Maths Project by Carlos Morales Socorro

1. Learning Situation (LS): Babies and The Moon
Teacher: Carlos Morales Socorro
(Original idea by Rosa Doran, NUCLIO)
High School: IES El Calero
Subject: Maths
Interdisciplinar? Physics
Level: 2º ESO LOE
Methodology: ProjectBL
Driving question: Is it true that more babies are born when there's a full moon? /
Are there really more births on full moons?
Final Product: Pecha Kucha: Babies and The Moon: Myth or Fact?
Expert: None
Products / Milestones:
(a<b, “a” has to be finished before “b”)
Test < Slideshow < Pecha Kucha
Resources needed: Compass, ruler, protractor, calculator and a computer
Duration: 3 weeks
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Criterios de Evaluación 2ESO LOE
x
1. Resolver problemas que involucren operaciones y propiedades con números enteros, fracciones, decimales y porcentajes relacionados con la
vida diaria.
x 2. Identificar relaciones de proporcionalidad numérica y geométrica y utilizarlas para resolver problemas en situaciones de la vida cotidiana.
x
3. Utilizar el lenguaje algebraico para simbolizar, generalizar y resolver problemas sencillos utilizando métodos numéricos, gráficos o
algebraicos.
4. Utilizar estrategias de estimación y cálculo para obtener áreas y volúmenes de cuerpos geométricos, expresando el resultado de la estimación
o el cálculo en la unidad de medida más adecuada.
5. Utilizar el teorema de Thales y los criterios de semejanza para interpretar relaciones de proporcionalidad geométrica entre segmentos y
figuras planas, y para construir figuras semejantes con una razón dada.
6. Obtener información práctica de gráficas sencillas (de trazo continuo) relacionadas con fenómenos naturales y la vida cotidiana.
7. Representar e interpretar tablas y gráficas cartesianas de relaciones funcionales sencillas, basadas en la proporcionalidad directa, y obtener la
relación de proporcionalidad entre dos magnitudes a partir del análisis de su tabla de valores y de su gráfica.
x
8. Planificar y realizar estudios estadísticos sencillos para conocer las características de una población, recoger, organizar y presentar los datos
relevantes, utilizando los métodos apropiados y las herramientas informáticas adecuadas.
x 9. Utilizar estrategias y técnicas de resolución de problemas, tales como el análisis del enunciado, el ensayo y error sistemático, la división del
problema en partes, así como la comprobación de la coherencia de la solución obtenida y expresar, utilizando el lenguaje matemático adecuado
a su nivel, el procedimiento que se ha seguido en la resolución.
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Contenidos
I. Estrategias,
habilidades,
destrezas y actitudes
generales
II. Números III. Álgebra IV. Geometría V. Funciones y
Gráficas
VI. Estadística y
Probabilidad
Todas 3,4,5 1,2 - - 1,2,3,5
1

2. Welcome to this new adventure!
Act 1: Read this article from an American newspaper and underline the main ideas:
( http://sacramento.cbslocal.com/2011/08/15/sacramento-hospital-has-record-breaking-baby-boom/ )
Sacramento Hospital Has Record-Breaking Baby Boom
SACRAMENTO, Calif. (CBS13) – Oh baby! A Sacramento hospital was hopping over the weekend breaking a
record when it comes to newborns. And the baby boom may have something to do with the moon.
Since Friday, 50 babies have been born at Sutter Memorial Hospital in Sacramento.
At times, doctors were delivering a baby about every half hour, according to hospital officials. Dr. Angela
Rosas has been a pediatrician for 20 years and can’t remember such a busy time.
“I don’t think I’ve ever seen this many babies born at any hospital I’ve ever worked at,” said Angela Rosas,
M.D., OB Pediatrician. “There is a myth between pediatricians and obstetricians that more babies are born
on a full moon.
Medical experts say the effect focuses on the moon’s gravitational pull.
It controls a woman’s body in the same way it affects the earth’s tides.
The moon theory has not been scientifically proven. But officials at Sutter Memorial believe this is the highest
number of babies born in 48 hours in the history of Sacramento.
There were so many women in labor at times there weren’t enough delivery rooms.
Of course, there are other theories about the baby boom. The San Francisco Giants did win the World Series
nine months ago. Perhaps there was a lot of celebrating going on.
Which are the main ideas?
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Act 2. Devise a plan to answer the Driving Question by means of a Pecha Kucha.
Your own plan:
The group of four plan:
2

