Counting with understanding up to 6
ES1 – A thinking mathematically context for practise focussed on deepening understanding of numbers by connecting quantities to language and symbols
Syllabus
Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023
Outcomes
- MAO-WM-01
- MAE-RWN-01
- MAE-RWN-02
- MAE-CSQ-01
- MAE-CSQ-02
Collect resources
You will need:
some pegs or paper clips
numeral cards. You can make these using sticky-notes and a marker.
pencils or markers
your mathematics workbook.
Watch
Watch Counting with understanding up to 6 part 1 video (1:29).
Michelle
Welcome back mathematicians. I’m here with my one of my most favourite little mathematicians today, Holly. Hi Holly.
Holly
Hi!
Michelle
Are you ready to do some maths with me?
[Screen shows one bag of coloured pegs and a set of white cards.]
Holly
Yeah.
Michelle
Excellent, so we have got some pegs here and some cards and can you turn this card over for me?
What number is that?
[Michelle points to coloured pegs and white cards. Holly turns over the first card in the pile which has 6 written on it.]
Holly
6.
Michelle
And then can you use these pegs to attach six pegs onto the cards? Yeah, I'll let you start.
[Michelle attaches one peg to the card, then removes it and empties the bag of pegs onto the floor. Holly starts attaching the pegs to the card.]
Holly
I am going to do it in a pattern.
Michelle
Ok.
[Holly attaches the pegs to one side of the card, one blue, one red, one white, one blue, one red, one white, totalling 6 pegs in a coloured pattern.]
Holly
It got so heavy.
Michelle
It is heavy. Can you prove to me or how do you know that is 6?
[Michelle points to the card and pegs with her finger.]
Holly
Because I lost track and I thought is that 6? So, I counted in my head, I was like 1, 2, 3... and you can even do it in twos like 2, 4, 6.
[Holly points and counts 2 pegs at a time.]
Michelle
Cool. You also said Holly, that you wanted to do it in a pattern, so can you show me where the pattern is that you made?
Holly
Well, I did blue, red, white, blue, red, white. And I did it in threes. See 3 plus 3 equals 6.
[Holly points to the coloured pegs indicating the pattern, one blue peg, one red peg and one white peg, then one blue peg, one red peg and one white peg. Holly then counts the pegs 3 at a time.]
Michelle
OK, let's try the next number. What about this one?
[Michelle moves the card with the number 6 to a new pile on the right and turns over the next card with the number 2.]
Holly
2.
[Holly pegs a red peg, then a blue peg to the card.]
Michelle
OK, and what about the next one?
[Michelle moves the card with the number 2 to the pile and turns over the next card with the number 0.]
Holly
0 so that means any.
Michelle
No pegs?
[Michelle moves the card with the number 0 to the pile.]
What about this number?
[Michelle turns over the next card with the number 1.]
Holly
It's 1.
[Holly pegs a red peg to the card. Michelle moves the card to the pile.]
Michelle
And what about this number here, Holly?
[Michelle turns over the next card with the number 3.]
Holly
Three. 1, 2, 3.
[Holly pegs a red peg, a blue peg and a white peg to the card and puts the card on the pile.]
Michelle
What about this number?
[Michelle turns over the next card with the number 5.]
Holly
5. 1, 2 ...
[Holly counts out 5 pegs. Holly pegs 2 blue pegs and 3 red pegs to the card and puts the card on the pile.]
Michelle
OK, and this is the last one. What about this number Holly? What's that number?
[Michelle turns over the last card with the number 4.]
Holly
4.
Michelle
OK, can you put that many pegs on there?
[Holly pegs 4 pegs to the card in a red, blue, red, blue pattern and puts the card on the pile.]
And we don't need these pegs so I'm going to move them out of the way.
[Michelle pushes unused pegs to the side. and spreads out the cards with pegs attached to them.]
And then Holly I was wondering if you could.
Now we've got all these numbers here, with the pegs on there. Could you order them for me from the smallest number over here to the biggest number over here?
[Michelle points to Holly’s left when she says the ‘smallest number over here’ and Holly’s right when she says the ‘biggest number over here’.]
Holly
That's the biggest number.
[Holly moves the card with the number 6 to the right.]
Michelle
Which is that one?
Holly
6. This one goes here.
[Holly moves the cards with the numbers 3, 4, and 5 into order from left to right and then moves cards with the numbers 0, 1 and 2 to the left, showing 0 to 6 in order from left to right.]
[Screen reads: You might also like to ask some other questions ...]
[Michelle takes away the card with the number 3.]
Michelle
What number is missing?
Holly
3.
Michelle
How do you know?
Holly
Because 1, 2. It goes 0, 1, 2 but it wouldn't go 4, 5, 6. So it has to go 3, but there’s no 3.
[Holly points to cards with the numbers 0, 1, 2, then 4, 5 and 6, demonstrating 3 is missing. She then points to the space where the card with the number 3 was.]
Michelle
So, if I put the 3 back.
[Michelle places the card with the number 3 back in place.]
Close your eyes again now for me, Holly.
[Michelle takes away the cards with the numbers 2 and 4.]
What about now? What's missing?
Holly
4 and 2.
Michelle
How do you know?
Holly
1, look. 0, 1, look 3 and 5, 6. it has to be 0, 1 and then 2 but there's no 2 and then it has to go, 3, 4 but there's no 4.
[Holly points at 0, 1, 3, 5 and 6. She then points to the spaces where the cards with the numbers 2 and 4 were.]
Michelle
Oh aha.
[End of transcript]
Watch
Watch Counting with understanding up to 6 part 2 video (5:39).
