations.
Lesson Content Objectives:
 Identify and draw rotations, reflections and translations of angles, polygons, and other
figures.
 Investigate rotations, reflections and translations of figures in a drawing by M.C.
Escher.
 Describe transformations using correct mathematical vocabulary.
Materials Needed:
 Lined or white paper
 Rulers
 Three colored pencils per student or pair
 One copy per student of M.C. Escher’s Angels and Devils drawing (included)
 One copy per student of the “Transformation Practice” sheet (included)
 Mirrors (optional)
 One copy per student of the “Transformation STEM Extension” (included)
1
An early version of this lesson was adapted and field-tested by Monica D. Williams-Davis and Layla
Nourbakhsh, participants in the California State University, Long Beach Foundational Level
Mathematics/General Science Credential Program.
STEM Activities for Middle and High School Students
Transformations and Illusions
2-1
Summary of Lesson Sequence
 Introduce the lesson by providing a copy of M.C. Escher’s Angels and Devils drawing
(included) for students to view and discuss.
 Lead students through compiling Cornell Notes on the vocabulary for the lesson
including transformation, reflection, translation, and rotation.
 Model writing letters and their transformations, providing an example of each.
 Guide students through their own practice drawing transformations of letters.
 Check for students’ understanding by allowing students to identify and color figures from
Escher’s Angels and Devils that are reflections, translations, and rotations.
 Allow groups to develop a way to teach the rest of the class how to reflect, rotate, and
translate a letter or polygon.
 To close the lesson, students may discuss in small groups examples of transformations
that may be observed inside the classroom or outside, then report to the whole class.
 For independent practice, students will complete an included activity sheet.
 Provide the optional Transformation Extension activity sheet and allow students to find
designs where transformations of shapes are used.
Assumed Prior Knowledge
Prior to this lesson students should know how to identify, draw, and measure shapes and
angles, and be familiar with the quadrants of the coordinate plane.
Classroom Set Up
Students will be asked to work in small groups for portions of this lesson.
Lesson Description
Introduction
Provide students with a copy of M.C. Escher’s Angels and Devils (included) and allow
students to view and discuss the piece.
Generate discussion by using probing questions: What elements of the piece are repeated
to form a pattern? Are there angles that are congruent? What is different about the
angles (direction and position)?
Input
Lead students through taking notes of the key vocabulary for the lesson:
transformation, reflection, translation, and rotation:
Transformation: a change. A transformation changes the position of a shape on a
coordinate plane. The shape moves from one place to another when it is transformed.
STEM Activities for Middle and High School Students
Transformations and Illusions
2-2
Reflection: a flip.
A reflection takes place when a
shape is flipped across a line and
faces the opposite direction. A
shape and its reflection are mirror
images of each other.
Demonstrate a reflection using an
object in the classroom and a mirror.
Translation: a slide.
An object is translated when it
moves in one direction from the
starting point to the end.
Demonstrate a translation by sliding
an object in the classroom across a
table.
Rotation: a turn.
An object that is rotated turns on a
point to face another direction like
the hand turning on the face of a
clock.
Demonstrate a rotation with an
object in the classroom or by
directing students’ attention to a
clock with rotating arms.
Model
Demonstrate a reflection, translation, and rotation of the letter E. Provide another
example if necessary without taking from students’ opportunity to explore
transformations during the guided practice. Be careful to choose a letter, which has some
asymmetry or students will not easily see that it has been changed.
Guide Students Through Their Practice
Move around the classroom checking students’ progress and allowing students to assist
each other after assigning the following transformations:
Reflect: p, m, T, nap, and their name.
Translate: S, V, e, and a square.
Rotate: L, w, C, and a triangle.
Check for Understanding
 Using their copy of M.C. Escher’s Angels and Devils, ask students to color one of the
figures in the picture (an angel or devil). Have them find a reflection of that shape and
color it in as well.
 Have students hold up their papers to check their understanding.
STEM Activities for Middle and High School Students
Transformations and Illusions
2-3

Ask students to use a different color to indicate another figure and its translation.
Using a third color, ask students to color a third figure and its rotation.
Student Team Teach
Allow students time to discuss a method for teaching how to perform a transformation on
a polygon. Assign a polygon and a transformation to each group, and after allowing time
to prepare, call on representatives of each group to teach the class how to perform the
transformation on their polygon.
Independent Practice
Provide students with the Transformation Practice activity sheet (included) to complete
independently.
Closure
Allow students to discuss in small groups examples of transformations that they observed
in the classroom or outside of the classroom and share with the whole class. Students may
be permitted to show with their own body a reflection, translation or rotation.
Ask students: Can you think of a situation where the result of a reflection may be the
same as the result of a rotation? (A 180 rotation yields the same result as a reflection;
you can point out that the term “180” is used in skateboarding, etc.).
Suggestions for Differentiation and Extension
 Explain to students that symmetry is commonly found in engineering and architectural
designs and allow students to share examples of designs they are familiar with that have
an element of symmetry.
 Provide students with the Transformation Extension activity sheet (included) so that they
may explore symmetry in designs on their own. Encourage students to use a digital
camera or cellular phone to take a photograph of a symmetric design they encounter so
that they may share it in class.
STEM Activities for Middle and High School Students
Transformations and Illusions
2-4
Transformation Practice
1. A translation ...
 flips a shape
 slides a shape
 turns a shape
2. A reflection ...
 flips a shape
 slides a shape
 turns a shape
3. What rotation would turn the
capital letter Z into a capital N?
 360 degrees
 90 degrees
 180 degrees
4. A triangle on a grid is rotated 90
degrees about the centre of the
grid. The distance between the tip
of the triangle and the centre of
the grid ...
 increases
 stays the same
 decreases
5. A drawing of a stick-man is
reflected in a mirror line. The eye
of the reflected man is ...
 the same distance from the mirror
line as the original shape.
 further from the mirror line than
the original shape.
 nearer the mirror line than the
original shape.
6. A dot at position (4,3) on a grid
is translated four squares to the
right. What are its new
coordinates?
 (0,3)
 (4,3)
 (8,3)
7. A dot at position (0,0) on a grid
is translated one square to the
right and two squares up. What
are its new coordinates?
 (0,0)
 (2,1)
 (1,2)
8. Which of these techniques can
transform the letter b into the
letter d?
 Reflection
 Rotation
 Translation
9. Which of these techniques can
NOT transform the letter M into
the letter W?
 Reflection
 Rotation
 Translation
STEM Activities for Middle and High School Students
Transformations and Illusions
2-5
Transformation Extension
Engineers, architects, and inventors often design objects that make use of transformed
shapes. Find a building, a machine, or any other man made object for which you can
identify a transformed shape in the design.
1. If possible, take a digital photograph of the object you found so that you may refer to
it to answer the next questions and so that you may share your findings with the class.
2. Draw a simple diagram of the object you found. Label the shape and its
transformation or transformations.
3. Explain how the transformed shape contributes to the design of the object.
STEM Activities for Middle and High School Students
Transformations and Illusions
2-6
The Soundinator1
Students construct an apparatus to make sound using plastic cups, string, and hangers and
investigate what is required to experience sound. Students will use the string to understand the
relationship between the length of the string and the frequency of the sound.
Suggested Grade Range: 6-8
Approximate Time: 1 hour
State of California Content Standards:
Science Content Standards Grade 6: Physical Sciences
Students know energy can be carried from one place to another by heat flow or by waves,
including water, light and sound waves, or by moving objects.
Science Content Standards Grade 7: Investigation and Experimentation
Scientific progress is made by asking meaningful questions and conducting careful
investigations. As a basis for understanding this concept and addressing the content in
the other three strands, students should develop their own questions and perform
investigations. Students will:
d. Construct scale models, maps, and appropriately labeled diagrams to communicate
scientific knowledge (e.g., motion of Earth’s plates and cell structure).
Science Content Standards High School: Physics
4. Waves have characteristic properties that do not depend on the type of wave. As a
basis for understanding this concept:
a. Students know waves carry energy from one place to another.
b. Students know how to identify transverse and longitudinal waves in mechanical media,
such as springs and ropes, and on the earth (seismic waves).
d. Students know sound is a longitudinal wave whose speed depends on the properties of
the medium in which it propagates.
Relevant National Content Standards:
Next Generation Science Standards: Middle School Physical Science
MS-PS4-1. Use mathematical representations to describe a simple model for waves that
includes how the amplitude of a wave is related to the energy in a wave. [Clarification
Statement: Emphasis is on describing waves with both qualitative and quantitative
thinking.] [Assessment Boundary: Assessment does not include electromagnetic waves
and is limited to standard repeating waves.]
1
An early version of this lesson was adapted and field-tested by Emily Sanders, Steven Richardt, Diane
Jackson, Krissy Cuevas, Janie Oetken, Mireya Valenzuela, and Angela Lytle, participants in the
California State University, Long Beach Foundational Level Mathematics/General Science Credential
Program.
STEM Activities for Middle and High School Students
The Soundinator
3-1
MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or
transmitted through various materials. [Clarification Statement: Emphasis is on both
light and mechanical waves. Examples of models could include drawings, simulations,
and written descriptions.] [Assessment Boundary: Assessment is limited to qualitative
applications pertaining to light and mechanical waves.]
Lesson Content Objectives:
 Construct a device to experiment with creating and experiencing sound, called a
Soundinator.
 Investigate and understand the necessary components for experiencing sound
including the vibrating source, the medium, and the receiver.
 Draw and appropriately label a diagram of a Soundinator to indicate the vibrating
source, the medium, and the receiver.
Materials Needed:
 1-2 feet of string per pair of students
 One metal hanger per pair of students
 Wire cutters (one or two per class)
 Optional
o One plastic cup per pair of students with a hole punched in the bottom (do not
use hard plastic cups because there needs to be some “give” in order to punch
a hole without cracking the cup)
o One paper clip per pair of students
STEM Activities for Middle and High School Students
The Soundinator
3-2
Summary of Lesson Sequence
 Introduce the lesson by leading students in a discussion about their experience with
sound.
 Guide students through building and experimenting with their sound experience
apparatus, the Soundinator.
 Check for students’ understanding by asking the key questions provided while
students are experimenting with the Soundinator.
 Allow students to practice their understanding of the three necessary components of
sound experience by drawing and labeling a model of the Soundinator.
 To close the lesson, have students verbally describe other devices for which they can
distinguish the vibrating source, medium, and receiver.
Assumed Prior Knowledge
Prior to this lesson students should have a basic understanding that energy can be carried
from one place to another by sound waves.
Classroom Set Up
Students should work in groups of two or three to construct and experiment with their
Soundinator.
Lesson Description
Introduction
Lead students in a discussion of their different experiences with sound by asking:
What experiences or situations have you been in when sound was different than normal?
Under what contexts is sound decreased?
Have you ever heard sounds under water? How is that different than hearing sounds in
the air?
How might we make different sounds from the same object?
Does anyone in the class play an instrument?
How do you create different sounds with that instrument?
When students have had an opportunity to share their experiences and knowledge about
sound, tell them:
Today we will determine the necessary components to experience sound and we will be
constructing a device with those components to experiment with.
