Suffolkmaths Homepage
Number Systems & Counting
Animated YouTube Clip on the Development
of Numbers 
Click here
Babylonian Maths
Motivate
has created a free online
multimedia resource pack for the
Key Stage 2/3 transition, based
around short video clips
introducing key concepts in
Babylonian mathematics. Each
pack includes related
investigative activities and
worksheets for students, and
teacher support notes.
Find the free multimedia
resource pack at
http://motivate.maths.org/BabylonianMaths
Babylonian Numbers 1 to 9 YouTube Clip  Click Here
Babylonian Numbers 10 to 50 YouTube Clip  Click Here
Babylonian Numbers 60 and beyond YouTube Clip  Click Here

Introduction to Roman Number
System 
Click here
References
and Resources
Silly YouTube Clip 
Click here
Selection of Worksheets 
Click here
Site with a range of related
resources 
Click here
Roman Numerals
Information
Roman Numerals PowerPoint 
Quiz
Roman Numerals Online Quiz 1 
Click here
Converting Roman Numerals Online
Quiz 2 
Click here
Roman
Numerals
Jigsaw Puzzle
The Roman
Numeric System
Click here
Converting
online 
Click here
Conversion
Worksheets
Click here
Investigation – The Secret Code
Click here
Tasks
(mostly suited to lower ability
sets)

Discussion: Where do we see
Roman numerals? Why do you
think the numbers 5 and 10
are so significant?

Simple
understanding of the system
– converting to and from
Roman Numerals

Investigation (using ‘The
Secret Code’)

Finding longest numbers

Encoding numbers



A lesson
on Binary 
Lesson Outline
Binary Birthdays
Binary Message
Binary Quiz 
Binary:
YouTube Counting in Binary
Click here
Binary
Lesson Plan
Counting in Binary
on Your Fingers
Online
Binary Game
Octal and
Hexadecimal
Click here
Spreadsheet for doing base
conversions.
Binary Clock
Tasks
(mostly suited to middle and
high ability sets)

Examining decimal (base 10)

What do we call the
column headings? (1, 10,
100 etc)

Why
do we use base 10? What
is significant about the
number 10? (fingers –
digits!)

Which digits/symbols do
we use? (0, 1, …, 8, 9)

We
don’t have a symbol that
means 10, we need to use
two.

How
do they relate to each
other?

What about the columns
to the right of the
decimal point? (0.1,
0.01 etc).

How
do we multiply by 10,
100 1000 etc? (shifting
left)

Examining octal (base 8).
This is a good first other
base to look at. I usually
introduce it by considering
an alien species who have 8
fingers.

What are the column
headings? (1, 8, 64, …)

Which digits can we use?
(0, …7. no symbol for
8)

The
‘point’ in now called
the ‘Octal Point’

Explain subscript
notation to indicate
which base we are using?
(e.g. 738)

Try
converting to and from
octal and decimal.

Addition and subtraction
using the column
method? Is it any
different?

What happens if we shift
the digits to the left
or right?

Examining binary (base 2). –
Follow same points as for
octal.

‘Binary digits’ are
called ‘bits’ for short

Counting activity. Have
a number of students on
chairs in a line – one
student per column (say
5). Standing up
represents 1, sitting
represents 0. Start
with them all sitting
(i.e. zero) then try to
count by standing and
sitting as necessary.

A
similar activity to the
above can by shading
squares on graph paper.
Each student will need
just one strip no more
than 8 small square
wide.

Note that computers use
binary as the memory is
made up of a number or
on/off (i.e. 1/0)
switches. That is why
we see number like 512,
1024 etc showing the
size of out USB memory
etc, 32bit games
systems)

Examining hexadecimal (base
16)

Need for more digit
symbols

Conversion to and from
binary is easy (bits
grouped into 4bit
‘nybbles’


Ancient Egyptian Maths Problems

Click here
Researching Egyptian Maths 
Click here
Maths Related to the Egyptian
Pyramids 
Click here
Pyramid Challenge Game 
Click here
Tower of Hanoi 1 
Click here
Tower of Hanoi 2 
Click here
The Ancient
Egyptians used unit fractions
(i.e. numerator of 1). To make
other fractions they added these
unit fractions.
Example:
3/4 = 1/2 + 1/4
Unit
fractions could not be repeated,
so 2/5 = 1/5 + 1/5 is not
allowed.
Egyptian
Maths 
PowerPoint Presentation
NRICH Task 
References
and Resources
Lots of
other references (complex)
Click here
Math Cats –
interactive creation of Egyptian
Fractions
Click here
Tasks

Show
3/5 = 1/2 + 1/10, 3/7 =
1/3 + 1/11 + 1/231

Write
fractions with 2 as the
numerator (e.g. 2/5, 2/7,
2/9, …) – describe any
patterns you notice. Can
you find a rule for writing
fractions of the form 2/n?

