What are Dots + Tods™ and how can they be used to teach concepts such as algebra and directed numbers?
Dots+Tods™ counters are Oakfield Learning’s teacher designed alternative to maths manipulatives such as double sided or two-colour counters and algebra tiles. They help pupils ages 9+ to develop a deeper understanding of the basic concepts of algebra and the rules involved in adding, subtracting, multiplying and dividing directed (positive and negative) numbers.
Our set of interlocking DOTS+TODS™ contains 50 white DOTS counters and 50 black TODS counters in a handy plastic compartment storage box to keep them organised. Each white DOT counter (representing a positive one) and each black TOD counter (representing a negative one) are made from durable, thick plastic so are easy to grasp, durable and simple to use.
Pupils are first introduced to positive and negative integers in KS2 in Year 4 when they are aged 8-9. They first learn to count back through zero using negative numbers mainly in the context of temperature using thermometers, vertical and horizontal number lines.
In Year 5 and 6 the England National Curriculum states that pupils need to be able to interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero. Our DOTS+TODS™ counters are suitable for use at this age and when used alongside number lines they can help pupils to become increasingly confident with solving problems involving positive and negative numbers.
In KS3, the National Curriculum for mathematics aims to ensure that all pupils ‘become fluent in the fundamentals of mathematics, including through varied and
frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately’. In order to do this, Year 7 pupils often use algebra tiles, double sided or two colour counters as visual representations of directed numbers (positive and negative numbers) and zero pairs. In secondary maths our DOTS+TODS™ counters are particularly beneficial to explore the rules of adding, subtracting, multiplying and dividing directed numbers, especially for pupils who require an alternative to number lines.
Rather than just learning rules with little conceptual understanding, our visual representations enable pupils to interact with concrete resources to explore what ‘ZERO PAIRS‘ are and why ‘A POSITIVE AND A NEGATIVE EQUALS A NEGATIVE‘ and ‘A NEGATIVE AND A NEGATIVE EQUALS A POSITIVE‘.
DOTS+TODS™ can also be used as an alternative to algebra tiles or counters to help pupils gain a deeper understanding of algebraic expressions and equations.
You may also like to read our article: HOW TO HELP CHILDREN UNDERSTAND POSITIVE AND NEGATIVE NUMBERS
Our DOTS+TODS™ are easy to keep clean and hygienic between uses. As they are made from durable plastic rather than foam or cardboard, they can be sink washed or put in a dishwasher inside a suitable bag.
The long-lasting, embossed design allows the counters to be re-used.
For more information about safety or care instructions, please click here to be redirected to our main website.
WARNING: CHOKING HAZARD – Small Parts Not Suitable for Children Under 3 Years (36 months)
Ages 9+ Adult Supervision and Instruction Required
UKCA/CE Certified EN-71 Tested. Meets US CPSC Safety Requirements
If you intend to buy this product for use outside the UK, EU or US, it is the your responsibility to check please check these standards comply and meet the specific requirements for your country.
Further information can be found on our website: https://oakfieldlearning.co.uk
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