STEM Activities for Middle and High School Students
The Soundinator
3-3
Input and Model
Demonstrate for students how to construct the Soundinator. There are two different
versions of the Soundinator.
1.
2.
3.
4.
5.
6.
Version 1
Each pair needs a cup, a piece of string, a paper clip, and a
metal hanger.
Tie one end of the string to the paper clip.
Thread the other end of the string through the hole punched
in the cup so that the paper clip is inside of the cup with the
string coming out through the bottom of the cup.
Tie the metal hanger to the string or simply hang it over the
string while holding the other end of the string.
Two students may listen at the same time if a second cup is
connected to the other end of the string as shown.
Tap the hanger and listen!
1.
2.
3.
4.
Version 2
Each pair needs a cup, a piece of
string and a metal hanger.
Tie the metal hanger to the string.
Hold the string up to your ear and
press against the bone outside your
ear.
Tap the hanger while holding the
string to your ear.
Note: the hanger does not need to be cut/bent as shown in the picture above. It could be a complete hanger
connected to two cups. Be sure to use a metal hanger (not plastic or one with a cardboard cover).
Guide Students Through Their Practice
Explain that each student will have the opportunity to be a “listener” and also a sound
“producer.” Allow students to choose who will be first as the “listener.”
Have students hold the cup so that the hanger is dangling from the cup in mid-air. Next,
tap the hanger and observe what kinds of sound they hear, including whether the sound is
loud or soft.
Next, the listener should stand up and hold the cup to their ear so that the string and
hanger may hang freely without touching anything. The producer will then produce
sound by gently tapping the hanger with their pencil on different places. The listener
should not tell the producer what they hear. Students should switch roles after some time.
After both students have had a chance to the listener, have them remove the cup and hold
the string with the hanger attached to their ear or jawbone. The producer should gently
tap the hanger. Students should switch roles so both get a chance to listen.
STEM Activities for Middle and High School Students
The Soundinator
3-4
Check for Understanding
Check for students’ understanding while they are experimenting by asking the following
key questions:
What parts of your Soundinator help you to experience sounds when you are the listener?
What was the purpose of the hanger?
What was the purpose of the string?
What was the purpose of the cup (if using version 1)?
Do you need all the different parts of the Soundinator to experience sounds?
What else do you need to experience sound?
You need a vibrating source, a medium, and a receiver to experience sound. Can you
identify these components as parts of your Soundinator?
When students have identified the three components necessary for experiencing sound,
and are experiencing sounds with the string, ask the following key questions:
Did it sound different if you hit different parts of the hanger?
Did it sound differently with and without the cup?
Do you think it would sound differently if you had a short piece of string versus a long
piece of string?
Do you think it would sound differently if you had a smaller or larger hanger, or only
part of the hanger?
Students should recognize that the size of the hanger makes a difference in terms of what
they hear. The vibrating hanger is the source. (If students have not figured this out,
encourage them to try listening to a whole hanger versus a hanger piece that has been cut
off. You will need wire cutters to do this investigation.)
Students should recognize that the length of string does not make a difference in terms of
what they hear. The string is the medium that carries or transmits the wave.
Independent Practice
After students have had the opportunity to use the Soundinator and have verbally
identified the vibrating source, medium and receiver components, instruct them to create
a drawing of the Soundinator. Students should label their drawing with the components
of the device and their functions (students will need to also draw a receiver, their ear, but
might need explicit direction to do so).
STEM Activities for Middle and High School Students
The Soundinator
3-5
Closure
To close the lesson, challenge students to think of other sound experiencing devices for
which they can identify the vibrating source, medium, or receiver. It might be worth
revisiting the pre-lesson questions to see if students are able to apply their understanding
of sound. At this point, ask students about sound in space (or a vacuum).
Can astronauts hear sounds in space? What is different in space than on Earth that
changes how we experience sound? What does this tell us about the accuracy of movies
or television shows that take place in outer space? (It is quiet in space. There is no
atmosphere, so no medium to vibrate and carry the sound.)
Suggestions for Differentiation and Extension

Sound Bite:
Have students slide a straw over a pencil or wooden dowel and place one end on a wall or
table. Ask students to bite on the pencil or dowel while plugging their ears and observe
what they hear without using their ears. (The straw is for sanitary purposes, it is not a
required element.)
http://www.exploratorium.edu/listen/activities/lisa/bone_conduction/listen_sound_bite.pdf

PHET Sound Simulation:
Visit the website http://phet.colorado.edu/en/simulation/sound and let students experience the
ranges of frequencies which they are able to hear by selecting the Listen to a Single
Source page. Enable the audio on the program to hear the sounds being generated and
adjust the frequency and amplitude. Discuss the relationship between the frequency and
wavelength and how those concepts are related to the length of the string from their
Soundinator and the sounds they experienced.
Visit the Listen with Varying Air Pressure page from the same PHET website to allow
students to hear how the volume decreases and eventually disappears as air pressure
decreases to a vacuous state.

Straw Kazoo:
Visit one of the websites below to get directions on how to make a kazoo from a straw.
The pitch of the kazoo will change as the length of the straw changes. The straw is
vibrating as the students blow through it. If the straw is cut the length of straw which
vibrates is shorter. A shorter wavelength means higher frequency or pitch. You can see
(and hear) the kazoo in action at http://www.youtube.com/watch?v=Z15l5gLnfo4.
http://pbskids.org/zoom/activities/sci/strawkazoo.html
http://www.wikihow.com/Make-a-Straw-Kazoo
STEM Activities for Middle and High School Students
The Soundinator
3-6
Drop of Doom!4
Students will use the function for the height of a free falling object to explore functions and their
graphs.
Suggested Grade Range: 7-12
Approximate Time: 1 hour
State of California Standards:
Mathematics Standards Grade 7: Algebra and Functions
1.2: Use the correct order of operations to evaluate algebraic expressions.
1.5: Represent quantitative relationships graphically and interpret the meaning of
a specific part of a graph in the situation represented by the graph.
Mathematics Standards Grades 8-12: Algebra I
23.0: Students apply quadratic equations to physical problems, such as the
motion of an object under the force of gravity.
Science Content Standards Grade 8: Physical Sciences
1. The velocity of an object is the rate of change of its position. As a basis for
understanding this concept:
b. Students know that average speed is the total distance traveled divided by the total
time elapsed and that the speed of an object along the path traveled can vary.
d. Students know the velocity of an object must be described by specifying both the
direction and the speed of the object.
e. Students know changes in velocity may be due to changes in speed, direction, or both.
f. Students know how to interpret graphs of position versus time and graphs of speed
versus time for motion in a single direction.
Science Content Standards Grades 9-12: Physics
1. Newton’s laws predict the motion of most objects. As a basis for understanding this
concept:
e. Students know the relationship between the universal law of gravitation and the effect
of gravity on an object at the surface of Earth.
Relevant National Standards:
Mathematics Common Core State Standards:
4
An early version of this lesson was adapted and field-tested by Katiria Hernandez and Gina Hryze,
participants in the California State University, Long Beach Foundational Level Mathematics/General
Science Credential Program.
STEM Activities for Middle and High School Students
Drop of Doom!
4-1
8.EE Understand the connections between proportional relationships, lines, and linear
equations.
8.F Define, compare, and evaluate functions.
Next Generation Science Standards:
5-PS2-1. Support an argument that the gravitational force exerted by Earth on objects is
directed down. [Clarification Statement: “Down” is a local description of the direction
that points toward the center of the spherical Earth.] [Assessment Boundary: Assessment
does not include mathematical representation of gravitational force.]
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion
describes the mathematical relationship among the net force on a macroscopic object, its
mass, and its acceleration. [Clarification Statement: Examples of data could include
tables or graphs of position or velocity as a function of time for objects subject to a net
unbalanced force, such as a falling object, an object rolling down a ramp, or a moving
object being pulled by a constant force.] [Assessment Boundary: Assessment is limited to
one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.]
Lesson Content Objectives:
 Evaluate functions using the correct order of operations.
 Describe and represent functions using tables and graphs.
 Make interpretations about an object’s motion and position based on its function and
graph.
Materials Needed:
 Lined or graph paper
 One copy per student of the warm-up activity sheet and “Drop of Doom!” activity
sheet (included)
Adapted From:
Rubin, K. (n.d.). Illuminations: Roller Coasting Through Functions. Retrieved from
http://illuminations.nctm.org/LessonDetail.aspx?id=L839.
STEM Activities for Middle and High School Students
Drop of Doom!
4-2
Summary of Lesson Sequence
 To introduce the lesson, connect students’ work on graphing functions from the warm up
(included) to their experiences with roller coaster rides by discussing how the motion of a
roller coaster may be described using formulas or graphs.
 Lead students through compiling notes while modeling how to evaluate and graph a
function that represents a falling object’s motion.
 Guide students through their own practice of evaluating a function, completing a table of
values, and graphing the function using the “Drop of Doom!” activity sheet (included).
 Check for students’ understanding by asking the key questions provided.
 To close the lesson, allow students to discuss in pairs how to find the time it takes for a
roller coaster to reach the bottom of a drop.
 For independent practice, students may create and graph their own function to represent
the motion of a roller coaster that they design.
Assumed Prior Knowledge
Prior to this lesson students should know how to use the correct order of operations to
solve equations and be able to graph ordered pairs to represent a function.
Classroom Set Up
Students will be asked to participate in discussions and work in pairs for portions of this
lesson.
Lesson Description
Introduction
Provide students with the “Warm Up: Preparing for the Drop of Doom” (included) to
focus their attention to working with functions. As students are finishing the warm up,
ask students to discuss what mathematics is associated with roller coaster rides.
Ask: How do you think roller coasters and math are related? [speed, height, formulas,
etc.] Explain that engineers use functions to determine a roller coaster’s height above
ground after a certain amount of time.
Input and Model
 Lead students through notes by modeling using the function describing the height of
an object in free fall dropped above Earth. Explain the following:
The height of an object that is dropped from above Earth can be determined using the
formula h = f(t) = ½ (-32)t2 + s, where s is the starting height of the object in feet.
Notice that the height of the object is a function of time and does not depend on the
object’s mass. The coefficient -32 comes from the fact that an object’s acceleration
due to gravity as it falls to Earth is -32 feet per second squared. The formula may be
simplified to f(t) = -16t2 + s, where: t = time in seconds and s = initial height in feet.
STEM Activities for Middle and High School Students
Drop of Doom!
4-3
The formula may be used to create a chart of values for the time and height of the object
which may be graphed as ordered pairs (t, f(t)).
For example, an object dropped from 144 feet above Earth, will have an initial height of
144 ft. (see table below).
Copy the following table in your notes:
Time in
Height in
Ordered Pair
2
f(t) = -16(t) + s
seconds
feet
(t, f(t))
2
f(0) = -16(0) + s
144
(0, 144)
0
2
f(1) = -16(1) + s
128
(1, 128)
1
2
3


2
f(2) = -16(2) + s
2
f(3) = -16(3) + s
80
0
(2, 80)
(3, 0)
Ask students to discuss what happens 3 seconds into the roller coaster ride.
