2120 Campus Drive, Evanston IL 60208
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http://ciera.northwestern.edu/GK12
Binary Numbers – Kristin Labby
Adapted from Computer Science Unplugged Activity 1: “Count the Dots-­‐ Binary Numbers” Purpose
This lesson introduces students to computation thinking (I am using it as the first of several lessons for
6th and 7th graders about computational thinking.) This lesson aims to introduce students to binary
numbers and binary code as a computer’s “language” of storing information. If this is a first lesson in
computational thinking / computer science, a goal of the introduction discussion is to assess students’
prior knowledge of computers.
Overview
Students will learn about binary numbers in a series of activities.
1. Assess prior knowledge: how do you think computers store information?
2. Demo with 5 volunteers and large binary cards.
3. Worksheet Activity 1: Binary Numbers, in small groups.
4. Worksheet Activity 2: Working with Binary Code, individually
5. Brief re-cap/ discussion: ASCII.
6. Worksheet Activity 3: Sending Secret messages, individually (homework/assessment).
Student Outcomes
Using addition and pattern recognition skills, students will be able to count and encode decimal numbers
into binary (and vice versa) in the 5 bit system used first. In the 8 bit system introduced later, students
will translate binary codes (using the ASCII code) to numbers and letters, like computers do.
I also like this objective from CS Unplugged:
“to understand that technological systems are represented by symbolic language tools and understand
the role played by the “black box” in technological system.”
Illinois State Science Standards:
11.A.3a Formulate Hypotheses. (Students never really test the hypothesis, but discover the answer
through these activities.)
13.B.3a Scientific knowledge and economics drive technological development. (To minimize store
space needed, binary numbers and 8-bit code is used. Discussed how computers get smaller and
smaller.)
Reach for the Stars is a GK-12 program supported by the National Science Foundation
under grant DGE-0948017. However, any opinions, findings, conclusions, and/or
recommendations are those of the investigators and do not necessarily reflect the views of
the Foundation.
2 Time
60 minutes
(Could cut some activities or turn into more lessons by using more of the CS Unplugged worksheets.
“Extra for Experts” could be done too.)
Level
6th and 7th grade science
Materials and Tools
Projector and computer to display ASCII table to students (if not available, could print copies of
the pdf and distribute 1 to each group).
• Large binary numbers cards (1, 2, 4, 8, 16 dots): 5 sheets of cardstock, Sharpie marker. See
preparation.
• Activity 1 packet: (1 per group) Photocopies of activity 1 worksheet, clear sheet projectors, set of
binary number cards (5 index cards, sharpie marker).
• ASCII tables (within this file)
• Activity 2 worksheet, one copy for each student
• Activity 3 worksheet, one copy for each student
Introduction
• Attached files include: Activity 1 worksheet, Activity 2 worksheet, Activity 3 worksheet,
Before Additional
giving out the
worksheet
on page
5, it can be helpful to demonstrate the principles
activities,
ASCII
Tables
•
Binary Numbers
to the whole group.
For this activity, you will need a set of five cards, as shown below, with dots on one side
Preparation
and nothing
the other.
Choose
fivedemochildren
demonstration
cards
at the to make 1, 2, 4, 8 or 16
Make
5 largeoncards
for the
in class
onto8hold
½” xthe
11”
cardstock, use
marker
front of the class. The cards should be in the following order:
dots:
If doing Activity 1 in small groups, photocopy 1 worksheet for each group, put in plastic sheet protector.
Discussion
Make
small sets of cards (same as above, but smaller) for each group (index cards and sharpie is fastest,
What photocopy
do you notice
about
of dots
the cards?
(Each card has twice as many
could
and
cut the
out)number
and tuck
intoon
sheet
protector.
as
the
card
to
its
right.)
Have powerpoint/ internet browser and projector or document camera to show students the ASCII code
table. (Alternatively 1 photocopy per group).
How many dots would the next card have if we carried on to the left? (32) The next…?
We can use these cards to make numbers by turning some of them face down and adding
Prerequisites
up the dots that are showing. Ask the children to make 6 (4-dot and 2-dot cards), then 15
None.
