Pre-Calculation: Counting
Learning Objectives
By the end of the session students will:
 recognise the developmental stages in
learning to count;
 relate EYFS curriculum to appropriate
learning activities for children;
 be familiar with approaches to counting;
 be aware that recording (numerals) with
young children should be within a meaningful
context (including mark-making).
What is Number?
Numbers in Everyday Life – at
home…..
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Counting
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Labelling
Counting Principles
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The one-one principle: There is a distinct counting
word to match each of the items counted.
The stable-order principle: The list of words must
be consistent.
The cardinal principle: The final word tells us how
many there are in the number of items counted.
The abstraction principle: You can count any
collection of objects whether real or imaginary.
The order irrelevance principle. It doesn’t
matter what order you count in as long as you count
each object only once you will get the same result.
 Gelman & Gallistel (1978)
How do children
learn to count?
Writing Numbers
From: DFES (2008)
Mark Making
Matters London:
DFES Publications
Matthew (3 years, 1 month)
He knows that marks carry meaning and they can sometimes represent
numbers. He also knows that you write numbers down.)
Recognising Numerals
Mathematic Vocabulary for Reception
number
zero, one, two, three... to twenty and
beyond
zero, ten, twenty... one hundred
none
how many...?
count, count (up) to
count on (from, to)
count back (from, to)
count in ones, twos... tens...
more, less, many, few
odd, even
every other
how many times?
pattern, pair
guess how many, estimate
nearly, close to, about the same as
just over, just under
too many, too few, enough, not enough
the same number as, as many
as
Of two objects/amounts:
greater, more, larger, bigger
less, fewer, smaller
Of three or more
objects/amounts:
greatest, most, biggest, largest
least, fewest, smallest
one more, ten more
one less, ten less
compare
order
size
first, second, third... tenth
last, last but one
before, after
next
between
above, below
Early Years Foundation Stage Curriculum
Specific Area: Mathematics
Early Learning Goals: Numbers
Children count reliably with numbers from 1 to 20,
place them in order and say which number is one
more or one less than a given number.
Using quantities and objects, they add and subtract
two single-digit numbers and count on or back to
find the answer.
They solve problems, including doubling, halving and
sharing.
EYFS Non statutory guidance observation
prompts for 40 – 60 months
Recognise some numerals of personal significance.
 Recognises numerals 1 to 5.
 Counts up to three or four objects by saying one number
name for each item.
 Counts actions or objects which cannot be moved.
 Counts objects to 10, and beginning to count beyond 10.
 Counts out up to six objects from a larger group.
 Selects the correct numeral to represent 1 to 5, then 1 to 10
objects.
 Counts an irregular arrangement of up to ten objects
 Estimates how many objects they can see and checks by
counting them.
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Cont ..
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Uses the language of ‘more’ and ‘fewer’ to compare two sets of
objects.
Finds the total number of items in two groups by counting all of them.
Says the number that is one more than a given number.
Finds one more or one less from a group of up to five objects, then
ten objects.
In practical activities and discussion, beginning to use the vocabulary
involved in adding and subtracting.
Begins to identify own mathematical problems based on own interests
and fascinations.
Records, using marks that they can interpret and explain.
How can we support
children’s counting
development?
Let’s play
some games.
Numbers and Patterns
The National Strategies Primary
Other activities
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List any nursery songs / rhymes which
you believe encourage the development
of counting strategies
Are some more difficult than others?
What is the best way to model them
with children?
Common Counting Errors
There are common errors that young children may
make when counting one-to-one:
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Touching an item to be counted more than once
so that it is counted twice:
Missing an item altogether;
Repeating a counting name;
Missing out counting names;
Using the wrong number name eg. confusing
fourteen and forty;
Failing to co-ordinate the touch and count.
Counting Errors: Hannah
Hannah
How any altogether?
8
Hannah - Diagnosis
She may have:
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Missed out some strawberries
Repeated a number name;
Not co-ordinated the touch and count
Teaching Points
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Recite the number names to 20 in unison with others;
Count aloud in one-to-one correspondence with hand claps;
Count while pointing to a number line labelled 0, 1, 2, 3, 4 …;
Count objects systematically, eg point one by one from top to
bottom, left to right.
Progression: NC 2014 Year 1:
Programme of Study
NUMBER: Number and place value
Pupils should be taught to:
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Count to and across 100, forwards and backwards,
beginning with 0 or 1, or from any given number
Count, read and write numbers to 100 in numerals, count in
different multiples including ones, twos, fives and tens,
Given a number, identify one more and one less
Identify and represent numbers using concrete objects and
pictorial representations including numberline and use the
language of: equal to, more than, less than (fewer), most,
least
Read and write numbers from 1 to 20 in digits and words
Because of Number One….Pam Gidney
I’ll tell you something funny –
The strangest thing under the sun.
There’s never an end to numbers,
Because of Number One.
You reach a thousand? Number One
Insists on going on.
You’re all worn out. A million comes:
But there’s still “A million-and-one.”
You think you’re clever when you count to twenty
–
The person who caused all this trouble
But then there’s twenty-one.
(When I could be out having fun)
So on you go, and thirty comes - Is the man who lived in the dim distant past
And then comes thirty-one!
And invented Number One
You reach a hundred! Then you think
That all your counting’s done.
But no! A little voice inside
Says, “Now a hundred-and-one.”