Graph the resulting ordered pairs on a height vs. time coordinate plane.
Guide Students Through Their Practice
Distribute the “Drop of Doom!” activity sheet (included) and allow students to work
independently or in pairs. Guide students by moving through the classroom assisting
those who need it and checking that students are using the correct order of operations.
Check for Understanding
Check for students’ understanding by orally guiding them through the key questions
below. These questions may be used to determine whether students are ready to do
similar work on their own.
1. Why are all of the graphical representations in the first quadrant only? [Time is on
the x-axis and we cannot have negative time. Height is on the y-axis, and roller
coasters do not go below ground or “0.”]
2. The equation we are using does not take into account certain things that may have an
effect on the roller coaster as it drops. What are some things that could affect the
drop? [e.g., friction, weight of people in the car, weather]
3. If you saw the ordered pair (3,112) in your data table, what would it mean? [After 3
seconds, the roller coaster is 112 feet above ground.]
4. Let t represent the time in seconds and f(t) represent the height above ground of the
roller coaster. What is a question that could represent the ordered pair (t, 60)? What
is a question that could represent the ordered pair (4.5, f(t))?" [The ordered pair (t,
60) represents the question, "How long will it take the roller coaster to be 60 feet
above ground?" The ordered pair (4.5, f(t)) represents the question: "How high above
ground will the coaster be after 4.5 seconds?"]
5. Which of the following ordered pairs would be unreasonable if it appeared in the
context of this problem?(1,144), (-2, 1000), (8, -124), (0,1)? Why? [The second, third,
STEM Activities for Middle and High School Students
Drop of Doom!
4-4
and fourth are unreasonable ordered pairs. The second is unreasonable because time
should not be negative. The third is unreasonable because roller coasters do not travel
124 feet below ground. The last is unreasonable because the initial drop is more than
1 foot tall.]
Independent Practice
Students may practice what they learned independently by designing a roller coaster
drop, writing the function for it’s height, finding values for the height at different times,
and graphing the results. To design their roller coaster, students are choosing the height,
s, of the drop in the formula: f(t) = -16t2 + s .
Closure
Allow students to discuss a way to find out the time it takes for a roller coaster to reach
the bottom of a drop in pairs and write their responses as a “ticket out the door.”
Suggestions for Differentiation
 Students who have difficulty evaluating functions or graphing ordered pairs could be
pulled into a small group to receive assistance while the class is working on their guided
practice.
 To extend the activity, advanced students may be introduced to the formula for the
motion of a roller coaster that has an initial velocity before it begins to fall: f(t) = – 16t2 +
vt + s.
STEM Activities for Middle and High School Students
Drop of Doom!
4-5
Warm Up
Preparing for the Drop of Doom
Directions: Complete each function table by finding the values for y. Show your work in the
space provided. Graph the ordered pairs (x, f(x)) for each equation.
1. f(x) = x – 5
x
Show work here:
Graph:
Show work here:
Graph:
f(x)
-2
1
2
4
2. f(x) = 2x
x
f(x)
-2 ½
0
2
3
STEM Activities for Middle and High School Students
Drop of Doom!
4-6
Drop of Doom!
Name _________________
A new roller coaster ride at Six Flags Magic Mountain recently opened in Valencia,
California. At the highest point of the ride, Drop of Doom drops thrill seekers from
a record-breaking height!
Use the formula f(t) = -16t2 + 400 to determine the height of the coaster at
several times during the descent and use the data to determine how long it takes
the coaster to reach the bottom.
1. Complete the table to determine how long it takes Drop of Doom to reach the
bottom of its highest drop:
Time t
f(t) = -16t2 + 400
Height (ft)
Ordered Pair (t, f(t))
(sec)
0
1
2
3
4
2. Graph the ordered pairs below:
STEM Activities for Middle and High School Students
Drop of Doom!
4-7
3. What is the height of the coaster before it
begins to drop? How do you know?
4. After how many seconds does Drop of Doom
reach the bottom? How do you know?
5. If you did not know the height of a specific drop on a roller coaster, how could
you find out the height without measuring it directly? Write a plan for how you
would collect the data you would need to determine the height of a drop on a
roller coaster you were watching or riding.
STEM Activities for Middle and High School Students
Drop of Doom!
4-8
Reflections on Light5
Students will explore the general behavior of light when it is reflected and the behavior of light
when it is reflected in specific angles.
Suggested Grade Range: 7-12
Approximate Time: 1 hour
State of California Content Standards:
Mathematics Content Standards Grade 5: Measurement and Geometry
2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and
triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor,
drawing software).
Science Content Standards Grade 7: Physical Science
6. Physical principles underlie biological structures and functions. As a basis for
understanding this concept:
c. Students know light travels in straight lines if the medium it travels through does not
change.
f. Students know light can be reflected, refracted, transmitted, and absorbed by matter.
g. Students know the angle of reflection of a light beam is equal to the angle of incidence.
Relevant National Standards:
Mathematics Common Core State Standard: High School Geometry G-CO
12. Make formal geometric constructions with a variety of tools and methods (compass
and straightedge, string, reflective devices, paper folding, dynamic geometric software,
etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.
Next Generation Science Standards:
MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or
transmitted through various materials. [Clarification Statement: Emphasis is on both
light and mechanical waves. Examples of models could include drawings, simulations,
and written descriptions.] [Assessment Boundary: Assessment is limited to qualitative
applications pertaining to light and mechanical waves.]
5
An early version of this lesson was adapted and field-tested by Karen Hardy, a participant in the
California State University, Long Beach Foundational Level Mathematics/General Science Credential
Program.
STEM Activities for Middle and High School Students
Reflections on Light
5-1
Lesson Content Objectives:
 Understand and use the vocabulary for the lesson: angle of incidence, angle of
reflection, normal line, and Law of Reflection.
 Use a flashlight, mirror, and construction paper to explore angles of incidence and
reflection.
 Generalize the results of the exploration to verify the Law of Reflection.
 Construct and describe a diagram of the light’s path
Materials Needed:
 One flashlight per group of three
 Several small mirrors per group
 Colored construction paper
 One compass and straightedge per student
 One laser pointer per group (optional as an extension)
STEM Activities for Middle and High School Students
Reflections on Light
5-2
Summary of Lesson Sequence
 Lead students through their note taking by providing the vocabulary for the lesson:
angle of incidence, angle of reflection, normal line, and Law of Reflection.
 Model for students the flashlight, mirror and construction paper set up.
 Guide students through their exploration reflecting light off a mirror onto a piece of
construction paper.
 Check for students’ understanding by asking the key questions provided while
students are working.
 Close the lesson by allowing students to verbally describe what they discovered the to
be Law of Reflection.
Classroom Set Up
This activity works well for students in groups of three or four.
Lesson Description
Introduction
Explain to students that they will be exploring how light is reflected off a mirror to
predict the Law of Reflection. Show students the general set up using a flashlight, mirror,
and construction paper. Do not turn on the flashlight when modeling the set up so that
students may explore the path of the light in their own groups. With a mirror resting flat
on a table, hold a flashlight at an angle pointing down toward the mirror. Explain that the
light will reflect upward off the mirror and they will need to use a piece of construction
paper to catch the light above the mirror.
Input and Model
Provide students with the vocabulary they will need for this activity so they may take
notes:
Angle of incidence: The angle formed by a ray of light that travels toward a surface and
a line perpendicular to the surface. (Demonstrate the angle using a flashlight and an
object, such as a string, that forms a line perpendicular to the mirror.)
Angle of reflection: The angle formed by a ray of light that travels away from the surface
and a line perpendicular to the surface. (Do not demonstrate this angle because it will be
the task of the students’ to determine it.)
Normal line: The imaginary line perpendicular to the surface of reflection. (Demonstrate
the normal line using an object, such as a string, perpendicular to the mirror’s surface.)
*Law of Reflection: (Explain that students will determine the Law of Reflection based on
their exploration.)
Guide Students Through Their Practice
Provide each group of three or four students with a flashlight, mirrors and construction
paper. Allow students to begin their exploration and remind them that their goal is to
predict the Law of Reflection. Advise students that their task is to reflect light from a
mirror onto the construction paper. Students should not lift the mirror from the table and
STEM Activities for Middle and High School Students
Reflections on Light
5-3
should not aim the light onto any surface other than the mirror and the construction paper.
Move around the room to ensure students are following these directions. They will be
shining the light onto the mirror from several different angles.
Check for Understanding
Check for students’ understanding while they are exploring by utilizing the following
questions/prompts:
Did you instinctively know where to hold the paper in order to catch the light?
What is the relationship between how you hold the flashlight and where the light goes?
What role does the mirror play?
Use your finger to outline the angle of incidence.
Use your finger to outline the angle of reflection.
Use your finger to outline the normal line.
Use the vocabulary you learned today to describe how the light is reflected.
Independent Practice
Using their understanding of the Law of Reflection, students should work independently
to construct and label a diagram of the light’s path using a compass and straightedge.
Diagrams should include a depiction of the following: flashlight, mirror, construction
paper, angle of incidence, normal line, angle of reflection, and an indication of the
congruent angles.
Closure
To close the lesson, allow students to describe verbally what they predict the Law of
Reflection to be. Encourage students to use the vocabulary presented in the lesson. Once
a few students have had an opportunity to state the Law of Reflection in their own words,
allow them to update their notes:
Law of Reflection: the angle of incidence measured from the normal line is equal to the
angle of reflection measured from the normal line.
STEM Activities for Middle and High School Students
Reflections on Light
5-4
Give students directions to write a description of their diagram using the Law of
Reflection.
Suggestions for Differentiation and Extension
 To extend this activity to outside of the classroom, allow students to find examples of the
Law of Reflection outside of class and return with a diagram of what they found. They
might find evidence of the law of reflection with light or sound but they might also find
that objects follow the law of reflection as well. A ball reflecting off a surface
(basketball, billiards, miniature golf, etc.) will also follow the law of reflection.
 To extend the activity in class, have students construct an arrangement of mirrors that
would reflect light from a fixed point A to another fixed target point B. As an added
challenge, place obstacles between the points to create a maze for students to work with
by adjusting mirror positions and angles. If available, laser pointers should be used for
this extension. Students could first predict the path of the laser then set up the maze to see
if their prediction was accurate using a figure such as the ones below.
STEM Activities for Middle and High School Students
Reflections on Light
5-5
Extension Activities:
Challenge students to make the light move down the prescribed pathway. They use mirrors and a
laser beam or flashlight.
STEM Activities for Middle and High School Students
Reflections on Light
5-6
Extension Activities:
Once students understand the law of reflection they can use their new knowledge to
predict the path of light. In this extension activity the teacher sets up a series of mirrors
and the starting point for a light beam (laser pointers work best for this). The students’
task is to determine where the light beams will be after being turned on. It is worth
noting that not all mirros will be used (they might be, but don’t have to be).
Sample arrangement of mirrors and incoming light beam.