Investigate writing other
fractions as Egyptian
Fractions (when the
numerator is 3, 4, 5, …)

Counting Systems
The
calculator has its history in mechanical
devices such as the abacus and slide
rule. In the past, mechanical clerical
aids such as abaci, comptometers,
Napier's bones, books of mathematical
tables, slide rules, or mechanical
adding machines were used for numeric
work. This semimanual process of
calculation was tedious and errorprone.
The first digital mechanical calculator
was invented in 1623 and the first
commercially successful device was
produced in 1820. The 19th and early
20th centuries saw improvements to the
mechanical design, in parallel with
analog computers; the first digital
electronic calculators were created in
the 1960s, with pocketsized devices
becoming available in the 1970s.
Abacus
‘Abaci’ – Powerpoint
presentation giving an overview
of the history
Different
Types
Click here
History
Click here
Chinese and
Japanese related materials 
Click here
Japanese
Abacus (Soroban)
YouTube Clips:
Introduction
Click here
Addition
Click here
Subtraction Click
here
Abacus being used by
experts
Click here


How to do
addition and subtraction (and
other operations) on a Japanese
abacus
Instructions
Superb set
of Activities using the Japanese
Abacus 
Click here
Software/online abacuses
School
type
Click here
Chinese
type
Click here
Chinese Abacus to Colour 
Click here
Japanese
type
Click here
Lower
ability student might find it
easier to look at 'school'
abacuses which have horizontal
wires with 10 beads on each.
The top wire represents units,
then tens, etc.
Higher
ability students may prefer to
look at 'Japanese' abacuses.
These are essentially base 10,
but each column is broken into
two parts. The top most bead
means 'add 5' to the bottom
beads. (see
Click here). Template for
use with counters 
Click here
Note about
addition and subtraction. If
you are adding with a Japanese
abacus (and several other types)
you have to be aware of number
bonds to 5 and 10. For example,
if a column already contains the
digit 8 and you wish to add 3,
you do not count on 3 and do the
carrying, instead you add 10
(i.e. one to the next column)
and subtract 2 (8 = 10 – 2).
Similarly, it the column
contains 4 and you wish to add
3, this is the same as adding 5
and then subtracting 2 (i.e. set
the ‘heaven’ bead and subtract 2
from the Earth beads).
Subtracting happens in the
opposite way – essentially
implementing ‘borrowing’.
Multiplication is very similar
to traditional long
multiplication except you add
the intermediate results as you
go.
Research
Tasks

Look at
types of abacuses

Which
number base (if any) do they
use?

How do
they deal with fractions?
Other Tasks

Learn
how to use an abacus to add
and subtract

Can you
redesign it to work in a
different number base?

Can you
work out how you might use
the abacus to multiply?

Slide Rules
Slide Rule:
How does it Work
Introduction
Make Your
Own Slide Rule 
Template 1
Template 2
Online Slide Rules
Click here
On this original version, the
cursor and the slide may be
moved with your mouse  just
click and drag. The number
overlay shows the reading and
identification of the scale
directly under the mouse pointer
(or the hairline reading if over
the cursor).
Click here
This applet is designed to be a
realtime, configurable, slide
rule emulator. It currently
supports zooming and onthefly
scale reconfiguration. The
emulator can handle multiple
slides, and multiple cursors.
Cursors can contain multiple
gauge marks and hairlines.
Scales can be placed anywhere on
the stators, slides, or cursors.
The size and texture of the rule
body/surface can be changed. In
short, it's totally
reconfigurable!
Click here
Instructions
The
following page gives numeric
examples of the basic
calculations that a slide rule
can do. Just follow the
stepbystep instructions and
you will be amazed by the power
and versatility of the venerable
slipstick.
Click here
Instruction Leaflet:
Front Side
Reverse Side
From
Wikipedia, the free encyclopedia:
Basic concepts
Multiplication , Division,
Roots and powers,
Trigonometry, Logarithms and
exponentials History
Click here
Various
downloadable Slide rule
Manuals
Click here
Making a
Slide Rule
The
Slide Rule Museum have pulled
together a large set of
templates to make your own slide
rules, including circular and
cylindrical versions.
Click here
Thanks
to some very publicspirited
slide rule experts (one in the
UK, one in Canada), we now can
provide some computerized tools
that will allow you to build
several different types of slide
rules.
Click here
Students
will learn about the history of
slide rules, how they work, and
then make their own.
Click here
Logarithms Explained:
Click here
Alternative Forms of the Slide
Rule
Otis
King Calculator 
Click here
Circular Slide Rule 
Click here 

Speed Calculations
Speed
Calculations 
Ideas 

Napier's Bones
Brief Outline of Napier's
achievements for display 
Click
here
Abacus, Napiers Bones, Slide Rule
and Logarithms  Interactive Features:
Click here
Napier's Bones printout of each
rod and exemplar calculation for display 
Click here
Napiers Chessboard Calculator 
Click here 

Other Calculating Machines
