The document discusses diagnostic tasks focused on counting and number sense education for young children, emphasizing the importance of various counting principles and activities. It outlines specific tasks and questions to assess children's counting skills while promoting the understanding of number quantities and sequencing. Additionally, it provides suggestions for future sessions aimed at enhancing mathematical knowledge through engaging activities.

1. Diagnostic task
discussion and
reflection
Tracey Armstrong
Sharon Lee
Swan View Primary School 2012

2. Focus Questions
1. Which student/s achieved the task?
Discuss the students that achieved or didn’t
achieve the checkpoints of your task.
2. What parts of the checkpoints did the child achieve
and what parts didn’t the child achieve?

3. Resource making

4. •Bead Sticks

5. HOW TO MAKE?
1. Put 4 groups of 5 beads on the stick. Each
group should be ONE colour.
2. Dip each end of stick into PVA glue and
push wall plug in.

6. Counting
Collections

7. Outcomes
1. The aim is to explore learning activities that
will help the children progress in their
understanding of developing a strong number
sense.
2. Providing a link between subitising
and partitioning and relating it to
counting collections.
3. Develop your own understanding of
Mathematical Knowledge the children
need to have.

8. What is counting?
In everyday use, to count has two meanings:
Counting can mean to recite whole number
names in the right order or it can also mean to
check a collection one by one in order to say how
many are in it.
The significance of counting is that it
enables us to decide how many are in a
collection or to make a collection of a given
size.

9. Why is the Concept of Counting Important for
Mathematical Foundations?
Young children initially need to learn to say the
counting number sequence and then learn to
connect the numbers in this sequence to the
quantity.

10. The Concept of Counting is an
Important Aspect to Develop a
Strong Number Sense.
To scaffold(build) young children's
mathematical knowledge they need to have
different experiences with subitising and
partitioning, counting collections, read, write
and saying numbers, all being interwoven.

11. Children Learn about Number as a
Representation of Quantity
Counting skills
Subitising
COUNTING
Use counting to get an amount
Choose to use counting to make
equivalent sets
Noticing the
ATTRIBUTE OF QUANTITY
Same/different more/less
PART-WHOLE
UNDERSTANDING
See groups within amounts
Add and subtract small amounts
SEE NUMBER AS A REPRESENTATION OF QUANTITY
Able to confidently break up numbers and rearrange the parts,
Knowing that the quantity has not changed

12. Focusing on the purpose for counting will help
students make sense of the counting process.
Children’s experience of counting games with adults
is often simply playful. So that means the quantity
of the numbers used in the games is not a focus.
Counting activities should always include a purpose
for the count.
What mathematics can you find in a story
book?
Birdsong by Ellie Sandall
Purpose for Counting

13. Counting Principle One
1. Each object to be counted must be
touched or „included‟ exactly once as the
numbers are said.

14. Birds and Nests
(One to one matching, oral counting)
1. One child chooses a number of nests and counts them
as they place them on the table.
2. Partner places a bird in each nest counting aloud as
they work.
FOCUS QUESTIONS
1.How can we find out how many there are?
2.What do I need to do when I count?
3.What is the first number I say?
4.Was the last number you and your partner said the
same?
LANGUAGE
How many? Last number, Next

15. Counting Principle Two
2. The numbers must be said once and
always in the conventional order.

16. Letters in my Name
(counting to find out how many, oral counting)
1. Write your name on the blank card
2. Each person takes a turn to stick a star above each
letter of their name, counting with the rest of the group
counting as they stick each star on.
3. Ask each child to say each sequence eg Linda, 5
letters, 1,2,3,4,5,
FOCUS QUESTIONS
1.Does anyone have 5 letters in their name?
2.Whose name has only 3 letters?
3.Who has more letters Claire or Jason?
4.Who has the most letters on their name card?
LANGUAGE
How many? More, Less, Same.