Sample of student work to show path of light beam and predicted exit point. Once students draw their light beam’s
path and predict the exit point they should be encouraged to test their prediction to see if they were correct.
target
STEM Activities for Middle and High School Students
Reflections on Light
5-7
Extension Activities:
Once students understand the law of reflection they can use their new knowledge to determine the placement of
mirrors so that a light beam can travel around obstacles in order to go from the entrance to the exit point in a
“maze”. You can either draw a series of obstacles on a piece of chart paper or you can place actual obstacles on the
tabletop for students to avoid. Indicate an entrance and exit point and have students predict where they should place
mirrors so that the light beam successfully travels from the entrance to the exit. Placing or drawing obstacles on
chart paper provides a writing surface for students to draw the light path, measure angles, etc. Once students have
placed all their mirrors they are allowed to test their predictions to see how they did.
Materials needed: small plane mirrors, small binder clips (attached to the bottom side edge of the mirror to hold the
mirror erect), laser beam (one per class is sufficient), protractors, rulers (helps for drawing straight lines), colored
markers
Sample maze
E
N
T
R
A
N
C
E
EXIT
OBSTACLES
Once students have successfully arranged mirrors so the light beam goes from entrance to exit you can challenge
them to do complete the task using a specific number of mirrors.
STEM Activities for Middle and High School Students
Reflections on Light
5-8
How Much Water Fits on a Penny?6
Students conduct an experiment to determine how many drops of water will fit on a penny and
apply their knowledge of the properties of water and chemical bonds to explain the phenomenon.
Suggested Grade Range: 7-9
Approximate Time: 1 hour
State of California Standards:
Science Content Standards Grades Nine through Twelve- Chemistry
2. Biological, chemical, and physical properties of matter result from the ability of atoms
to form bonds from electrostatic forces between electrons and protons and between atoms
and molecules. As a basis for understanding this concept:
a. Students know atoms combine to form molecules by sharing electrons to form covalent
or metallic bonds or by exchanging electrons to form ionic bonds.
b. Students know chemical bonds between atoms in molecules such as H2, CH4, NH3,
HCCH, N, Cl, and many large biological molecules are covalent.
Science Content Standards Grade Seven- Investigation and Experimentation
7.0 Scientific progress is made by asking meaningful questions and conducting careful
investigations. As a basis for understanding this concept and addressing the content in
the other three strands, students should develop their own questions and perform
investigations. Students will:
c. Communicate the logical connection among hypotheses, science concepts, tests
conducted, data collected, and conclusions drawn from the scientific evidence.
Mathematics Standards Grade 8: Probability and Statistics
10.0 Students know the definitions of the mean, median, and mode of distribution of data
and can compute each of them in particular situations.
Relevant National Standards:
Mathematics Common Core State Standard: 7.SP
2. Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated samples) of
the same size to gauge the variation in estimates or predictions. Gauge how far off the
estimate or prediction might be.
6
An early version of this lesson was adapted and field-tested by Sherri Gonser, Karen Hardy, and David
Macander, participants in the California State University, Long Beach Foundational Level
Mathematics/General Science Credential Program.
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-1
Next Generation Science Standards:
MS-PS1-1. Develop models to describe the atomic composition of simple molecules and
extended structures. [Clarification Statement: Emphasis is on developing models of
molecules that vary in complexity. Examples of simple molecules could include ammonia
and methanol. Examples of extended structures could include sodium chloride or
diamonds. Examples of molecular-level models could include drawings, 3D ball and stick
structures or computer representations showing different molecules with different types
of atoms.] [Assessment Boundary: Assessment does not include valence electrons and
bonding energy, discussing the ionic nature of subunits of complex structures, or a
complete depiction of all individual atoms in a complex molecule or extended structure.]
Lesson Content Objectives:
 Practice using a pipette to be able to release one drop of liquid at a time.
 Be able to define surface tension, covalent bond, and cohesion.
 Conduct an experiment and analyze the data using central measures of tendency to
determine how many drops of distilled water and soapy water will typically fit on a
penny and compare the results.
 Be able to explain the phenomenon applying knowledge of the properties of water.
Materials Needed:
 One pipette for each pair of students
 Two pennies for each pair of students
 One beaker of distilled water for each pair of students
 One beaker of soapy water for each pair of students
 Paper towels
 One copy per student of the “How Much Water Fits on a Penny?” activity sheet
(included)
 Food coloring
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-2
Summary of Lesson Sequence
 Introduce the lesson by allowing students to observe that drops of water can be added
to a beaker already filled to the top without it spilling and by engaging students’ prior
knowledge of the properties of water to explain what might be happening.
 Lead students through a discussion and note taking of the terms for this lesson:
cohesion, surface tension, and covalent bond.
 Allow students to practice using a pipette before beginning their experiment.
 Guide students through their experiment to determine how many drops of distilled
water will fit on a penny and how many drops of soapy water will fit on a penny.
 Check for students’ understanding by asking the provided key questions while
students are experimenting.
 Close the lesson by allowing all the pairs of students to share their data to compile
and analyze in a classroom discussion.
 Students work independently to summarize their understanding of the properties of
water as they relate to this experiment by responding to comprehension questions on
the “How Much Water Fits on a Penny?” activity sheet (included).
Assumed Prior Knowledge
Prior to this lesson students should already be familiar with the chemical properties of
water and have an understanding of covalent bonds. Students should be able to calculate
the mean of a data set and interpret the mean as a measure of central tendency of
collected data.
Classroom Set Up
Each pair of students will need a pipette, a beaker of distilled water, and a beaker of
soapy water to conduct the experiment. Paper towels should be available for each pair of
students. To prevent students working with the pipettes and pennies prematurely, do not
provide the pipettes or pennies until the guided practice portion of the lesson.
Lesson Description
Introduction
Fill a beaker to the brim with distilled water colored with food coloring. Ask students: Is
the beaker full? Because the beaker is filled to the brim, students may respond that it
appears full. Begin to carefully add more water, one drop at a time, with a pipette. Ask
students to count out loud how the number of drops added before the water begins to spill
over the top.
Engage students in a discussion connecting to their prior knowledge of the properties of
water by asking: What chemical properties does water have? What have you learned
about water that may help us understand why more water can be added to a full beaker
without spilling over?
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-3
Inform students: Today you will conduct an experiment and apply your knowledge of the
chemical properties of water to understand its cohesive behavior. Before the experiment,
we will review a few key concepts and you will practice using a pipette.
Input and Model
Lead students in their note taking by providing them with the key terms for the lesson:
Cohesion: Water molecules are attracted to other water molecules. The oxygen end of
water has a negative charge and the hydrogen end has a positive charge. The hydrogen
atoms of one water molecule are attracted to the oxygen end of another water molecule.
This attractive force is what gives water its cohesive property.
Ask students: How could you draw a picture depicting the cohesive nature of several
water molecules? What might be another, non-technical word for cohesion? If water
molecules “stick” together, how can water be a liquid and not a solid? [The attraction
that causes cohesion is different from the bonds that form to make a solid.]
Surface tension: the cohesion of water molecules at the surface of a body of water.
Covalent bond: a chemical bond that involves sharing a pair of electrons between atoms
in a molecule.
Guide Students Through Their Practice
Provide pairs of students with a pipette with which to practice making single drops.
Guide students by moving around the room and checking each student can carefully
make one drop at a time onto a paper towel. If necessary, have students further practice
by forming their initials with single drops of water onto a paper towel. The goal is for
students to create similar sized drops of water each time.
When each student has had practice using the pipette correctly, provide each pair with
two pennies. Pairs of students will drop distilled water on one penny and soapy water on
the other.
Check for students’ understanding while they begin their experiment by asking them to
predict:
Do you think the number of drops of distilled water will be the same as the soapy water?
How will you know when no more drops fit on the penny?
How can you prevent water splashing off the penny?
Provide each student with the “How Much Water Fits on a Penny?” activity sheet.
Guide students through their experiment by giving them the following directions:
Each student will have a chance to drop distilled water on one penny and drop soapy
water on the other penny.
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-4
When one student is dropping the water, the other student should be watching, counting
out loud the number of drops, and recording the number of drops before the water spills
over the edge of the penny.
When a drop causes the water to spill over the edge of the penny, stop!
Do this with the distilled water on one penny, then soapy water on the other penny.
Dry off your pennies and switch roles with your partner so that your team can get data
from multiple trials. It is important that each partner performs the experiment with both
the distilled water and the soapy water because they may create different sized drops.
We want to discover how many drops of water will fit on a penny and be able to explain
what happens using our understanding of the properties of water.
Move around the room to ensure students are using the pipettes carefully and counting
the number of drops accurately.
Checking for Understanding
When everyone has had the opportunity to record their results, allow each pair of students
to share their data with the rest of the class. Every student should record all of the data on
his/her activity sheet (although they will be working in pairs, each students will be
responsible for completing the activity sheet). The class should then calculate the average
number of drops of distilled water and soapy water that will fit on a penny. During a
whole class debrief, lead a discussion with the following questions:
What causes the water to stay on the penny?
What did you notice about the number of drops of soapy water versus the number of
drops of distilled water?
Based on the class data averages, what happens to the cohesion between water molecules
when soap is added to water? (Teacher note: Soap causes the cohesiveness of the water
molecules to decrease so they are not as strongly attracted to each other. Because of this,
when soap is added to the water the number of drops that can be placed on the penny will
decrease. The water molecules can't 'stick' together as well, so the water on top of the
penny spills off sooner than it would with non-soapy water.)
What are some reasons students might not get the exact same number of drops?
Independent Practice
Students should work independently to summarize their understanding of the properties
of water as they relate to this experiment by analyzing the collected data and responding
to comprehension questions on the “How Much Water Fits on a Penny?” activity sheet.
Suggestions for Differentiation and Extension
To extend this activity, students may explore the cohesiveness of other liquids, such as
rubbing alcohol or vegetable oil, on their own and report their results to class.
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-5
How Much Water Fits on a Penny?
1. Complete the chart with your data, your partner’s data and then data from the rest of the class.
Team #
1
Partner 1
Partner 2
2
Partner 1
Partner 2
3
Partner 1
Partner 2
4
Partner 1
Partner 2
5
Partner 1
Partner 2
6
Partner 1
Partner 2
7
Partner 1
Partner 2
8
Partner 1
Partner 2
9
Partner 1
Partner 2
10
Partner 1
Partner 2
11
Partner 1
Partner 2
12
Partner 1
Partner 2
13
Partner 1
Partner 2
14
Partner 1
Partner 2
15
Partner 1
Partner 2
Drops of Distilled Water
Drops of Soapy Water
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-6
2. Calculate the mean number of drops for the class for distilled water to complete your chart.
Calculate the mean number of drops for the class for soapy water to complete your chart.
Use your understanding of the properties of water and the experimental data to respond to the
following:
3. Draw a diagram several water molecules in distilled water showing how they might interact.
Use arrows in your diagram and words such as: oxygen, hydrogen, bond, and attraction.
4. Describe what caused several drops of water to stay on the penny using the concepts and
vocabulary you learned for this lesson. Why do you think the results were different for distilled
and for soapy water?
STEM Activities for Middle and High School Students
How Much Water Fits on a Penny?
