Download Model Solar System Lesson

Summer Mathematical Enrichment Class for Girls 2012
Model Solar System
Author(s): John Quintanilla
Date/Time Lesson to be Taught: July 2, 2012
Technology Lesson:
Yes
No
Course Description:
Name: Summer Mathematical Enrichment Class for Girls 2012
Grade Level: Mostly 3rd graders
Honors or Regular: Honors
Lesson Source: JQ
Objectives:
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SWBAT identify a scale from a map.
SWBAT multiply and divide by powers of 10, moving the decimal point as necessary.
SWBAT make conversions involving kilometers, meters, centimeters, and millimeters.
Texas Essential Knowledge and Skills:
§111.16. Mathematics, Grade 4.
(b) Knowledge and skills
(6) Patterns, relationships, and algebraic thinking. The student uses patterns in
multiplication and division. The student is expected to:
(B) use patterns to multiply by 10 and 100.
(11) Measurement. The student applies measurement concepts. The student is
expected to estimate and measure to solve problems involving length (including
perimeter) and area. The student uses measurement tools to measure capacity/volume
and weight/mass. The student is expected to:
(A) estimate and use measurement tools to determine length (including
perimeter), area, capacity and weight/mass using standard units SI (metric) and
customary
(B) perform simple conversions between different units of length, between
different units of capacity, and between different units of weight within the
customary measurement system
Materials List and Advanced Preparations:
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Maps that show a scale (like 1:2,000,000) in the legend. My experience is that AAA/CAA
maps work well for this; not all road maps have a scale pre-printed, unfortunately. It’d be
nice to have maps (possibly insets of a big map) over a range from a city to a state to a
country, so that scales are quite different.
Globe that shows a scale (like 1:43,000,000). The scale and legend of a globe is usually
printed somewhere in the south Pacific.
Worksheet for multiplying and dividing by powers of 10
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Summer Mathematical Enrichment Class for Girls 2012
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Worksheet for metric system
Worksheet for solar system
Calculators (optional)
Tape measure that measures in metric
Transparent tape
Pencil
Accommodations for Learners with Special Needs (ELL, Special Ed, 504, GT, learning
styles, etc.): None provided below, though this could be added.
5Es
Page 2 of 9
Summer Mathematical Enrichment Class for Girls 2012
ENGAGEMENT
What the Teacher Will Do
Time: 3 Minutes
Probing/Eliciting
Questions
On the table, you will see a
whole bunch of maps. Please
pick one. [Also use insets of
maps if they show a scale.]
[Teacher has a map also.] In
the corner of my map is
something called the legend.
Student Responses and
Misconceptions
[Students select a map.]
What place(s) are shown in
your map?
[Answers vary.]
Can you find the legend of
your map?
[Students find the legend.]
Evaluation/Decision Point Assessment
All students have maps and have found the legend.
Student Outcomes
None yet.
Page 3 of 9
Summer Mathematical Enrichment Class for Girls 2012
EXPLORATION
Time: 15 Minutes
What the Teacher Will Do
Probing/Eliciting Questions
In the legend is something
called the scale. For my map,
the scale is 1:2,000,000 [or
whatever it is… write on the
board]. That means that every
inch on this map represents
2,000,000 inches in real life.
What is the legend of your map?
Student Responses
and Misconceptions
[Answers vary --- all
answers are written on
the board.]
Which number is the smallest?
[Students identify.]
Who had the map with that
number?
[Student raises hand.]
And what place does that map
show?
[Student answers,
probably a city.]
Now, which number is the largest?
[Students identify.]
Who had the map with that
number?
[Student raises hand.]
And what place does that map
show?
[Student answers,
probably a country.]
Why do you think different scales
are needed?
Countries are a lot
bigger than cities!
What is this?
A globe!
And what does the globe
represent?
The whole world!
Very good. And what kind of scale
do you think this needs?
A big number!
How big?
[Students guess.]
That’s right. For something like
a map of the whole country, we
need a big scale. But for
something smaller like a city,
we need a small scale.
[Shows globe.]
It turns out that the scale of this
globe is 1:42,000,000 [or
whatever the number is…
writes on board]
Wow.
And why is the scale so big?
Because the world is
big!
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Summer Mathematical Enrichment Class for Girls 2012
OK, let’s find that place on the
map.
Good. Now, has anyone here ever
been on vacation to an island (like
Hawaii) or another country, maybe
in Europe?
[Hopefully somebody
has. Canada or Mexico
probably won’t work for
this question --- it
needs to be an island
or else a “small”
country.]
Did you have your vacation in a
teeny, tiny spot like this?
No, it was bigger than
that!
So why do you think it looks so
small on this globe?
I guess because
Hawaii [or other place]
is small compared to
the whole world.
That’s right. Hawaii [or other
place] is a big place, but the
whole world is much, much
bigger. So on a globe, Hawaii
[or other place] looks really
small, even though it’s not that
small.
