DOTS+TODS™ Directed Number and Algebra Counters

interlocking red and yellow two colour counters for algebra and directed numbers

A simple and effective alternative to algebra tiles

DOTS+TODS™ counters are a great alternative to maths manipulatives such as double sided or two-colour counters and algebra tiles.

They are concrete representations of the dots and anti-dots or piles and holes analogies. Pupils use these concepts to help them understand directed numbers and zero pairs.

Pupils ages 9+ can use them to get a deeper understanding of the rules involved in adding, subtracting, multiplying and dividing directed numbers. Basic concepts of algebra can also be explored. More importantly they give a clearer representation of a zero pair than other resources available.

Set of DOTS+TODS alternative to algebra tiles. 50 white positive one DOT counters and 50 black negative one TOD counters. zero pairs.


Set of 100 interlocking counters
50 x Black negative one (-1) TOD counters
50 x White positive one (+1) DOT counters
Plastic compartment box 

Overview of key benefits:

  • A different way to teach zero pairs, directed numbers and algebra to two sided counters or algebra tiles
  • Interlocking pieces for a clearer representation of zero pairs
  • Comes in a handy storage box
  • Durable and thick plastic – easy to grasp
  • Concrete resources develop deep understanding of abstract mathematical concepts

Discover the benefits of DOTS+TODS™ as an alternative to algebra tiles


Each white dot is a value of positive one (+1).  This is the same as the yellow side on algebra tiles.

The white plastic counters are 23 mm in diameter and 2.5 mm thick.

Unique interlocking alternative to algebra tiles designed to represent zero pairs in maths

Like the piles and holes analogy, the white DOTS or ‘piles’ fit inside the black TODS or ‘holes’ to make a clear representation of a zero pair.  

A zero pair is when the sum of two opposite positive and negative numbers equals zero.

For instance +1 and -1 are opposites that make a zero pair because when positive one and negative one are added together they make 0.  
Other examples of zero pairs are:
+5 and -5 or +7 and -7




Each black TOD is a value of negative one (-1).  This is the same as the red side on algebra tiles.

The black counters are 28 mm in diameter and 5mm thick at the rim. 

Furthermore, on both sides there is a recessed centre.  Therefore a white DOT can be put inside either of these ‘holes’.  So this makes them quicker to use.

Boxed Set of 100

Each set contains 50 white DOTS counters and 50 black TODS counters in a handy plastic compartment box.  As a result, they are easy to store and to keep organised. 

Long-lasting, quality and affordable resources

 Like all our plavalmat®  range of place value resources, DOTS+TODS™ are made from durable plastic.  This means they are long lasting and easy to keep clean* unlike cardboard or foam resources.

Easy to use

A further advantage of our DOTS+TODS™ are that they are made from thick plastic, making it easy for pupils to grasp them.

More tutorial videos and product information can be found on our main website

When do children first learn about negative numbers and algebra?

Pupils first find out about negative integers in Year 4. They learn how to count back through zero using real-life examples such as temperature.  Due to this many children use resources like thermometers and most importantly number lines.

Later, in Year 5 and 6 pupils learn to interpret negative numbers in context. They also need to be able to count forwards and backwards through zero.  DOTS+TODS™ counters can be used with number lines to help children become more confident with this.

Finally, in secondary schools Year 7 pupils often use concrete resources like two colour counters or algebra tiles.  DOTS+TODS may be another way for pupils to understand the following:

  • What are Zero pairs?
  • Positive and positive equals a positive
  • Negative and negative equals a positive
  • Negative and positive is equal to a negative and/or a positive and a negative is equal to a negative

Moreover DOTS+TODS™ are great for pupils who need additional maths support. 
As pupils can sometimes find using algebra tiles or two colour counters confusing,  DOTS+TODS™ may offer a simpler and clearer choice.  Furthermore, pupils who have special educational needs or have difficulties with fine motor skills will find them easier to pick up and use than other resources.

Want to know more about how to use DOTS+TODS™ instead of Algebra tiles?

We are making a series of ‘HOW TO’ videos for DOTS+TODS™.  The first video looks in more detail at the product.  The second gives more examples of zero pairs.  Then the next few videos explore how to add, subtract, multiply and divide directed numbers.  In addition, there will be more videos added to show how to use them to support basic algebra.

To watch these videos, or for more information about how DOTS+TODS, visit this page on our main website.  You may also like to read this article or go to our YouTube channel.

Finally, If you would like more help or information about our DOTS+TODS sets or any of our place value products, please get in touch.  We may also be able to make customised sets so please let us know if you have any specific requirements.

plavalmat® is a registered trademark of Oakfield Learning Ltd. is Oakfield Learning Ltd’s international online store.  You may also like to visit where there is more specific information about the primary maths curriculum in England. 

For more information about the sustainability of our products, please click here

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