(8-, 4-, 2- and 1-dot cards), then 21 (16, 4 and 1)…
Now try counting from zero onwards.
Background
No
requirements.
Addition
skills
arechange
needed
Themajor
rest ofbackground
the class needs
to look closely
at how the
cards
to to
see“count
if they the
can dots”,
see a pattern recognition
n
skills
areinneeded
students
haveflips
the half
skills,
power
series
pattern
how thetoo.
cardsIfflip
(each card
as they
often may
as therecognize
one to its aright).
You
may (2 ), but not
necessary.
Minimal
familiarity
computers (ex. Typing in word processor and “saving” a file).
like to try this
with more
than one with
group.
When a binary number card is not showing, it is represented by a zero. When it is
showing, it is represented by a one. This is the binary number system.
Teaching Notes
Students will learn about binary numbers in a series of activities. This is adapted from CS Unplugged
(http://csunplugged.org/). I found my 6th and 7th graders needed clearer instructions on the worksheets,
so I modified them to hopefully be more straightforward.
1. Assess prior knowledge. I did this by following the students “science journal format”. The title of
the lesson is Binary Numbers and the key question: “How do computers store information?”
(Write these out on chalkboard. Students copy this into their notebooks, and then write their
hypothesis). The question is very open ended, but the title of the lesson is Binary Numbers, so
some students put it together and describe what they know or have heard about binary numbers,
others may give very vague answers.) If time could do think-pair-share, or have students write
Introduction
their
hypothesis on notecards, or just have a discussion.
students
towardon
thepage
idea5,that
if we
need totostore
lots of information,
Before (Guide
giving out
the worksheet
it can
be helpful
demonstrate
the principles we can
to the whole
group.
maximize storage by encoding it into “switches” of 1s or 0s.)
2. Demo with 5 volunteers and large binary cards. Explain that computers use just ones and zeros
this numbers
activity, you
need(Ia set
of five
as shown
below,Only
with two
dots states:
on one side
toFor
store
andwill
letters.
made
the cards,
analogy
to a switch.
on or off.) Have
and
nothing
on
the
other.
Choose
five
children
to
hold
the
demonstration
cards
the 5 volunteers hold their large binary cards (I made my own quickly outatofthe
cardstock and a
front of the class. The cards should be in the following order:
Sharpie marker.)
Binary Numbers
Ask the following questions:
Discussion
What
do you notice about the number of dots on the cards?
What
do youdots
notice
aboutthe
thenext
number
dots if
onwe
thecarried
cards? (Each
has twice as many
How many
should
cardofhave
on to card
the left?
as the
its right.)
We
cancard
usetothese
cards to make numbers by turning some of them face down, and adding up the
dots that are showing. How can we make “6”? “15”? “21”?
How many dots would the next card have if we carried on to the left? (32) The next…?
Lets
count up from zero.
Did
notice
(maybe
thenumbers
1 dot orby
2 dot
volunteer)
the cards
flip while we count
We you
can use
these
cards toask
make
turning
some ofhow
themoften
face down
and adding
up
from
zero?
up the dots that are showing. Ask the children to make 6 (4-dot and 2-dot cards), then 15
Now
lets
numbers:
is 01001? What is “17” in binary?
(8-, 4-,
2-go
andfrom
1-dotbinary
cards),tothen
21 (16, what
4 and number
1)…
Repeat with different students, or continue with similar questions.
3. Worksheet
Activity
1: Binary
Numbers
Now try counting
from
zero onwards.
Have the students work in small groups (3 or 4) to work through Activity 1: Binary Numbers. I
The rest
the class
needsgroup
to lookand
closely
the cards
to see
if they
caninsee
a of 5 index
made
oneofcopy
for each
put itatinhow
a clear
pagechange
protector
and
tucked
a set
pattern
in
how
the
cards
flip
(each
card
flips
half
as
often
as
the
one
to
its
right).
You
may
cards with dots (I made them rather than photocopying and cutting. Faster for me that way, and
like towaste
try thistime
withhaving
more than
one group.
didn’t
students
cut cards.) I had them continue writing their answers in their
science
notebooks or on a loose-leaf sheet of paper.