6-7
Snack Time!7
Students will analyze nutritional information labels from several foods and represent data from
the labels in multiple forms. They will summarize their findings by writing how to determine
how healthy a snack item may be based on multiple measures. Students will also recognize that
the nutritional content of similar foods can vary.
Suggested Grade Range: 6-8
Approximate Time: 2 hours
State of California Standards:
California Standards: 8th Grade Probability and Statistics
6.0 Students know the definitions of the mean, median, and mode of a distribution of data
and can compute each in particular situations.
8.0 Students organize and describe distributions of data by using a number of different
methods, including frequency tables, histograms, standard line and bar graphs, stem-andleaf displays, scatterplots, and box-and-whisker plots.
Relevant National Standards:
Mathematics Common Core State Standard: 7.SP
Draw informal comparative inferences about two populations.
Use measures of center and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations.
Next Generation Science Standards:
5-PS3-1.Use models to describe that that energy in animals’ food (used for body repair,
growth, motion, and to maintain body warmth) was once energy from the sun.
[Clarification Statement: Examples of models could include diagrams, and flow charts.]
Lesson Content Objectives:
 Gather data from several nutrition labels.
 Represent the data in a bar graph, box-and-whisker plot, and pie chart.
 Compare the data to write a summary of how to determine whether a snack is
healthy by reading the nutrition label.
Materials Needed:
 Lined paper
 Nutrition labels for foods (several are provided)
 One copy per student of the “Five Number Summary: Warm Up”, “Guided
Notes”, and “Stack Time! Activity Sheet”(included)
7
An early version of this lesson was adapted and field-tested by Katrina Hernandez and Gina Hryze,
participants in the California State University, Long Beach Foundational Level Mathematics/General
Science Credential Program.
STEM Activities for Middle and High School Students
Snack Time!
7-1

Healthy snack of choice for students (optional)
STEM Activities for Middle and High School Students
Snack Time!
7-2
Summary of Lesson Sequence
 Assign an anticipatory set of exercises to create a five number summary as well as the
mean and mode for a set of data.
 Introduce the lesson by leading a classroom discussion about students’ prior knowledge
of the information provided on food labels.
 Review by modeling an example of creating a five number summary and box-andwhisker plot from a set of data, and creating pie charts and bar graphs.
 Guide students through their own practice of organizing the data from provided nutrition
labels to create a five number summary, box-and-whisker plot, pie chart, and bar graph.
 Check for students’ understanding by asking guiding questions while students analyze
food labels and write a summary of which foods would be healthiest for them.
 To close the lesson, allow students to share their summaries of how to assess whether a
snack is healthy based on their data analyses.
 For independent practice, students may be assigned the task of analyzing food labels at
home to create a box-and-whisker, pie chart, or bar graph at home.
Assumed Prior Knowledge
Prior to this lesson students should know how to create a five number summary of a set
of data, determine the mean and mode, and be able to create a box-and-whisker plot, bar
graph, and pie chart from data. Students will be using what they already know about
representing data to analyze and make conjectures about real data from nutrition labels.
Classroom Set Up
Students will be asked to work in pairs for portions of this lesson.
Lesson Description
Introduction
 Provide students with the “Five Number Summary: Warm Up” sheet (included) to
allow them to practice finding the minimum, maximum, mean, upper quartile and
lower quartile as well as the mean and mode of a data set.
 When students have completed the warm up, lead a discussion about what students
know about food labels by asking: “If you wanted to have a healthy snack, how would
you decide what have?”, “What information have you noticed is provided on food
labels?”, “What information on food labels do you pay attention to and why?”,
“What information do you usually ignore and why?”
 Allow a few students to contribute ideas after they have shared with a partner.
 Tell students: “Today you will apply your ability to represent data in multiple forms
to analyze the information on nutritional food labels in order to assess whether a
snack is healthy.”
Input and Model
 Lead students through the “Guided Notes” (included) by providing them with the key
vocabulary for the lesson:
STEM Activities for Middle and High School Students
Snack Time!
7-3
Box-and-Whisker Plot – a graph that displays five statistical measures, a minimum, a
maximum, and three quartiles, for a data set.
Five-Number Summary – a form of referring to the five statistical measures graphed on a
box plot as a whole.
a. Minimum value – smallest data point; the end of the left whisker on the box-plot.
b. Maximum value – largest data point; the end of the right whisker on the box-plot.
c. Median– the data point inside the box that represents the middle of the entire data set.
To find the median in data set: 1) Arrange data points in order from lowest to highest;
2) Find middle value: middle value for odd data set or average of two middle values
for even data set.
d. Lower Quartile– the beginning of the box that represents the median of the lower half
of the data.
e. Upper Quartile– the end of the box that represents the median of the upper half of the
data.
Q1
Q2 (Median)
Q3

Minimum

Maximum
 Using a random data sample provided on the guided notes page, model how to find
each value of the five-number summary and create a box-and-whisker plot.
 Use another data set to model creating a pie chart for representing portions of a whole
and a bar graph of the same data to represent data category comparisons.
Guide Students Through Their Practice
 Provide students with the “Snack Time! Nutrition Labels” pages and “Snack Time!
Activity” (included).
 Allow students to work in pairs to complete the activity
Check for Understanding
As students are working together, ask the following key questions to check for their
understanding:
Before you create the box-and-whiskers for the nutritional data, can you predict whether
they will be similar based on the data?
What does the shape of the box-and-whisker plots tell you about two data sets when you
compare them?
When is the mean of a data set useful for making estimates?
When is the mean of a data set not useful for a data set?
STEM Activities for Middle and High School Students
Snack Time!
7-4
What does the bar graph help you to identify quickly about a data set?
How can the pie charts you created help someone who is trying to stay fit make decisions
about what snacks to eat?
Closure
Provide students with the opportunity to reflect on what they have learned and discuss
which snacks would benefit them the most based on their personal situations.
Suggestions for Differentiation and Extension
 Students may analyze nutritional labels at home to compare the amount of protein and
fiber in several foods.
 To extend the lesson, students may create box-and-whisker plots using a graphing
calculator.
 Students may also be asked to analyze food labels given certain dietary needs of they
have or their family members have, such as gluten sensitivity or allergies.
 Students may be given the task to find and compare the percent of calories per serving
size for several foods.
STEM Activities for Middle and High School Students
Snack Time!
7-5
Five-Number Summary: Warm Up
1. Create a five number summary for each data set.
a) 50, 66, 45, 53, 62, 49, 59
b) 25, 32, 18, 29, 35, 15, 25, 30
2. Find the mean for each set of numbers.
a) 50, 66, 45, 53, 62, 49, 59
b) 25, 32, 18, 29, 35, 15, 25, 30
3. Find the mode for each set of numbers.
a) 50, 66, 45, 53, 62, 49, 59
b) 25, 32, 18, 29, 35, 15, 25, 30
STEM Activities for Middle and High School Students
Snack Time!
7-6
Guided Notes (Teacher Copy)
A Review of Five Number Summaries, Box-and-Whisker Plots, Bar Graphs, and Pie Charts
Vocabulary
 Minimum value - smallest data point; represented at the end of the left whisker on the box-plot.
 Maximum value - largest data point; represented at the end of the right whisker on the box-plot.
 Lower quartile (Q1) - the beginning of the box that represents the median of the lower data set.
 Median (Q2) - the middle value in the data set, represented by the line inside the box.
 Upper quartile (Q3) - the end of the box that represents the median of the upper data set.
 Box-and-Whisker Plot: a graph that displays five statistical measures (also known as five number
summary) for a data set.
Create a box-and-whisker plot using the following example data set: 70, 30, 26, 90, 42, 10
1) Order data from least to greatest: 10, 26, 30, 42, 70, 90
2) Find the minimum value: 10
3) Find the maximum value: 90
4) Find the median (Q2): 36
5) Find the lower quartile (Q1): 26
6) Find the upper quartile (Q3): 70
7) Plot the data on Box-and-Whisker Plot
Min: 10

Q1: 26
Q2: 36
Q3:70
Max: 90

Create a bar graph and a pie chart using the following data:
A classroom with 25 students was surveyed to find out how many students would choose a
specific sport as their favorite. (Solution is on the following page.)
Sport
Number of Students
Percent
Baseball
Basketball
Football
Soccer
Golf
Surfing
5
10
2
4
1
3
20%
40%
8%
16%
4%
12%
STEM Activities for Middle and High School Students
Snack Time!
Degrees in Circle–Pie Chart
(% x 360 degrees)
72
144
28.8
57.6
14.4
43.2
7-7
12
10
8
6
4
2
0
Favorite Sports
Basketball
Baseball
Soccer
Football
Golf
Surfing
STEM Activities for Middle and High School Students
Snack Time!
7-8
Guided Notes
A Review of Five Number Summaries, Box-and-Whisker Plots, Bar Graphs, and Pie Charts
Vocabulary
 Minimum value - smallest data point; represented at the end of the left whisker on the box-plot.
 Maximum value - largest data point; represented at the end of the right whisker on the box-plot.
 Lower quartile (Q1) - the beginning of the box that represents the median of the lower data set.
 Median (Q2) - the middle value in the data set, represented by the line inside the box.
 Upper quartile (Q3) - the end of the box that represents the median of the upper data set.
 Box-and-Whisker Plot: a graph that displays five statistical measures (also known as five number
summary) for a data set.
Example Data Set: 70, 30, 26, 90, 42, 10
1) Order data from least to greatest:
2) Find the minimum value:
3) Find the maximum value:
4) Find the median (Q2):
5) Find the lower quartile (Q1):
6) Find the upper quartile (Q3):
7) Plot the data on Box-and-Whisker Plot
Create a bar graph and a pie chart using the following data:
A classroom with 25 students was surveyed to find out how many students would choose a
specific sport as their favorite.
Sport
Number of Students
Baseball
Basketball
Football
Soccer
Golf
Surfing
5
10
2
4
1
3
Percent
STEM Activities for Middle and High School Students
Snack Time!
Degrees in Circle–Pie Chart
(% x 360 degrees)
7-9
Snack Time! Activity
In this activity you will be collecting data from nutrition labels of different snacks. As you
collect, organize, and display the data in different forms, assess which snacks might be healthiest
for you.
1. Complete the following table using the nutrition labels provided:
Food
Ex: pretzels
Serving Size
1 oz
Calories
110
Fat Calories
10
Sodium(mg)
230
Carbohydrates(g)
23
Mean:
2. Using the Calories data above, create a five number summary and box-and-whisker plot.
3. Using the Carbohydrates data above, create a five number summary and box-and-whisker
plot.
4. Compare the box-and-whisker plots for the calories and carbohydrates you created. What can
you summarize about the amount of calories found in typical snack foods? What can you
summarize about the amount of carbohydrates found in the same snack foods? Is the mean of the
calories or the mean of the carbohydrates more useful for estimating the amount of either in a
typical snack?
5. Create a bar graph to represent the amount of Sodium using the data from your table. Label
each bar with the food that it represents so that you can compare the amount of sodium in
different types of snacks.
STEM Activities for Middle and High School Students
Snack Time!
7 - 10
6. What types of foods had the most sodium?
Which had the least?