Today, we’re going to make our
own model. It’s going to be a
model of the entire solar
system. That means the sun
and all of the planets.
Whoa.
What kind of scale do you think
we’ll need for the entire solar
system?
Well, the model that we’re
going to make will be about
1:14,000,000,000 [change the
number if the handout is
changed.]
Evaluation/Decision Point Assessment
Students have an intuitive understanding of scales.
[Students guess.]
Whoa.
Student Outcomes
The students can
identify the scale on a
map and know that big
scales are needed for
big places.
Page 5 of 9
Summer Mathematical Enrichment Class for Girls 2012
EXPLANATION 1: Multiply/Divide by Powers of 10
What the Teacher Will Do
Probing/Eliciting
Questions
Time: 20 Minutes
Student Responses and
Misconceptions
Before making the solar system, we need
to go over the rules for multiplying and
dividing by powers of 10.
[Go over the first Warm-Up page, one
problem at a time.
Expect real difficulty when decimal points
are introduced for the first time. These
can be explained monetarily… if 100
people have $54.34, then the total
amount of money that they have is
$5,434.
Another difficulty for students will be
placing the commas correctly for big
numbers, like writing 12,000,000 instead
of 120,000,00. In other words, there could
be a tendency to start from the left when
counting groups of three digits instead of
the right.
Likewise, if $89 is evenly divided among
100 people, then each person gets
$0.89.]
Evaluation/Decision Point Assessment
Students are comfortable with moving the decimal point when
multiplying and dividing by a power of 10.
Student Outcomes
Students are able to correct
multiply and divide by
powers of 10, including
working with decimals.
Page 6 of 9
Summer Mathematical Enrichment Class for Girls 2012
EXPLANATION 2: Converting Units in Metric
What the Teacher Will Do
Probing/Eliciting
Questions
[Next, go over the second Warm-Up
page, one line at a time, on the metric
system. Students may be unfamiliar with
the metric system. Emphasize that the
civilized universe switched to metric a
generation ago, but we’re stuck with
customary units in the U.S. Also,
emphasize that it’s far easier to multiply
and divide by a power of 10 than by 12,
36, or 5280.]
Evaluation/Decision Point Assessment
Students are comfortable with moving the decimal point when
converting units of distance within the metric system.
Time: 20 Minutes
Student Responses and
Misconceptions
Student Outcomes
Students work with
kilometers, meters,
centimeters, and millimeters.
Page 7 of 9
Summer Mathematical Enrichment Class for Girls 2012
ELABORATION
What the Teacher Will Do
Time: 75 Minutes
Probing/
Eliciting
Questions
Student
Responses and
Misconceptions
[Finally, divide students into groups to perform calculations
for the model solar system. Each group only does 2 or 3 of
the pages. If time is an issue, here’s the order of
importance:
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Sun, eight planets, Moon
Voyager 1, speed of light, Alpha Centauri system
Dwarf planets
The scale of about 1:14,000,000,000 was chosen so that
the eight planets would fit on a straight section of sidewalk
about 350 meters long. Obviously, the scale should be
modified to fit the space that’s available.
Another reasonable choice would be to build the solar
system only to Saturn and then ask the class roughly how
much further Uranus and Neptune would be. This has the
desirable effect of making the planets a bit larger and
hence easier to build.
After the calculations, the class builds the Sun, planets, and
other objects. Rolling up bits of paper will do for most of
them. For the inner planets, it might be easiest to toast
some bread, shake off some crumbs, and then select
crumbs of appropriate size. All objects are taped to pieces
of paper. (The Earth and Moon should be taped on the
same piece of paper at the appropriate distance apart.)
Finally, using the metric tape measure, the class goes
outside and places the objects at the appropriate distances
from the Sun. If the tape measure is 5 meters long, it’s best
to have a team of students measure distances from the Sun
in 5-meter increments, rather than having to walk all the
way back to the Sun after each planet is placed.
Fun things to discuss as the solar system is built:

Look at the model Sun after the Earth/Moon system
is placed, and then ask the class if the Sun in the
sky appears that big.
Page 8 of 9
Summer Mathematical Enrichment Class for Girls 2012
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Mention it took about three days for astronauts to
travel to the Moon.
Walk at the speed of light… in the 1:14 billion
model, that’s a very slow walk of about 1.3 meters
per minute.
Give commentary about the number of years it took
Voyager 2, travelling over 20,000 kilometers per
second and one of the fastest manmade objects
ever built, to reach the outer planets (launched
1977, Jupiter 1979, Saturn 1981, Uranus 1985,
Neptune 1989.)
Look at the model Sun after Neptune is placed…
from that distance, the Sun appears to be just a
bright star and not a circle.
]
EVALUATION
What the Teacher Will Do
Time: 10 minutes
Probing/Eliciting Questions
Student Responses and
Misconceptions
Post-Assessment
Page 9 of 9