When a binary number card is not showing, it is represented by a zero. When it is
showing, it is represented by a one. This is the binary number system.
4. Worksheet Activity 2: Working with Binary
Students worked individually on Activity 2 worksheet, “Working with Binary Code”. I
photocopied and shrank it so students could paste into their notebooks after their title, question,
hypothesis and Activity 1.
5. Re-cap/ discussion of ASCII table :
After this activity, I brought the class back together, showed them ASCII code, how computers
really store data: symbols, letters or numbers get translated to binary numbers. Explained real
computers are 8-bit; this dot-card system is 5-bit.
Ask the children to make 01001. What number is this in decimal? (9) What would 17 be
in binary? (10001)
Try a few more until they understand the concept.
3 4 Use chalkboard to draw out 8 bit examples.
Start with 8 blank “cards”, ask students how they should be filled in. (From right to left : 1, 2, 4,
8, 16, 32, 64, 128.)
Ask students: what’s the maximum decimal number you can count to in 8-bit binary?
On the chalkboard, practice a few conversions between decimal and 8-bit binary.
Put up ASCII table, explain the columns: focus on “decimal” “binary” and “symbol”.
If time, go through some examples of translating 8-bit binary to decimals, then to the
corresponding letters/ symbols.
6. Worksheet Activity 3: Sending Secret messages. Could be used as an assessment. Work on in
class if time allows or at home as homework. (Shrink the copy to be pasted in to science
notebook if desired.)
7. If time allows: do “extra for experts” activities or use other CS unplugged worksheets.
Assessment
•
•
•
Feedback from the class during discussions- intro and recap/ASCII.
Questions students ask during “group work” time; teacher can circle and watch student progress
during “Group work time on Activity 1”.
Activity 3 worksheet graded as homework.
Additional Information
http://csunplugged.org/binary-numbers
Great website, contains a lot of information, even has videos!
7'2#1,18)&"9)(")+"41()
7'2#1,18)&"9)(")+"41()
So, you thought you knew how to count? Well, here is a new way to do it!
So, you thought you knew how to count? Well, here is a new way to do it!
Did you know that computers use only zero and one? Everything that you see or
thethat
computer—words,
and that
evenyou
sound
Didhear
you on
know
computers use pictures,
only zeronumbers,
and one? movies
Everything
seeisor
stored
using
just
those
two
numbers!
These
activities
will
teach
you
how
hear on the computer—words, pictures, numbers, movies and even sound isto send
secret
messages
to your
friends using
exactly
the same
method
a computer.
stored
using
just those
two numbers!
These
activities
will teach
youashow
to send
Activity
1: Binary
Numbers
secret messages to your friends using exactly the same method as a computer.
Adapted from CS Unplugged: page 5, “Worksheet Activity: Binary Numbers”
:1%(#4+(,"1%)
Instructions:
:1%(#4+(,"1%)
Cut out the cards on your sheet and lay them out with the 16-dot card on the left
1. Working in your small group, clear some workspace and take out the index cards from your
shown
here:
Cutasout
the
cards
on lay
yourthem
sheet
laythe
them
out card
with on
thethe
16-dot
on the
left
packet
and
outand
with
16-dot
left ascard
shown
below:
as shown here:
Binary Numbers
Introduction
Before giving out the worksheet on page 5, it can be helpful to demonstrate the principles
to the whole group.
For this activity, you will need a set of five cards, as shown below, with dots on one side
and nothing on the other. Choose five children to hold the demonstration cards at the
front of the class. The cards should be in the following order:
Make sure the cards are in the same order as shown above.
Make sure the cards are placed in exactly the same order.
(This probably seems backwards to you since in English, we read words from left to right! In
Make sure the cards are placed in exactly the same order.
codessothe
lowest5 number
is on the right
weincount
up towards
Now flipbinary
the cards
exactly
dots show—keep
yourand
cards
the same
order!the left.)
Now flip the cardsDiscussion
so exactly 5 dots show—keep your cards in the same order!
2. Flip the cards to show exactly 5 dots:
What do you notice about the number of dots on the cards? (Each card has twice as many
as the card to its right.)
How many dots would the next card have if we carried on to the left? (32) The next…?