3. Our plan:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Step 8:
Step 9:
Step 10:
Step 11:
Step 12:
Step 13:
Step 14:
Step 15:
NOTES:
3

4. Our plan:
Step 1: Find out how to design a Pecha Kucha: Question + people's opinion + Phases of the Moon + Experiment +
Conclusions
Step 2: Find out how the Scientific Method works
Step 3: Review the available research results about the question
Step 4: Find out how the moon moves and the Phases of the Moon
Step 5: Design a survey and select a sample of people: ask them for their opinion: “Is there any relationship between
the Moon and Baby births?” / “Could you please explain your answer?”.
Step 6: Fill in the frequency tables for the collected data
Step 7: Plot diagrams for this table: Bar diagrams and Pie charts
Step 8: Draw conclusions about people's general bilief.
Step 9: Construct a hypothesis (or more)
Step 10: Design an experiment
Step 11: Find out if there is a formula to determine the Moon phase on any date . Use Stellarium to check our own
dates of birth. Optionally, find out if there is a formula to determine the day of the week on any date.
Step 12: Collect data from all the students of IES El Calero and fill in a frequency table. Use the discovered formulas
to complete each row by means of a spreadsheet.
Step 13: Plot diagrams for this table
Step 14: Draw conclusions: Myth or Fact.
Step 15: Design the slideshow to be used during the Pecha Kucha session
Step 16: Pecha Kucha day!
4

5. Act 1. Find out how to design a Pecha Kucha.
 Watch these videos:Cómo armar un Pecha Kucha:
https://www.youtube.com/watch?v=M3F1h_BbUx0
 RoboTIX Pecha Kucha: https://www.youtube.com/watch?t=2&v=oWEqu2t4UAA
 Basket VSK Pecha Kucha: https://youtu.be/Cccd3VTnUKM
Which are the main aspects we have to take into account to design a good Pecha Kucha?
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This a possible structure of your Babies and the Moon PechaKucha:
Introduction + Question + people's opinion + Phases of the Moon explanation + Hypothesis + Experiment +
Conclusions
And here you may find images without copyright limitations:
 https://openclipart.org/
 http://www.techradar.com/news/internet/web/12-best-places-to-get-free-images-for-your-site-624818
5

6. Act 2: Find out how the Scientific Method works
Vídeo: https://www.youtube.com/watchv=MIAhDCxUWiw
Before going on with the next question, which is your
hypothesis?
[ ] FACT: “More babies are born on full moon days”
[ ] MYTH: “No, no more babies are born on full moon
days”.
Act 3. Review the research results about the question.
Highlight the main ideas.
6

7. Act 4. How does The Moon move? What are the Moon Phases?
 Video: Moon Phases demostration_
https://www.youtube.com/watch?v=wz01pTvuMa0
 Lunar Phase simulator:
http://astro.unl.edu/naap/lps/animations/lps.html
 Understanding the Moon Phases:
http://www.moonconnection.com/moon_phases.phtml
Look at the picture:
In which phase is the moon closest to The Earth? ______________________________________________________
[…]
Moon Phases Simplified
It's probably easiest to understand the moon cycle in this order: new moon and full moon, first quarter and third
quarter, and the phases in between.
As shown in the above diagram, the new moon occurs when the moon is positioned between the earth and sun. The
three objects are in approximate alignment (why "approximate" is explained below). The entire illuminated portion of
the moon is on the back side of the moon, the half that we cannot see.
At a full moon, the earth, moon, and sun are in approximate alignment, just as the new moon, but the moon is on the
opposite side of the earth, so the entire sunlit part of the moon is facing us. The shadowed portion is entirely hidden
from view.
The first quarter and third quarter moons (both often called a "half moon"), happen when the moon is at a 90 degree
angle with respect to the earth and sun. So we are seeing exactly half of the moon illuminated and half in shadow.
Once you understand those four key moon phases, the phases between should be fairly easy to visualize, as the
illuminated portion gradually transitions between them.
7