17. Counting Principle Three
3. The objects can be touched in any
order, and the starting point and order
in which the objects are counted does
not affect how many there are.

18. Row of Blocks
(counting to find out how many)
1. Start with a new collection of items and place in a
line.
2. Count the blocks but start in the middle.
FOCUS QUESTIONS
1.Can you count how many (blocks) and make this
one (pointing to the middle block) number one?
2.Can you count how many (blocks) and make this
one (pointing to the second last block) number one?
LANGUAGE
How many? start, each one.

19. Counting Principle Four
4. The arrangement of the objects does
not affect how many there are.

20. Eggs in the egg carton
•In pairs you need an egg carton, dice and blocks.
•One person rolls the dice and places that many blocks into
the egg carton counting as they drop each block.
•Other person changes the arrangement of blocks in their
partner’s egg carton and asks ‘how many now?’
•Swap over and repeat.
•Take turns in changing the arrangement in the egg carton
and ask ‘how many now?’
LANGUAGE
How many? One, two, three, four, counting, count, match
numbers

21. Counting Principle Five
5. The last number said tells “how
many” in the whole collection. It does
not describe the last object touched.

22. FISH OUT OF WATER (partner activity)
•Toss the die.
•Count your fish into the bowl.
•Partner then asks ‘So how many fish are there?’
•The partner says ‘Show me what 6 means?’
LANGUAGE
How many? show me, counting, number sequence, last
number, group, collection

23. 1. Each object to be counted must be touched or
„included‟ exactly once as the numbers are said
2. The numbers must be said once and always in the
conventional order
3. The objects can be touched in any order, and the
starting point and order in which the objects are
counted does not affect how many there are.
4. The arrangement of the objects does not affect how
many there are.
5. The last number said tells “how many” in the whole
collection. It does not describe the last object
touched.
5 Principles of Counting

25. • There is often no purpose in counting until a
task involves more than the children can
subitise.
• Overemphasis on counting can undermine
children‟s trust in their ability to subitise. In
other words a child who can subitise to 6 should
not be asked to recount collections of objects
up to 6 again and again.
• Students need to trust the count and, without
prompting, „choose‟ counting as a way of
solving problems.
Subitising and Counting

27. Connecting Number
Names, Numerals and Quantities
1. By the end of Pre-Primary, students should
establish understanding of the language and
processes of counting by naming numbers in
sequences, initially to and from 20, moving
from any starting point.
2. The focus of teaching needs to continue on
the same path but with larger quantities
moving up to 20 and then developing
knowledge to 100 items.

28. Skip Counting
Students who only learn to ‘skip count’ by
reciting, may not realise that skip counting tells
you ‘how many’.
Students will need a lot of practical experience in
order to see that pulling out 3 at a time and
counting by 3’s gives the same answer as counting
by 1’s.

29. GROUPING ACTIVITY
Focus : Invite students to rearrange a collection of things
to make them easier to count.
Can we rearrange ourselves so it is easier to count? (record count)
Is there another way? (record count) Is there another way? (record
count)
What do you notice about how many we get every time we count?
Why don’t we get a different number if we start with a different
person?
Which number tells us ‘how many’ we have?
What stays the same? What’s different?

30. CONSTANT ADDITION
In pairs, use the constant function on a calculator to
work out how many chair legs are in the room.
One person uses the calculator. The other person records the count.
1. Key in 1 + = for the first leg, then = for each remaining leg.
2. Repeat the count by 4s for each set of legs; press
4 + = for the first chair, then = = = for each other chair.
3. Record how many legs. Ask: Should we get the same result each
time? Why? Why not?

31. WHERE TO NEXT ?
1. Place Value
2. Diagnostic task to complete for the next session in Term 3 is ‘Counting to
Say How Many K-2’.
3. Using your bead stick think of an activity / game related to subitising,
partitioning or counting collections for the next session. Ideas you bring
will be collated and sent to your school after the next session.
4. Please fill in your Feedback Sheet.