We can use these cards to make numbers by turning some of them face down and adding
up the dots that are showing. Ask the children to make 6 (4-dot and 2-dot cards), then 15
(8-, 4-, 2- and 1-dot cards), then 21 (16, 4 and 1)…
Now try counting from zero onwards.
The rest of the class needs to look closely at how the cards change to see if they can see a
Find out how to
getin3,how
12,
19.
Isflipthere
more
number?
pattern
thethe
cards
(each
card
flipsthan
half
asone
oftenway
as theto
oneget
to itsany
right).
You may
Remember
to keep
cards
in the
same
order.
like to
this19.
withIs
more
than
group.
What
thetobiggest
you
canone
make?
What
the smallest?
there any
Find
out is
how
get
3,trynumber
12,
there
more
than
oneisway
to get anyIsnumber?
number
can’t
make
between
the
smallest
biggest
numbers?
What
is theyou
biggest
number
you can
make?
Whatitand
is
the
smallest?
Is there any
When
binary to
number
cardthe
is not
showing,9.
is represented by a zero. When it is
3. Now flip
thea card
make
number
number you can’tshowing,
make itbetween
thebysmallest
biggest
numbers?
is represented
a one. This and
is the binary
number
system.
Write howTry
you
did this
your notebook
Can you work out a
Extra for Experts:
making
theinnumbers
1, 2, 3,like
4 inthis: order.
and reliable
the1,cards
increase
byout
one?
Extralogical
for Experts:
Try method
making of
theflipping
numbers
2, 3,to
4 in
order. any
Can number
you work
a
logical and reliable method of flipping the cards to increase any number by one?
9 = 4. Do the Ask
same
findtoout
how
to What
get the
numbers
3, 12 and
19. Sketch
in your notebook too.
the to
children
make
01001.
number
is this in decimal?
(9) What
would 17 these
be
in binary? (10001)
5. Answer these questions in your notebook. Remember to use complete sentences.
5
Tryuse
a few
more until they understand the concept.
Photocopiable for classroom
only.
a.
Is
there
more
than one way to make any number?
©
2002
Computer
Science
Unplugged
(www.unplugged.canterbury.ac.nz)
Photocopiable for classroom use only.
5
There
are
five
optional
follow-up
extension
to be used for reinforcement. The
What is the biggest
number
youactivities,
can make?
© 2002 Computer Scienceb.
Unplugged
children(www.unplugged.canterbury.ac.nz)
should do as many of them as they can.
c. What is the smallest number you can make?
d. Is there any number you can’t make between the biggest and the smallest numbers?
4
Photocopiable for classroom use only.
© 2005 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)
5 6 !"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.)
Activity 2: Working with Binary Code
Adapted from CS Unplugged: page 7, “Worksheet Activity: Working with Binary”
The binary system uses zero and one to represent whether a card is face up or
not. binary
0 shows
that auses
cardzero
is hidden,
1 means that
you acan
see
The
system
and oneand
to represent
whether
card
is the
facedots.
up orFor
not. 0 shows that a card is
example:
hidden,
and 1 means that you can see the dots. For example, for the number 9:
!"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.)
We call the series of 0s and 1s binary numbers, while 9 that is represented is called a decimal number.
Can you work out what 10101 is? What about 11111?
The binary system uses zero and one to represent whether a card is face up or
shows
that you
acards
card
is help
hidden,
1 means
that
canyour
see the dots. For
Questions:
(use
5 binary
to
if needed)
What day ofnot.
the0your
month
were
born?
Write
itand
in binary.
Find
outyou
what
example:
friend’s birthdays are in binary.
1. Can you work out what 10101 is as a decimal number? _________
2. What is 11111 in decimal? _________
4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/)
3. What date of the month were you born in (in decimal)? ________
What is that in binary numbers? ___ ___ ___ ___ ___
Can you work out what 10101 is? What about 11111?
4. Write the birthdays of two friends too (decimal and binary):
What day of the month were you born? Write it in binary. Find out what your
_____
= ___birthdays
___ ___ ___
___
friend’s
are in
binary.