8. An easy way to remember and understand those "between" lunar phase names is by breaking out and defining 4
words: crescent, gibbous, waxing, and waning. The word crescent refers to the phases where the moon is less than half
illuminated. The word gibbous refers to phases where the moon is more than half illuminated. Waxing essentially
means "growing" or expanding in illumination, and waning means "shrinking" or decreasing in illumination.
Thus you can simply combine the two words to create the phase name, as follows:
After the new moon, the sunlit portion is increasing, but less than half, so it is waxing crescent. After the first quarter,
the sunlit portion is still increasing, but now it is more than half, so it is waxing gibbous. After the full moon
(maximum illumination), the light continually decreases. So the waning gibbous phase occurs next. Following the
third quarter is the waning crescent, which wanes until the light is completely gone -- a new moon.
The Moon's Orbit
You may have personally observed that the moon goes through a complete moon phases cycle in about one month.
That's true, but it's not exactly one month. The synodic period or lunation is exactly 29.5305882 days. It's the time
required for the moon to move to the same position (same phase) as seen by an observer on earth. If you were to view
the moon cycling the earth from outside our solar system (the viewpoint of the stars), the time required is 27.3217
days, roughly two days less. This figure is called the sidereal period or orbital period. Why is the synodic period
different from the sidereal period? The short answer is because on earth, we are viewing the moon from a moving
platform: during the moon cycle, the earth has moved approximately one month along its year-long orbit around the
sun, altering our angle of view with respect to the moon, and thus altering the phase. The earth's orbital direction is
such that it lengthens the period for earthbound observers.
Although the synodic and sidereal periods are exact numbers, the moon phase can't be precisely calculated by simple
division of days because the moon's motion (orbital speed and position) is affected and perturbed by various forces of
different strengths. Hence, complex equations are used to determine the exact position and phase of the moon at any
given point in time.
Also, looking at the diagram (and imagining it to scale), you may have wondered why, at a new moon, the moon
doesn't block the sun, and at a full moon, why the earth doesn't block sunlight from reaching the moon. The reason is
because the moon's orbit about the earth is about 5 degrees off from the earth-sun orbital plane.
However, at special times during the year, the earth, moon, and sun do in fact "line up". When the moon blocks the sun
or a part of it, it's called a solar eclipse, and it can only happen during the new moon phase. When the earth casts a
shadow on the moon, it's called a lunar eclipse, and can only happen during the full moon phase. Roughly 4 to 7
eclipses happen in any given year, but most of them minor or "partial" eclipses. Major lunar or solar eclipses are
relatively uncommon.
[…]
8

9. Let's look at this lunar month calendar and identify the phase of each day:
Moon calendar: http://www.moonconnection.com/moon_phases_calendar.phtml
- - - - Waning
Gibbous
Waning
Gibbous
Waning
Gibbous
Wanning
Gibbous
3ºQ 3ºQ 3ºQ Waning
Crescent
Waning
Crescent
Waning
Crescent
Waning
Crescent
New New New New Waxing
Crescent
Waxing
Crescent
Waxing
Crescent
1ºQ 1ºQ 1ºQ 1ºQ Waxing
Gibbous
Waxing
Gibbous
Waxing
Gibbous
Waxing
Gibbous
Full Full Full Full Waning
Gibbous
Notes:
9