7. Use the data from your table to calculate what percent of calories in the food are from fat.
Create a pie chart to represent the percent of calories from fat that are present in the food. You do
not need to create a pie chart for those foods with 0% calories from fat.
Food
Calories
Fat Calories
% Calories from Fat
ex: pretzels
110
10
10/110 ≈ .09 = 9%
Degrees in Circle–Pie
Chart
(% x 360 degrees)
32.4º
Example: Pretzel Calories
Fat Cals
8. Summarize: Using what you have learned about the amount of calories, carbohydrates,
sodium and calories from fat in different snack foods, write a summary on a separate page
describing which snacks would be most beneficial for you. Your answer may depend on your
personal needs, the time of day, and your fitness plans for the day.
STEM Activities for Middle and High School Students
Snack Time!
7 - 11
Snack Time! Nutrition Labels
Pretzels and Doritos
STEM Activities for Middle and High School Students
Snack Time!
7 - 12
Ice Cream and Frozen Yogurt
STEM Activities for Middle and High School Students
Snack Time!
7 - 13
An Apple and a Snapple
STEM Activities for Middle and High School Students
Snack Time!
7 - 14
Stretching It
Students will measure the stretch of a rubber band using varying weights and find a linear
relationship, in the y = mx + b form, between the rubber band’s length and the weight used to
stretch it. This activity is meant to allow students to apply their knowledge of linear relationships
in a practical setting.
Suggested Grade Range: 6-8
Approximate Time: 1 hour
State of California Standards:
California Standards Grade 6: Algebra and Functions; Statistics, Data Analysis, and
Probability
AF 1.0 Students write verbal expressions and sentences as algebraic expressions and
equations; they evaluate algebraic expressions, solve simple linear equations, and graph
and interpret their results.
AF 2.0 Students analyze and use tables, graphs, and rules to solve problems involving
rates and proportions.
SDAP 1.0 Students compute and analyze statistical measurements for data sets.
California Standards Grade 7: Algebra and Functions; Statistics, Data Analysis, and
Probability
AF 1.0 Students express quantitative relationships by using algebraic terminology,
expressions, equations, inequalities, and graphs.
AF 3.0 Students graph and interpret linear and some nonlinear functions.
SDAP 1.0 Students collect, organize, and represent data sets that have one or more
variables and identify relationships among variables within a data set by hand and
through the use of an electronic spreadsheet software program.
California Standards Grade 8: Algebra I
AF 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph
2x + 6y = 4). They are also able to sketch the region defined by linear inequality.
AF 7.0 Students verify that a point lies on a line, given an equation of the line. Students
are able to derive linear equations by using the point-slope formula.
California Science Standards Grade 8: Physical Science
2. Unbalanced forces cause changes in velocity. As a basis for understanding this
concept:
a. Students know a force has both direction and magnitude.
b. Students know when an object is subject to two or more forces at once, the result is the
cumulative effect of all the forces.
c. Students know when the forces on an object are balanced, the motion of the object does
not change.
STEM Activities for Middle and High School Students
Stretching It
8-1
d. Students know how to identify separately the two or more forces that are acting on a
single static object, including gravity, elastic forces due to tension or compression in
matter, and friction.
Relevant National Standards (Mathematics):
Mathematics Common Core State Standard: 6RP
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams,
or equations.
Mathematics Common Core State Standard: 7EE
4. Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the
quantities.
Mathematics Common Core State Standard: 8EE
5. Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Compare two different proportional relationships represented in different ways.
Mathematics Common Core State Standard: 8F
3. Interpret the equation y = mx + b as defining a linear function, whose graph is a
straight line.
4. Construct a function to model a linear relationship between two quantities.
Next Generation Science Standards:
5-PS2-1. Support an argument that the gravitational force exerted by Earth on objects is
directed down. [Clarification Statement: “Down” is a local description of the direction
that points toward the center of the spherical Earth.] [Assessment Boundary: Assessment
does not include mathematical representation of gravitational force.]
MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s
motion depends on the sum of the forces on the object and the mass of the object.
[Clarification Statement: Emphasis is on balanced (Newton’s First Law) and unbalanced
forces in a system, qualitative comparisons of forces, mass and changes in motion
(Newton’s Second Law), frame of reference, and specification of units.] [Assessment
Boundary: Assessment is limited to forces and changes in motion in one-dimension in an
inertial reference frame and to change in one variable at a time. Assessment does not
include the use of trigonometry.]
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion
describes the mathematical relationship among the net force on a macroscopic object, its
mass, and its acceleration. [Clarification Statement: Examples of data could include
tables or graphs of position or velocity as a function of time for objects subject to a net
unbalanced force, such as a falling object, an object rolling down a ramp, or a moving
STEM Activities for Middle and High School Students
Stretching It
8-2
object being pulled by a constant force.] [Assessment Boundary: Assessment is limited to
one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.]
Lesson Content Objectives:
 Construct rubber band stress apparatus to collect and analyze data.
 Measure and record the length of a rubber band by stretching it with various weights.
 Construct a scatter plot to represent the data and make a conjecture about the
relationship between the variables.
 Determine an equation that models the observed data in the y = mx + b form.
Materials Needed:
 One meter stick per group of three to four students
 One plastic bag stapled to one end of a heavy duty rubber band per group
 One C-clamp per group
 One nickel and ten quarters per group (washers or any other uniformly massed
objects can be used in place of quarters)
Adapted from:
Laub, M. (2011). Linear relationship activities. CMC ComMuniCator, 36(2), 38-42.
STEM Activities for Middle and High School Students
Stretching It
8-3
Summary of Lesson Sequence
 Introduce the lesson by describing the set up of the experiment and asking discussion
questions about the relationship between the variables involved.
 Guide students through their experiment as they make measurements and organize
and analyze their data.
 Check for students’ understanding by asking the provided key questions.
 Allow students to write a summary of the relationship between the variables
independently.
 Close the lesson with a discussion about why there might have been variances in the
groups’ data and by allowing students to summarize the relationship between the
length of the rubber band and the weight attached to it.
Assumed Prior Knowledge
Prior to this lesson students should know how to create a scatterplot from data and should
be able to determine the linear relationship between variables in the form of y = mx + b
from a graph.
Classroom Set Up
To set up the rubber band stress apparatus, clamp the rubber band to a rigid table so that
the plastic bag that is stapled to it suspends below the edge of the table. Insert one
quarter into the plastic bag to eliminate any slack in the rubber band before beginning.
STEM Activities for Middle and High School Students
Stretching It
8-4
If C-clamps are not available, a large index card or piece of cardboard may be used.
Staple a rubber band to the card. Use an open paperclip and hook one end on the rubber
band and place the coins on the other end of the hook or in a plastic bag attached to the
hook. Students can mark the displacement of the rubber band directly on the card.
This activity works well for groups of three to four students.
Lesson Description
Introduction
Inform students that they will be conducting an experiment to determine the relationship
between two variables.
Describe the set up for the experiment and provide the necessary materials to each group
of three or four students and allow them to set up the experiment.
Before permitting students to begin, ask the following questions:
What do you think will happen if you add a quarter (or other objects with uniform mass
such as washers, nickels, pennies, etc.) to the plastic bag? Two quarters? Three? [The
rubber band will stretch and be longer each time a quarter or other chosen object is
added.]
What method will you use to measure the rubber band? [If students measure the entire
rubber band they will find that b (in y = mx + b) equals the length of the unstretched
rubber band. If students measure the amount the rubber band stretches they will find b=0
(in y = mx + b).]
STEM Activities for Middle and High School Students
Stretching It
8-5
What are the two variables we will be measuring and keeping track of? [The number of
objects added and the length of the rubber band.]
How should you keep track of your data? [With a table; the x value is the number of
objects and the y value is the length of the rubber band.]
What would be a good way to analyze the relationship between the variables once you
have collected your data? [Construct a scatterplot.]
What kind of relationship do you think there is between the variables? [Answers may
vary. Depending on their prior knowledge, students should recognize the relationship as
linear or describe the relationship as a direct variation.]
Guide Students Through Their Practice
Ensure each group has set up their apparatus correctly and they have measured the length
of the rubber band without any of the uniform objects in the bag (one nickel or other
weight should be in the bag at the start to ensure there is no slack in the rubber band
before beginning).
Model for each group how they should be measuring the length of the rubber band: from
the top of the table to the end of the rubber band that is attached to the plastic bag.
Remind students that it is important to make the measurement using a consistent method.
Allow students to add one quarter and measure the length of the rubber band, then add a
second quarter and measure again. Students should continue until they have added all ten
quarters to the bag and measured the length of the rubber band.
Every student should create a table of values for the data with the number of quarters as
the x value and the length of the rubber band as the y value.
Students should then construct a scatterplot of the data to make a conjecture about the
relationship between the variables. Encourage students to try to determine a linear
relationship in the form of y = mx + b that models their observed data.
Ask groups to predict what the length of the rubber band would be if 13 quarters were in
the plastic bag and report their prediction by writing it on the board.
Check for Understanding
While students are working, check for understanding by moving around to each group
and noting their progress. Ask the following key questions:
What do you notice about the relationship between the number of quarters and the length
of the rubber band?
Was there a time in your experiment when the x value was zero? What about the y value?
STEM Activities for Middle and High School Students
Stretching It
8-6
With a linear relationship, describe what may be found when the x value is zero.
If there is a data point on your scatter plot that does not seem to fit with the rest of your
data in the linear model, what might you do?
If you look at your data and your friends’ data you will likely see that they are different.
What are some reasons you would get different data? [Different rubber bands will stretch
differently – some are easy to stretch, others hard, some of the teams may have measured
the total length while others only measured the change in length, some teams may have
used quarters while others used pennies or washers.]
Closure
Prompt a whole class discussion of the predictions each group has made for the length of
the rubber band with a weight of 13 quarters and why they might vary. Ask a volunteer
group to verify in front of the class the length of the rubber band after adding 13 quarters
to the bag. Discuss with the class how their graph and this information can be used to
predict length for a very large amount of quarters (e.g., 100).
Suggestions for Differentiation and Extension
 Different rubber bands will have different spring constants. This will result in some
difference between results. It could be an interesting discussion or extension activity to
try this with thin and thick rubber bands. It will take more quarters (or washers) to stretch
a thick rubber band the same distance as a thin rubber band. This experiment
demonstrates Hook’s Law, which states that the restoring force of a spring is directly
proportional to a small displacement. In equation form, we write:
F = -kx


where x is the size of the displacement. The proportionality constant, k, is specific for
each spring. Students may explore the different proportionality constants of different
rubber bands as an extension to this activity.
Graphing calculators may be used to find the line of best fit for the scatterplot if they are
available.
Technology extension activity: The PHET Simulation, Masses & Springs, allows students
to explore different masses. Each spring has its’ own spring constant. Students can collect
and graph data and find the mass of unknown objects using the data they collect with
known masses. The simulation is free and downloadable and sample lesson plans for use
with the simulation are included on the website:
http://phet.colorado.edu/en/simulation/mass-spring-lab
STEM Activities for Middle and High School Students
Stretching It
8-7
Run!8
Students will practice creating and analyzing distance-time graphs by engaging in timed runs and
using their collected data to plot distance-time graphs. They will recognize the slope of a line on
a distance-time graph represents the object’s speed.