_____ = ___ ___ ___ ___ ___
5. Try to work out these coded numbers. Some are 5 bit binary codes; some are only 4-bit, 3-bit, 2bit or 1-bit. Its important to remember that in binary we count up from the right, not the left.
4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/)
Write the decimal number next to the “ = ”. Translate the codes to 0s and 1s first if it helps you.
Extra for Experts: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you
can make any length up to 31 units. Or you could surprise an adult and show them
how they only need a balance scale and a few weights to be able to weigh those heavy
things like suitcases or boxes!
Photocopiable for
classroom
only.
Extra
for use
Experts:
Using a set of rods of length 1,
© 2002 Computer can
Science
Unplugged
(www.unplugged.canterbury.ac.nz)
make any length up to 31 units. Or you could
7 how you
2, 4, 8 and 16 units show
surprise an adult and show them
some computer person still working away late into the night. How could he
attract her attention? Tom looks around to see what he could use. Then he has a
brilliant idea—he can use the Christmas tree lights to send her a message! He
finds all the lights and plugs them in so he can turn them on and off. He uses a
simple binary code, which he knows the woman across the street is sure to
understand. Can you work it out?
Activity 3: Use Binary Code to Send Secret Messages!
Adapted from CS Unplugged: page 8,
“Worksheet Activity: Sending Secret Messages”
!"#$%&''()*+(,-,(./)0'12,13)0'+#'()4'%%53'%)
Tom is trapped on the top floor of a department store. It’s just before Christmas
and he wants to get home with his presents. What can he do? He has tried
calling, even yelling, but there is no one around. Across the street he can see
6) 7) 8) 9) :) ;) <) =) >) 6?)
some computer person still working away late into the night. How could he
5) @) +) 2) ') A) 3) &) ,) B)
attract her attention? Tom looks around to see what he could use. Then he has a
69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78)
brilliant idea—he can use the Christmas tree lights to send her a message! He
1) ") E) F) #) %) () G) -) H)
finds all the lights and plugs them in so he can turn them on and off. He uses a
simple binary code, which he knows the woman across the street is sure to
Can you work it out?
Tom is trapped on the top floor of a department store. It’s just before Christmas
ment store. It’sunderstand.
just before Christmas
8
and he wants to get home with his presents. What can
he do? He has tried
. What can he do? He has tried
calling,
even
yelling,
but
there
is
no
one
around.
Across
the street
he can
see
und. Across the
street
he
can
see
Directions: Tom’s building is shown below. Each row is a floor of 5 rooms. Decode
Tom’s
message
by
some computer person still working away late into the night. How could he
te into the night.
How
could
he
first translating each floor intoattract
binary,
then
into
decimal
numbers.
Finally,
use
the
decoding
table
at
the
her attention? Tom looks around to see what he could use. Then he has a
ee what he could use. Then he has a
bottom
to
translate
the
decimal
numbers
into can
letters.
brilliant
idea—he
use the Christmas tree lights to send her a message! He
lights to send her a message! He
finds
all
the
lights
and
plugs them in so he can turn them on and off. He uses a
an turn them on and off. He uses a
simple
binary
code,
which
he
knows the woman
across the street is sure to
Binary
Decimal
Letters
man across the street is sure to
understand. Can you work it out?
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Photocopiable for classroom use only.
© 2005 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)
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Photocopiable for classroom use only.
© 2005 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)
7 8 Extra for Experts: (from CS Unplugged worksheets)
Activity 1: Try making the numbers 1, 2, 3, 4 in order. Can you work out a logical and
reliable method of flipping the cards to increase any number by one?
Activity 2: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make
any length up to 31 units. Or you could surprise an adult and show them how they only
need a balance scale and a few weights to be able to weigh those heavy things like
suitcases or boxes!
(these ideas –weights or rods – could be expanded into additional activities)
See CS Unplugged pages 9, 10 , 11 and 12 for additional worksheets relating to this lesson.
Other extensions: could extend ASCII table, make a “coded message” in Binary, have students translate
to the letters and numbers via ASCII.
Could have students define vocabulary words: binary numbers, decimal numbers, ASCII table.
Taken from: http://www.ascii-code.com/
9 10 11 12