How students come into school

Three dimensions of mathematical understanding

True Counting Vs Rote counting

Most kids learn through rote - memorisation

Principals about how to count

= Principals about how to count

= principals about what can be counted

Try counting in a rectangle - do they know when to stop or do they keep counting around the shape

Change from always being in a line

Vary the way you arrange counters

Helps with learning when to stop - I’ve counted the set now I need to stop

How many XX are in this picture

Number lines that don’t start at zero - zero being last concept to be taught

Subitising

1-4 instantly see no matter what arrangement it has

Above or seeing the pattern quazi subitising is above only see it if it’s in pattern otherwise can’t see it

Digits and numbers

Ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Numbers can be made up of more than one digit

Hundreds board can cause issues with realising 10 is two digits

Number charts

Knowing that once they’ve counted they don’t have to count again

Tagging with mats

Looking at where it moves within the sets is it part of the set are the sets the same?

Using set lines for different counting

Ensuring that students know that 5 means the whole set not just the tag at the end

Different sets of things to count

Order of counting is irrelevant being able to count from any counter not just in a line

Last digit to be taught 0

Compensation

Being able to see the equals sign

Knowing that part whole can be done with any number

Knowing what to do with broken numbers when adding by circling the whole set and left to add is the rest

Knowing when subtracting that I subtract 3 to get 10 and then I need to subtract 4

13-7

Place value

Ensuring children understand ten more ten less and by colour coding students can see the digit follow through

Do they have visual spatial awareness

Counting assessment tool