Starting with Dots! Louise Langford Numbers Count 2 Starting with Dots! Louise Langford

What is subitizing? Why is it important? Subitizing is the ability to say how many are in a set without counting e.g. recognising dice patterns. Most children can subitize up to 5 or 6 items. Some children cannot subitize e.g. Dyscalculics do not have this ability. Subitizing is an important maths skill as it allows children to recognise the number pattern as a composite of parts and as a whole. (Clements 1999) For example seeing 6 on a dice as; 3+3, Double 3, 4 and 2, 6… This develops both fluency and number sense.

Starting with dots! Dot patterns support the development of subitizing through providing children with a visual image of a number. Structured dot patterns allow children to see other numbers ‘hiding’ and therefore support the development of number facts. When using the dots as a mental image children begin to reason through counting, comparing and grouping. Dot activities develop strategies that support ‘numerosity’ and grouping to subitize larger numbers.

Different dot patterns. Dot patterns taken from ‘The Dyscalculia Solution’ By Jane Emerson and Patricia Babtie

Dot patterns taken from ‘The trouble with maths’ by Steve Chinn.

Examples of ‘Ten frames.’

Variety of dot patterns.

What can you see?

Give children experience of making the dot patterns themselves using counters.

Multi sensory approach. Make feely dot cards. Finger paint dot cards. Draw the pattern as you hear them drop. Flip cards.

Link to addition and subtraction facts One more/one less. Hide some, what can you see? Triads. Visualise. Missing number problems. Problem solving e.g. ladybirds. Each ladybird has 9 spots. How many different Patterns of spots can you find?

Link to other linear concrete images. Bead string. Cuisenaire. Number track. Number line.

Link to abstract.

Doubles Start with dot patterns, double them, use dominoes, counters, make butterflies! Link the dot patterns to a linear image. Line up counters/beads to show doubles in a row. Link to squares on paper, reinforce using Cuisenaire rods.

Near Doubles Using two coloured counters line up a row of 4 red and below a row of 5 yellow. Can they see the double hiding? Turn over the counters to show double 4 and 5 as one more than 4. Make it explicit that 5 is one more than 4 so 4+5 is double 4 plus one more. Explore more near doubles with Cuisenaire. This same strategy can be used to teach double and one less. 4 is one less than 5 (demonstrate using the two coloured counters,) so 4+5 is double 5 minus one.

Multiplication facts. Use a multiplication mat (Emmerson and Babtie 2014) to keep adding the same number to build up multiplication facts using dot patterns. Use counters, potato printing, pebbles in the sand…

Other ideas for activities involving dots. Dominoes. More problem solving e.g. Seven spots. Dice games. Link dot patterns to linear dot patterns, beadstrings and number tracks. Link dots to ‘ten’ frame activities.

Dots and calculation. Dot patterns can support children with calculation by giving them strong visual images to connect maths facts and develop fluency. Double 4 pattern is 8. If you add one more to make the pattern of 4 and 5 you have 9. If you subtract one to make the pattern of 4 and 3 you have 7. When totalling two numbers such as 7 and 8 dot patterns help a child ‘see’ this as (5+2) + (5+3) so 5+5=10 and 2+3=5 so 10+5=15. Totalling three numbers. Using dots bonds for 10 can be identified to support calculation e.g. 3+5+7= so 7+3=10 then add 5 equals 15. Dots support the relationship between addition and subtraction facts and help secure the concept of ‘inverse.’

Dot patterns can be rearranged to support the development of other areas of calculation. Linear dots support children to visualise ‘Bridge through ten’ either subtracting or adding. This links in well with the beadstrings. Linear dots can be used to look at all areas of subtraction through taking away, comparing, equalising and finding the difference. This links in to number tracks and then number lines. Arrays can be made from dots to introduce and explore multiplication and division.

Starting with dots! Dots in a variety of patterns are a memorable image to support children’s thinking. Once the dot patterns are established children start to manipulate numbers by ‘visualising’ or drawing the patterns to support number work. Dot patterns can then be linked to linear images such as beadstrings, Cuisenaire and number tracks or lines. Dots are not the only answer in supporting children to learn but they are certainly a good start!

References: Chinn, S. (2012) The trouble with maths. 2nd edition. Abingdon: Routledge. Clements, D. (1999) Teaching children mathematics; Subitizing What is it? Why teach it? Emerson, J and Babtie, P. (2014) The Dyscalculia Solution foreword by Butterworth. Croydon: Bloomsbury Education.