A lesson using the Slavonic Abacus
The article ‘Using the Slavonic Abacus in the Classroom’
gives a brief introduction to some of the theory that underlies an approach
to mathematics education that may be supported by the use of the Slavonic
Abacus, especially with visual and kinaesthetic learners. The more detailed
notes given below may be used to plan one or more lessons using the Slavonic
Abacus (available from xavier.bangor.ac.uk) to establish and practise
some key concepts relating to Number and Place Value.
Lesson Aims
 Establish a concrete, visual model of numbers up to 10, with numbers
between 6 and 10 being composed of 5 +.
 Understand complements to ten.
 Establish a concrete, visual model of numbers of tens up to 100,
with numbers between 60 and 100 being composed of 50 +.
 Understand complements to 100 in tens.
 Establish a concrete, visual model of 2digit numbers composed of
tens and units.
 Understand complements to 100.
Demonstrations on the Slavonic Abacus
Numbers to 5
Use the top row of a large Slavonic abacus to show numbers between 1
and 5. Move all the beads in a single movement, not one at a time.
Without counting, pupils call out each number as you show it
on the abacus.
Between numbers, lift and tilt the abacus to move the beads back to the
‘unmoved’ (zero) position.
For example…

'two'... 
tilt 
'four' 
Singledigit numbers and their complements
to 10
Use the top row of a large Slavonic abacus to show any singledigit
number.
Point first to the number, and then to its complement to 10.
Without counting, pupils call out the number, and then they call
its complement to 10.
For example…

'eight'... 

'and two make ten' 
Numbers of 10s and their complements to 100
Explain that each row on the abacus has ten beads.
Since we can see how many rows have been moved, we can see a number of
tens at a glance, without counting.
Use the Slavonic Abacus to show a number of tens, being careful to move
all the rows of ten in one movement.
Point first to the number, and then to its complement to 100.
Without counting, pupils call out the number, and then they
call its complement to 100.
For example…

'forty'... 

'and sixty make a hundred' 
Twodigit numbers and their complements to
100
Use the Slavonic Abacus to show a twodigit number, being careful to
move all the rows of ten in one movement.
Point first to the number, and then to its complement to 100.
Without counting, pupils call out the number, and then they
call its complement to 100.
For example…



'thirty'... 
'...seven...' 
'and sixtythree make a hundred' 
These activities may form part of a single lesson for older pupils,
or they may be spread out over a longer period with more opportunities
to practise recognising first singledigit numbers, then numbers of
tens, then twodigit numbers. The idea of complements to ten or a hundred
may be introduced later if this is more appropriate to your pupils.
The key point, at whatever level they are working, is that the pupils
(and you) should learn to just see the numbers of beads being shown
on the Slavonic Abacus, without counting.
This work may be reinforced with the Pupil Sheets. Pupils will
need access either to a real or to the electronic Slavonic Abacus, both
available from xavier.bangor.ac.uk.
The first of the Pupils Sheets presents exercises using both numbers
and money. Money offers a useful alternative concrete model of twodigit
numbers and complements to 100, with which many pupils (particularly
in secondary school) are likely to be familiar. The coins shown on the
Pupil Sheet are in sterling, but graphics for other decimal currencies
may be substituted.
Many more ideas for working with visual and kinaesthetic learners
in the mathematics classroom may be found in the book Teaching
Maths to Pupils with Different Learning Styles, by Tandi ClausenMay
(London: Paul Chapman Publishing, 2005, ISBN 1412903599).
Tandi ClausenMay, March 2005
tandi.clausenmay@virgin.net