Suggested Grade Range: 6-12
Approximate Time: 1 hour
State of California Content Standards:
Science Standards Grade 8: Physical Science
Motion 1. The velocity of an object is the rate of change of its position. As a basis for
understanding this concept: c. Students know how to solve problems involving distance,
time, and average speed. f. Students know how to interpret graphs of position versus time
and graphs of speed versus time for motion in a single direction.
Science Standards Grades 9-12: Physics
1. Newton’s laws predict the motion of most objects. As a basis for understanding this
concept: a. Students know how to solve problems that involve constant speed and average
speed.
Mathematics Standards Grade 6: Algebra and Functions
2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates
and proportions: 2.3 Solve problems involving rates, average speed, distance, and time.
Relevant National Content Standards:
Mathematics Common Core State Standard: 8.EE
Understand the connections between proportional relationships, lines, and linear
equations: 5. Graph proportional relationships, interpreting the unit rate as the slope of
the graph. Compare two different proportional relationships represented in different
ways. For example, compare a distance-time graph to a distance-time equation to
determine which of two moving objects has greater speed.
Mathematics Common Core State Standard: 8.F.B
5. Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch
a graph that exhibits the qualitative features of a function that has been described
verbally.
8
An early version of this lesson was adapted and field-tested by Beverly Wiegand, a participant in the
California State University, Long Beach Foundational Level Mathematics/General Science Credential
Program
STEM Activities for Middle and High School Students
Run!
9-1
Mathematics Common Core State Standard: 7.RP.A
2d. Explain what a point (x, y) on the graph of a proportional relationship means in
terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the
unit rate.
Next Generation Science Standards:
MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s
motion depends on the sum of the forces on the object and the mass of the object.
[Clarification Statement: Emphasis is on balanced (Newton’s First Law) and unbalanced
forces in a system, qualitative comparisons of forces, mass and changes in motion
(Newton’s Second Law), frame of reference, and specification of units.] [Assessment
Boundary: Assessment is limited to forces and changes in motion in one-dimension in an
inertial reference frame and to change in one variable at a time. Assessment does not
include the use of trigonometry.]
Lesson Content Objectives:
 Accurately use a stopwatch to collect data for timed runs.
 Use a table to organize the collected data.
 Create and compare distance-time graphs for different travel modes (running, walking
skipping, etc.).
 Make inferences from the distance-time graphs to determine their quickest and
slowest travel modes.
Materials Needed:
 One copy per student of the “Run! Warm Up” activity sheet (included)
 One copy per student of the “Run! Data Record Sheet” (included)
 One piece of graph paper per student
 One ruler per student
 One stopwatch for each pair of students
 Masking tape to mark the beginning and end points of the run distance
 Space to run
STEM Activities for Middle and High School Students
Run!
9-2
Summary of Lesson Sequence
 Allow students to use the data provided on the “Run! Warm Up” activity sheet
(included) to find the slope of the line of best fit to introduce the lesson.
 Students will work in pairs to time each other as they run, walk, and choose a third
mode to travel a designated distance.
 Students will organize their data in a table provided on the “Run! Data Record
Sheet.”
 Students will use their own data to create distance-time graphs for each of their three
trials on one coordinate plane to compare their speeds during each trial.
 The teacher will check for understanding by asking the provided key questions.
 To close the lesson, the teacher will lead a discussion about how the graphical
representation of the students’ trials was useful for understanding how they travel at
different speeds using different modes of travel.
Assumed Prior Knowledge
Prior to this lesson students should be able to organize data into a table and graph data on
a coordinate plane. Students should be familiar with the slope of a line and be able to
calculate it. Students should also be able to calculate the average speed of an object using
measured distance and time.
Classroom Set Up
Students should work in pairs to time each other and have space to run in a straight line
for about 15 meters. Students may measure a path to travel using meter sticks and mark
the beginning and end points using masking tape, or specific landmarks may be used to
designate the path such as the beginning and end of a grassy field. Students will need to
know the exact distance that they travel and students may measure this distance or it may
be measured ahead of time for them.
Lesson Description
Introduction
Provide each student with the “Run! Warm Up” activity sheet (included) and allow them
to plot the data, find a line of best fit, and calculate the slope of the line. Students should
be able to relate the provided data to the speed of an object and understand that a steeper
line indicates a faster speed while a more shallow line represents a slower speed.
Explain to students: Today you will be traveling a designated distance by running,
walking and choosing a third way to travel such as skipping, hopping, dancing, walking
backwards, etc. Your partner will time you for each trial. You will keep track of your
times in a table so that you can create a distance-time graph to represent your three
trials on one coordinate plane. You will then be able to use your graphs to understand
how your speed differed during each trial. Maybe you can predict how your speed will
compare for each of the trials already, can you predict how the graphs of each of your
trials will compare?
STEM Activities for Middle and High School Students
Run!
9-3
Model and Guided Practice
Assemble students, along with their materials, in an area where each pair has space to run
about 15 meters or some other designated distance.
Model for the entire class how each pair will be timing each other as they complete three
trials. Each student should run the entire distance, walk the entire distance, and choose a
third way to travel (skip, hop, dance, speed walk, etc.) while their partner times each trial
for them.
Students should record their own trial times on their data sheet.
As students are completing their trials, ask the following questions:
For which trial were you fastest? Slowest?
How could you find your speed for each trial from the data you collected?
When each pair has had the opportunity to complete their trials and collect their data,
bring the class back into the classroom to create distance-time graphs and analyze them.
Check for Understanding
Check for students’ understanding while they are creating a distance-time graph for their
trials by asking the following key questions:
For which trial were you fastest?
For which trial were you slowest?
Describe the slope of each trial and how it relates to your speed.
Move around the room checking with individual students by asking the key questions
while helping students create distance-time graphs using the data from their trials.
Independent Practice
Allow students to work independently to write a description of their distance-time graphs
by comparing their mode of travel, times, and the graphs of their trials. Students should
relate their speed during each trial to the slope of each trial and make comparisons among
the three trials.
Closure
To close the lesson, students may share their descriptions and compare graphs. Asking
the following questions may generate a discussion:
How was it useful to have a graphical representation of your trials in order to analyze
your different speeds?
STEM Activities for Middle and High School Students
Run!
9-4
Describe how the distance-time graph representing a fast runner would compare to a
slower runner.
Suggestions for Differentiation and Extension
 PHET Simulation:
Visit the website http://phet.colorado.edu/en/simulation/moving-man which provides a
downloadable simulation activity showing a distance-time graph for a person standing
still, moving away from, and moving towards an observer.
 Students may use graphing calculators to graph their trials on the same screen to compare
them.
STEM Activities for Middle and High School Students
Run!
9-5
Run!
Warm Up
Several students in Mr. Hall’s class collected the following data representing the height of a
growing seedling over several days. Plot the data on a coordinate plane and find the line of best
fit to create a distance-time graph. From the distance-time graph, calculate the slope of the line of
best fit.
Day
1
2
3
4
5
8
9
10
11
12
Height (cm)
2
2.5
3.5
3.5
4.5
7
8
8.5
8.5
9
How can you use the graph above to find the average growth rate of the seedling?
STEM Activities for Middle and High School Students
Run!
9-6
Run!
Data Record and Analysis Sheet
Record the data for your three trials in the table then create a distance-time graph for each trial.
You should graph one line for each trial using the origin (0,0) as one point and your timedistance data (seconds, meters) as your second point. The result will be one coordinate plane
with three lines beginning at the origin. Be sure to label the axes and graphs with titles.
Travel Mode
Time (seconds)
Distance (meters)
Slope (m/s)
Walk
Run
Other:
Summarize Your Findings
1.Use your distance-time graphs to compare the slopes for each of your trials and describe your
observation.
2. Describe what the slope represents in this activity.
3. If you looked at all the distance-time graphs that your classmates created, what would you
look for to find out who is a very fast runner?
STEM Activities for Middle and High School Students
Run!
9-7
Peas in a Pod9
Students will investigate the relationship between the length of a peapod and the number of peas
inside, as well as between the length of a peapod and length across (average size) of the peas, by
collecting and analyzing data. Students will plot their data on a coordinate plane to determine the
correlation between the variables and construct a function to model the linear relationship
between the length of a peapod and the number of peas inside, and length of a peapod and the
average size of a pea.
Suggested Grade Range: 7-9
Approximate Time: 2 hours
State of California Standards:
Mathematics Standards Grade 7: Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology,
expressions, equations, inequalities, and graphs.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the
number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the
plot and understand that the slope of the line equals the quantities.
Mathematics Standards Grade 7: Statistics, Data and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables
and identify relationships among variables within a data set by hand and through the use
of an electronic spreadsheet software program:
1.2 Represent two numerical variables on a scatterplot and informally describe how the
data points are distributed and any apparent relationship that exists between the two
variables (e.g., between time spent on homework and grade level).
Mathematics Standards Grades 8-12: Algebra I
7.0 Students verify that a point lies on a line, given an equation of the line. Students are
able to derive linear equations by using the point-slope formula.
Relevant National Standards:
Mathematics Common Core State Standard: 7.EE
B.4 Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the
quantities.
Mathematics Common Core State Standard: 8.F
Use functions to model relationships between quantities:
9
This lesson was adapted and field-tested by Andrea Johnson, Co-Editor.
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 1
4. Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or
from two (x, y) values, including reading these from a table or from a graph. Interpret the
rate of change and initial value of a linear function in terms of the situation it models,
and in terms of its graph or a table of values.
Mathematics Common Core State Standards: High School Algebra
CED.A.2. Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
Lesson Content Objectives:
 Measure the length of several peapods, count the number of peas inside each, and
measure the length across (diameter) of each pea in each pod. You will calculate the
average size of the peas in each pod using the data you collect.
 Organize the collected data in tables, recognizing that length of a peapod, number of
peas inside, and the average length across a pea are variables in the context of this
lesson.
 Determine the correlation between the variables by creating a scatterplot for the data.
 Construct a function that models the linear relationship between the length of a
peapod and the number of peas inside, and between the length of a peapod and the
average size pea (measured length or diameter).
Materials Needed:
 One copy per student of the “Peas in a Pod” activity sheet
 10 peapods per pair of students (select a wide variety of lengths)
 One ruler per student
 One graphing calculator per student (optional)
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 2
Summary of Lesson Sequence
 Introduce the lesson by leading a discussion about the structure and function of a
peapod to a pea plant. Ask students to make predictions about how many peas are
inside a specific peapod by just looking at it.
 Model a method for accurately measuring the length of a peapod in centimeters then
counting the number of peas in a peapod and organizing the data into a table.
 Model a method for then measuring across (diameter as measured across outside)
each pea, and then finding the average of those lengths.
 Guide students through their practice as they collect data, create scatterplots,
estimating the lines of best fit, and find functions to represent the two sets of data.
 Check for students’ understanding by asking the key questions provided while
students are working on the guided practice.