10. Act 5. Design a survey and select a sample of people: ask them for their opinion: “Is there any relationship between
the Moon and Baby births?” / “Could you please explain your answer?”.
N Español English
1 Edad: Age:
2 Sexo: [ ] Hombre [ ] Mujer Gender: [ ] Male [ ] Female
3 ¿Hay alguna relación entre el número de partos y la
fase lunar? [ ] Sí [ ] No
¿En qué fase crees que hay más nacimientos?
Subraya la respuesta: Luna nueva, cuarto creciente,
primer cuarto, cuarto creciente giboso, luna llena,
cuarto menguante giboso, tercer cuarto, cuarto
menguante, luna nueva,…
Is there any relationship between the number of child
births and the Moon phase? [ ] Yes [ ] No
In which phase do you think there are more births?
Underline the answer: New moon, waxing crescent, first
quarter, waxing gibbous, full moon, waning gibous, third
quarter, waning crescent, new moon, …
4 ¿Por qué piensas eso? Why do you think so?
And now …
a) Choose the sample of people at random, but they have to be 64 adults (32 men and 32 women) and 64 teenagers (32
boys and 32 girls). Each student will ask the questions to one person only.
b) Fill in this table:
Variable Type of variable (Qualitative.
Quantitative discrete. Quantitative
continuous)
Type of question (closed, opened)
Age
Gender (Male/Female)
Relationship between child births and
Moon phase (yes / no)
Phase with more child births
Opinion / Reason
Act 6. Fill in these frequency tables with the data you have collected / gathered:
Is there any relationship
between the Moon phase and
the birth rate?
fi fri %i
Complete Yes
No
Adults Yes
No
Teenagers Yes
No
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11. Male Yes
No
Female Yes
No
- Complete sample:
Phase of the moon with
more baby births
fi fri %i
New moon
Waxing crescent
First quarter
Waxing gibbous
Full moon
Waning gibbous
Third quarter
Waning crescent
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- By gender: Male
Phase of the moon with
more baby births
fi fri %i
New moon
Waxing crescent
First quarter
Waxing gibbous
Full moon
Waning gibbous
Third quarter
Waning crescent
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- By gender: Female
Phase of the moon with
more baby births
fi fri %i
New moon
Waxing crescent
11

12. First quarter
Waxing gibbous
Full moon
Waning gibbous
Third quarter
Waning crescent
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By age (Adults):
Phase of the moon with
more baby births
fi fri %i
New moon
Waxing crescent
First quarter
Waxing gibbous
Full moon
Waning gibbous
Third quarter
Waning crescent
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By age (Teenagers):
Phase of the moon with
more baby births
fi fri %i
New moon
Waxing crescent
First quarter
Waxing gibbous
Full moon
Waning gibbous
Third quarter
Waning crescent
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12

13. Act 7. Each group must choose at least one of the tables and…
a) Draw a pie chart and a bar diagram (by hand with grid paper).
b) Draw a pie chart and a bar diagram with LibreOffice Calc and upload it to the Moodle Forum.
(Remember to represent the phases in order: from New Moon to Waning crescent; and compare “a” and “b” to check
results)
Table Group(s)
Complete sample
By gender (Male)
By gender (Female)
By age (Adults)
By age (Teenagers)
(Add a blank paper with your diagrams)
Act 8. Draw conclusions about people's general bilief (According to the data … / As we may see in the picture … / X
% of female/male/adults/teenagers think that … ).
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Act 9. Construct a hypothesis (or more).
Hypothesis 1 Hypothesis 2
Act 10. Design an experiment
Experiment: Let's collect all the dates of births we have available at IES El Calero. If we determine the % of
births for each moon phase and we graph them with bar diagrams, we'll find out which hypothesis is really correct.
Bar diagram we should get if Hypothesis 1 is correct Bar diagram we should get if Hypothesis 2 is correct
13