[Screen shows 5 white cards with numbers on them. From left to right, the cards are numbered 0, 1, 3, 5 and 6. The cards numbered 1, 3, 5 and 6 have the matching number of pegs attached. The cards numbered 2 and 4 are missing.]
Michelle
What about now? What's missing?
Holly
4 and 2.
Michelle
How do you know?
Holly
one...
1, look. 0, 1, look 3 and 5, 6. it has to be 0, 1 and it has to go 2 but there's no 2 and then it has to go, 3, 4 but there's no 4.
[ Holly points to the numbers 0 and 1, then to the empty space where 2 should be, then to the number 3, and then to the empty space where 4 should be.
Michelle
So, the numbers have to go in order.
Is that right? OK and maybe.
[Michelle places 4 and 2 in the wrong order.]
Is that right now?
Holly
No, it doesn't go 0, 1, 4, 3, 2, 5, 6.
[Holly points to cards.]
Michelle
How does it go?
[Holly puts 2 and 4 in the correct order.]
Every time.
Holly
Yes. So, for example, if this was me.
I'd go like, so this goes here and that goes here. I'm done. And that goes 0, 1, 6, 4, 3, 5, 2. Not how it goes. They need to go in their exact same spot.
[Holly moves cards around while she is talking, putting cards in the wrong order of zero, one, 6, 4, 3, 5, 2. Holly then puts the cards in the correct order.]
Michelle
And that's the right order? We always count in the same order, is that right?
Holly
Uhuh
[End of transcript]
Watch
Watch Counting with understanding up to 6 part 3 video (1:52).
[Screen shows 4 white cards with numbers on them. From left to right, the cards are numbered 3, 4, 5 and 6. Each card has the matching number of pegs attached.]
Michelle
I have one other question for you Holly. Let's look at…. So, let's choose the number 5. Are you still 5?
[Michelle removes all the cards except the card with the number 5.]
Holly
Yes
Michelle
So, let's choose the number 5 because it's the same age as you. So how many pegs are on that card Holly?
Holly
5.
[Holly picks up the card with the number 5.]
Michelle
And what happens now, may I have the card, is it OK?
[Holly puts the card with the number 5 back].
What happens if I like spread them out like this? Do you need to count them again?
[Michelle spreads the pegs out on the card.]
Holly
No.
Michelle
How many are there?
Holly
There's still 5.
Michelle
What if I move this on this side?
[Michelle moves one red peg from the right side of the card and pegs it on the left side of the card.]
How many pegs are on the card?
Holly
There's still 5.
Michelle
What if I go like this?
[Michelle moves a white peg from the right side of the card and pegs it on the left side of the card.]
Holly
Still 5.
Michelle
What if I change this white peg for this clip? How many things are still attached to the card?
[Michelle removes the white peg on the left side of the card and replaces it with a small clip.]
Holly
5.
Michelle
So, are you saying to me Holly that it doesn't matter if they are really close together, or really spread out, or even on one side and the other side, it's still 5?
[Michelle moves the red peg from the left side of the card back to the right side of the card, and picks up the white peg and puts it on the right side of the card, so there are 5 pegs on the right side of the card. Michelle removes the small clip from the left side of the card and spreads the pegs out on the right side of the card. Michelle then takes one red peg from the right side of the card and pegs it to the left side of the card.]
Holly
Yeah.
Michelle
Even if I swapped one peg for a clip, I still have five things attached.
[Michelle removes the red peg from the left side of the card and adds one small clip instead.]
Holly
Yeah look. I'll show you.
Michelle
Show me.
Holly
When they're all spread out, see 1, 2, 3, 4, 5. And when they're on the other side... 1, 2, 3, 4, 5.
[Holly counts the 4 pegs on one side of the card and one small clip on the other side. She then moves one peg to the other side so it is beside the clip.
Michelle
And so, 5 doesn't, say. You know how you counted 1, 2, 3, 4, 5? Five doesn't tell me that this peg's name is 5 like your name is Holly or my name is Michelle. The five says this is how many things are here.
[Michelle points and counts each peg. She holds one peg when talking about names. Michelle then points to the five pegs when talking about how many things are on the card.]
Holly
Yeah.
Michelle
Oh, so it doesn't matter if I go 1, 2, 3, 4, 5, 1, 2, 3, 4, 5 or change these.
[Michelle counts the three pegs on the right side of the card and then the peg and small clip on the left side of the card, then counts back. Michelle removes one peg from the left side of the card and puts a spare peg in its place.]
It's just about how many things are attached. Is that right?
Holly
Yes!
Michelle
Thanks, Holly.
Holly
Bye bye.
Michelle
See you.
[End of transcript]
Instructions
Use a set of number cards within an appropriate number range. For this example, we are using 0-6.
Shuffle the cards.
Turn one card over at a time and read the numeral.
Match the number of pegs (or some other item) with the numeral card.
Order the cards from smallest to biggest, or, biggest to smallest.
Close your eyes as someone at home removes one of your cards.
- Which card is missing?
- How did you work out?
- Another way to play: use cards that have a numeral and matching dot pattern so you can attach one peg for each dot.
Reflection
What do you need to remember when counting?
Share/Submit
Share your work with your class on your digital platform. You may like to:
share your responses to the reflection questions
write comments
share pictures of your work
comment on the work of others.
Advice for parents
Choose one card, for example 5.
Ask your child how many pegs are on the card in order to establish and confirm that there are 5.
Support your child’s understanding of conservation by spreading the pegs out, bringing them in close together and swapping 1 peg for a clip.
Encourage them to use reasoning to determine that there are still 5 things in the collection even if they are close together or far apart, or, when one thing is swapped for another.