Year 7 mathematics 2013 MMXIII
CAT 1: INVESTIGATION task
Ancient number systems
Due Date:
Instructions:
Attempt all questions on this sheet. All working must be your own. This assignment is to be handed
in by the due date. Complete your answers on loose-leaf paper (not in your workbook). Use full
sentences for ALL answers.
eg. “The Melbourne Olympic Games were held in MCMLVI which means in 1956.”
The ancient number system you are probably the most familiar with is the Roman System. They are
on clock faces, in prefaces of books or in the credits of movies to show the year it was produced. The
Roman symbols are based on fives. The symbols are shown below.
Numbers are written by combining symbols and the order the symbols are written in is important.
The Roman Numerals from 1 to 10 are:
I
II
III
IV
V
VI
VII
VIII
IX
X
Questions:
1. What happens when I is just before V in the number?
(1)
2. What happens when I is just after V in the number?
(1)
3. What happens when I is just before X in the number?
(1)
4. What would you expect to happen if I is just after X in the number?
(1)
5. Write the Roman Numerals for 11 to 20. (set up a table)
(4)
6. What numbers are represented by the following Roman Numerals
a) XXV
b) XXXIV
(2)
7. Write the Roman Numerals for the following numbers:
a) 26
b) 39
(2)
8. What numbers are represented by the following Roman Numerals:
a) LV
b) XL
c) CC
d) DC
e) CM
f) XLII
g) LXXIV
h) MDCCCXXIII
(8)
9. Write the Roman Numerals for the following numbers:
a) 356
b) 1650
c) 94
d) 179
e) 2243
f) 931
g) 428
h) 1085
(8)
Year 7 mathematics 2013 MMXIII
10. State which year the following films were produced:
a)
Grease
MCMLXXVII
b)
Titanic
MCMXCVII
c)
ET
MCMLXXXII
d)
Snow White & the Seven Dwarfs
MCMXXXVII
(4)
More ancient number systems
11. Write down your telephone number in the Chinese number system.
(2)
12. Rewrite these equations in the Babylonian system, and then solve them
a)
25 16 
b)
73 
c)
12  4 
d)
27  9 
13. Write your age and date of birth in the Mayan number system.
(4)
(2)
(40 marks)
Year 7 mathematics 2013 MMXIII
Create your own number system
You need to design your own number system.

You will need to choose a base (eg. 5, 10, 20) and

The required number of symbols.

Note down the benefits of changing our system to the system you have devised.

Discuss why/why not you system requires a symbol for 0.

Show how addition and subtraction would be set out using your system.
(20 marks)
Work Habits Rubric:
Criterion/Score
Following
Instructions
Presentation
0
1
2
3
4
Did not follow
Followed few of
Followed some
Followed most
Followed the
the instructions
the instructions
of the
of the
instructions fully
instructions
instructions
and accurately
Disorganised
Some effort was
Work is mostly
Some of the
Neat, well set
work, very little
made to present
neat and well
work is
out work, easy
effort taken to
the work neatly
presented
disorganised,
to read and
but very good
follow
present it well
overall
Whole
Answers were
Only a few
Approximately
Majority of the
All answers were
not in sentences
questions were
half of the
answers were in
in full sentences
answered in full
answers were in
full sentences
sentences
full sentences
Work was not
Only a few
Approximately
A few questions
All questions
completed
questions were
half of the
were incomplete
were completed
completed
questions were
sentences used
Completion of
work
completed
Submission by
due date
Work was not
Submitted more
Submitted 2
Submitted 1 day
Submitted on
submitted
than 2 days late
days late
late
due date or
earlier
(20 marks)
TOTAL = 80 marks
Your Score =
marks
This CAT is worth 3 ACE points.