14. Act 11. Find out if there is a formula to determine the Moon phase on any date. Optionally, find out if there is a
formula to determine the day of the week on any date.
Let's start watching the Stellarium Tutorial [ https://www.youtube.com/watch?v=V8XOXI6Fwx0 ]. We may use
this software to check the Moon phase the day we were born; but if we really want to know it without doubt, we have
to use a very special formula:
,
Where d = date of birth; basedate = date of a well-known full moon; p= 29,530588 days (synodic lunar period).
And where MoonPhase is a number from 0 to 1, so that …
Don't worry, we'll use it in a spreadsheet to make it easy!!
And don't forget to watch this videotutorial: https://www.youtube.com/watch?v=Qk7SbDIk0S8
By the way, we may use the Zeller's Congruence of the Gregorian calendar1
[
https://es.wikipedia.org/wiki/Congruencia_de_Zeller ] to find out the day of the week we were born:
The power of Algebra!!
where:
h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
q is the day of the month
m is the month (3 = March, 4 = April, 5 = May, ..., 14 = February)
K the year of the century (year mod 100).
J is the zero-based century - actually truncate(year/100) - For example, the zero-based centuries for 1995 and
2000 are 19 and 20 respectively (to not be confused with the common ordinal century enumeration which
indicates 20th for both cases).
IMPORTANT NOTE: In this algorithm January and February are counted as months 13 and 14 of the
previous year. E.g. if it is 2 February 2010, the algorithm counts the date as the second day of the fourteenth
month of 2009: q=2, m=14, K=9.
1 The Gregorian calendar, also called the Western calendar and the Christian calendar, is internationally the most widely used
civil calendar. It is named for Pope Gregory XIII, who introduced it in 1582.
14

15. Examples:
1. For 1 January 2000, the date would be treated as day=1, month=13 and year=1999, so the values would be:
q = 1
m = 13
K = 99, because 1999 mod 100 = 99
J = 19
So the formula evaluates as (1 + 36 + 99 + 24 + 4 + 95) mod 7 = 259 mod 7 = 0 → Saturday
Let's check it:
2. For 1 March 2000, the date is treated as the 3rd month of 2000, so the values become
q = 1
m = 3
K = 0
J = 20
So the formula evaluates as (1 + 10 + 0 + 0 + 5 + 100) mod 7 = 116 mod 7 = 4 → Wednesday
Let's check it:
Let's play a little bit with this formula… The calendar software is based on it!
Let's think of three different dates and find out the day of the week of each one:
a)
b)
c)
15

16. Act 12. Collect data from all the students of IES El Calero and fill in a frequency table. Use the discovered formulas to
complete each row by means of a spreadsheet.
(First 100 students, out of 922)
Let's go!! Open your Spreadsheet software (LibreOffice Calc) and follow these videotutorials step by step:
https://www.youtube.com/watch?v=IvqRYwWfUjM
As you may see, we need these formulas:
(In Spanish)
= contar.si(A10:A20;2) → Cuenta el número de celdas del intervalo que va desde A10 hasta A20 que cumplen
el criterio celda=2
= suma(B2:B12) → Suma las celdas del intervalo desde B2 hasta B12.
= díames(C3) → Devuelve el número de día de la semana de la fecha almacenada en la celda C3: 1 Domingo,
2 Sábado, 3 Lunes, …
= mes(C3) → Devuelve el mes de la fecha almacenada en la celda C3.
= A2/$A$20 → Divide la celda A2 entre A20. En el caso de copiar la fórmula a otras celdas, el sistema
actualizará automáticamente A2, pero NO A20.
=entero(B4) → Devuelve el redondeo inferior de B4
=abs(C3) → Devuelve el valor absoluto de C3
=buscarv(E1;K11:L19;2) → Busca el valor de E1 en la tabla definida por el rango K11:L19 y, una vez
encontrado, devuelve el valor de la segunda columna del rango, es decir, de la columna L.
16

17. Fill in these tables:
(N= people)
Phase of the
moon
% of births Day of the
week
% of births Month % of births
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- - - -
- - - -
- - - -
- - - - -
Act 13. Plot diagrams for these tables.
(Add a blank paper with them)
Act 14. Draw conclusions: Which is the correct hypothesis? Myth or Fact?
Act 15. Design the slideshow you will use during the Pecha Kucha show. You may use the template provided by your
teacher and remember all what we learned about Pecha Kuchas!
Notes:
Act 16. Pecha Kucha day!
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