 Close the lesson by allowing students to compare their results and discuss possible
reasons for any variation among results. Lead students in a discussion of the
relationship between the length of a peapod and the number of peas inside based on
their investigation, as well as the relationship between the length of a peapod and the
average pea size.
Assumed Prior Knowledge
Prior to this lesson students should be able to construct a function based on a graphical
representation of a relationship between two variables. Students should be able to find the
slope of a line from a graph.
Classroom Set Up
Students will work in pairs to collect data by measuring length of a peapod, length
(diameter) of each pea, and counting the number of peas.
Lesson Description
Introduction
Provide one peapod per pair of students to observe. Lead a discussion of the structure and
function of the peapod as a part of a pea plant. Explain:
The peas of a pea plant are the seeds of the plant and are encased in a pod that protects
the seeds during the plant’s development. Peas are technically fruits because they are
seeds that develop from the flower of the plant, but in cooking they are referred to as
vegetables.
Without opening your peapod, can you predict how many peas are inside? [Allow
students to respond by holding up their fingers to respond.]
Without opening your peapod, can you predict the average diameter of the peas?
What characteristic about the peapod may help us predict how many peas are inside?
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 3
Today we will investigate if the length of a peapod is related to the size of the peas or the
number of peas inside. You may already be confident that a longer peapod will contain a
larger number of peas, but we will also consider the average size of the peas to see if
there is a correlation between the length of a peapod and the size of the peas. To do so,
we will be measuring the length of several peapods, then counting the number of peas
inside and measuring the size of each pea.
Model
Use one peapod to model for students an accurate method for measuring the length of a
peapod in centimeters using a ruler. Show how to open the peapod at the seam and count
the number of peas in one pod. Explain that peas that are not fully developed should also
be counted and measured. Demonstrate measuring the length of each pea from a peapod,
while recording the results. Be sure to demonstrate finding the length of the longest
dimension of the pea, since they may not be perfectly round. Explain that students will
repeat this procedure with a partner for their ten peapods.
Guide Students Through Their Practice
Allow students to work in pairs and select at least ten peapods from which to collect data.
As students are measuring and organizing their data in the tables provided on the activity
sheet; walk around the room to check that they are using their ruler to measure accurately
and using centimeter units.
When students have collected data for at least ten peapods, they should create two
scatterplots for their data; one representing the number of peas versus the length of the
pod and one representing the average pea size versus the length of the pod. Ensure that
students are plotting the correct measurements for the x and y values.
Students should then estimate and draw a line that best fits the data for each scatterplot
and determine how the variables correspond (positive, negative, or they do not
correspond).
Guide students through choosing two points on each of their lines to calculate the slopes.
From the slopes, students should construct a function representing the relationship
between the length of the peapod and the number of peas, as well as the length of the
peapod and the average length of the peas.
Check for Understanding
Check for students’ understanding while they are working on the guided practice by
asking the following key questions:
What are the variables in the context of our activity?
How do the variables correspond on your scatterplot?
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 4
Are there any data points that seem to be outliers? Describe the peapod that provided the
outlying data point.
What could help you make a better estimation of the line of best fit?
How can you find the slope of the line of best fit?
Closure
To close the lesson, allow students to share their results and discuss why there are
varying results in the classroom. Ask students: Based on your investigation today,
describe the relationship between the length of a peapod, the number of peas inside, and
the average size of a pea. Using your understanding about the structure and function of
peapods, write why you think a long peapod wouldn’t have a small number of peas or a
short peapod have a large number of peas. How would those situations impact the pea
plant?
Suggestions for Differentiation
 Graphing calculators may be used to find a line of best fit from the scatterplot.
 If students are not yet able to determine a function from a line of best fit, the activity may
be truncated at the point when students create a scatterplot. The discussion would remain
unchanged because students should still be able to recognize the relationship between the
variables from their scatterplot.
 Model for students the format for the table and the scatterplot if necessary.
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 5
Peas in a Pod
Choose ten peapods. Be sure to select some short ones and some long ones.
1. Measure the length of a peapod, then open the peapod and count the peas. Measure length
of each pea and calculate the average size of a pea for each peapod while recording your
data in the table below. Continue to collect data for all ten peapods.
Peapod Length (cm)
EX:
8 cm
Number of Peas
Length Across of Each Pea (cm)
Average Size of Pea (cm)
5
1, 1.2, .9, 1, 1.3
1.08
2. Create two scatterplots for the data you have collected using your table of values.
Peapod Length vs. Number of Peas
Peapod Length vs. Average Pea Size
3. Estimate and draw a line of best fit for each scatterplot using a ruler.
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 6
4. Choose two points on each line to find the slope for each.
Peapod Length vs. Number of Peas Slope:
Peapod Length vs. Average Pea Size Slope:
5. Construct two functions, one representing each line, so that f(x) represents the
relationship between the peapod length and the number of peas and g(x) represents the
relationship between the peapod length and the average pea size.
f(x) =
g(x) =
6. On the back of this page, respond to the following questions:
a. Based on your investigation today, describe the relationship between the length of a
peapod and the number of peas inside, and the length of a peapod and the average pea
size.
b. Using your understanding about the structure and function of peapods, write why you
think a long peapod wouldn’t have a small number of peas or a short peapod have a large
number of peas. How would those situations impact the pea plant?
c. What does the slope represent in each of your functions?
STEM Activities for Middle and High School Students
Peas in a Pod
10 - 7
Happy Birthday to You10
Students will investigate the patterns that arise in calendars by comparing the day of the week for
a particular date and use division to explain why the patterns occur. Students will then use
observed patterns to ultimately find the day of the week on which they were born.
Suggested Grade Range: 6-8
Approximate Time: 1 hour
State of California Content Standards:
California Standards Grade 6: Number Sense
2.0 Students calculate and solve problems involving addition, subtraction, multiplication,
and division.
California Standards Grade 7: Number Sense
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and
terminating decimals) and take positive rational numbers to whole-number powers.
Relevant National Standards:
Common Core State Standard: 7NS
3. Solve real-world and mathematical problems involving the four operations with
rational numbers.
Lesson Content Objectives:
 Describe the pattern that occurs in calendars for the day of the week for a particular
date.
 Use division to justify why the day of the week changes for a particular date.
 Use observed patterns to determine the day of the week for dates in the future and/or
past.
Materials Needed:
 One “America’s Birthday” activity sheet per pair of students (included)
 One “Days of Week Investigations” activity sheet per student (included)
Adapted From:
http://illuminations.nctm.org
10
An early version of this lesson was adapted and field-tested by Gina Hryze and Katiria Hernandez,
participants in the California State University, Long Beach Foundational Level Mathematics/General
Science Credential Program.
STEM Activities for Middle and High School Students
Happy Birthday to You
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Summary of Lesson Sequence
 Introduce the lesson by asking students whether they know their birthday–that is, the
day of the week on which they were born.
 Guide pairs of students through their investigation of the patterns that arise in
calendars for the day of the week for a particular date using the “America’s Birthday”
activity sheet (included).
 Link students’ findings to finding days of week in multiple contexts through guided
practice using the “Days of the Week Investigations” activity sheet (included).
 Check for students’ understanding by asking the provided key questions while they
are working.
 To close the lesson, students will determine the day of the week on which they were
born.
Assumed Prior Knowledge
Prior to this lesson students should know how to divide whole numbers and understand
what the remainder and the quotient of a division problem represent.
Classroom Set Up
Students will be asked to work in pairs for portions of this lesson.
Lesson Description
Introduction
Begin a class discussion by asking if any students know their birthday. Many students
will likely respond by sharing their birth date. Ask if any students know the day of the
week on which they were born. If any students do know the day on which they were
born, let them know that they will be exploring a method for finding this day.
Input and Investigation
Provide student pairs with the “America’s Birthday” activity sheet (included). Allow
students to work in pairs to find a pattern in the calendars for the 4th of July. Ask: Is
there a pattern for how the day of the week changes from one year to another? Students
should develop conclusions based on their observations. [The date moves to the next
day of the week each year, or moves forward two days in some years due to leap year
(years that have February 29th). Leap year occurs every four years.]
Call on pairs of students to share what they have concluded about the patterns they
observed. Students should notice that the date moves forward one day in most years and
moves forward two days in leap years. Ask students to try to determine why.
Ask: How many weeks are there in a year? How many weeks in a leap year? Then have
students divide the number of days in a year by the number of weeks to realize that the
STEM Activities for Middle and High School Students
Happy Birthday to You
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remainder after dividing is the number of days that the date will move. [365/52 = 7
remainder 1; 366/52 = 7 remainder 2]
Encourage students to relate the remainders they find to the pattern on the “America’s
Birthday” activity sheet and then determine which years were leap years.
Guided and Independent Practice
Provide each student with the “Days of Week Investigations” activity sheet. After
students attempt problem #1, have students share their responses, and then discuss this
problem as a whole class. Students should complete the rest of the activity independently.
Check for Understanding
As students are working independently, check their understanding by moving around the
room and asking the following key questions:
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What pattern helps to predict the day of the week for a particular date from one year
to the next year? [Dates move forward one day every year, except in leap years when
they move forward two days.]
Why does a particular date always change from one year to the next? [The number of
weeks in a year is not a whole number.]
How do the math problems 365 ÷ 7 and 366 ÷ 7 explain the calendar pattern for the
day of the week on which a date falls from year to year? [The remainders tell how
many days the date move forward.]
What do you need to know in order to figure out what the day is for a particular date?
[You must know which day the date is for a specific year so that you can work
forward or backward.]
What is the challenge for finding the day for a particular date in the far future or
past? [Years that end in double zeroes (such as 1900, 1800, etc.) do not follow a
regular pattern for leap years.]
Closure
First, have students meet in pairs; have them share and discuss their solutions for birth
day. As a whole class, have volunteers share their conjectures for their birth day, as well
as how they arrived at their solution. Compare methods. Close with a discussion of key
questions listed above.
Suggestions for Differentiation and Extension
 Students who are struggling during the independent work may be encouraged to work
with a partner or may benefit from discussing the key questions further with a partner or
with the instructor.
 Encouraging students to find the day one of their family members was born on may
extend this activity.
 There are websites that calculate the day of the week for any particular date. Students can
check several websites to see if they all give the same results.
STEM Activities for Middle and High School Students
Happy Birthday to You
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STEM Activities for Middle and High School Students
Happy Birthday to You
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Days of the Week Investigations
1. In 2009, Mother’s Day was Sunday, May 10. Using division as discussed in class, what
day of the week was June 10, 2009? __________________________
Explain how you arrived at your solution. Verify your result with the calendar at the end of
this activity.
2. I do my laundry every 20 days. Last week, laundry day fell on a Friday. On what day of the
week must I do my laundry again? ___________________ Show your work.
3. For this problem, you will find the day on which you were born (your actual birth day).
(a) What is your birth date (mm/dd/yy)? ______________________
(b) What was the matching day for your birth date in 2009? Use the provided 2009 calendar
at the end of this activity sheet. _____________________________
(c) On what day were you born? Justify your answer. ___________________________
STEM Activities for Middle and High School Students
Happy Birthday to You
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STEM Activities for Middle and High School Students
Happy Birthday to You
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