Hei Tūhura i ngā Kaupapa Tau

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Te Kaupae Ako
He Tauira Whakawhitiwhiti Kōrero
Tatau Pitomata
(Pre-counting) 
Use whatever items the children are playing with to compare the size of sets without counting. Sometimes children will be able to compare sets by looking at them, but where the sets have a similar number of items they will need to pair items to find out which set has more.
 
Which has more/fewer? Why do you think that?
He maha ake ēnei i ēnā, kāore rānei?
He aha i pēnā ai ō whakaaro? Whakamāramatia mai.
Ko tēhea te taraka he maha rawa atu ngā wīra?
Ko tēhea te whare he ruarua noa iho ngā matapihi?
 
Who has more/fewer? How do you know?
He maha ake ngā motukā o Hīria i ō Matiu, he ruarua ake rānei?
He aha koe i mōhio ai?
Kei a wai te maha rawa o ngā taonga?
 
Are there enough? Tell me more.
He rahi rawa ngā āporo mā tātou?
Hoatu he kapu mā tēnā, mā tēnā o tātou. He rahi rawa?
 
Can you make sets that are more/fewer/same as Jamie's?
Can you find sets that are more/fewer/same as Anna's?
Tīkina ētahi poraka, kia ōrite/nui ake/iti iho te maha i ā Hēmi.
Hangaia he rōpū poraka, kia ōrite/nui ake/iti iho te maha i ā Ana.
 
Follow the comparisons with questions that ask children to describe their thinking:
 
How do you know?
He aha koe i mōhio ai?
 
Why do you think that?
He aha i pēnā ai ō whakaaro?
 
Tell me about that.
Whakamāramatia mai.
 
Are you sure?
Kei te tika tēnā?
 
How could you check?
Me āta tirotiro.
Me pēhea e āta tirotiro ai?
 
Watch for:
Are the children able to identify which set has more/less by looking at the two sets? Can they match the items from two sets to see which has more/fewer? Note they do not need to be able to say how many there are to do this successfully.
Tatau Pānga Tahi
(One-to-one counting)
As appropriate contexts arise, ask children to form a set of a certain number of items. Start with small sets of up to five items.
 
I see you have some animals. Can you find 3 bears?
Ka rawe ō kararehe. Kimihia kia toru ngā pea. Homai kia rua ngā hipi.
 
Isn't that an interesting picture. Can you see 2 frogs?
Ka mau te wehi o tēnā pikitia. E kite ana koe i ētahi poraka e rua? Kei hea ngā hōiho e toru?
 
What a lot of crayons you have. Can you pick up 6 crayons each?
Te maha hoki o ngā pene hinu. Tangohia kia ono.
Tangohia kia whā ngā pene hinu mā tēnā, mā tēnā o koutou.
 
Aren't they pretty flowers. Who can find me 4 of them?
Kātahi te ātaahua o ngā putiputi. Homai kia whā māku.
Mā wai e whakarite kia toru ngā putiputi ki tēnei ipu?
 
What sticky fingers you have. Can you show me three fingers?
Te hāpiapia hoki o ō matimati. Whakaaturia mai kia toru.
Whakatūria kia whā ngā matimati i tō ringa mauī.
As opportunities present themselves ask children to count the number of items in a set.
 
What a lovely tea party you have set up. How many cups do you have?
Te rawe hoki o te tēpu. E hia ngā kapu?
 
Thanks for bringing in some apples to share. Can you count the apples?
Kei a koe mō te hari āporo mai e Hine. Tatauria ngā āporo.
Mā wai e tatau ngā āporo?
 
What a great red hat you have on. How many people are wearing hats today?
Kātahi te pōtae pai e Tama. Tokohia e mau pōtae ana i tēnei rā?
 
Follow up counting with questions that ask children to describe their thinking:
How do you know?
He aha koe i mōhio ai?
 
Why do you think that?
He aha i pēnā ai ō whakaaro?
 
Tell me about that.
Whakamāramatia mai.
 
Are you sure?
Kei te tika tēnā?
 
How could you check?
Me āta tirotiro.
Me pēhea e āta tirotiro ai?
Practice the counting sequence from any number, both forwards and backwards.
 
Let’s start counting from 5. “5, 6, 7, 8 …”
Me tatau ake i te rima, “rima, ono, whitu, waru ...”
Tīmata i te toru ka tatau ake, “toru, whā, rima, ono ...”
 
Let’s count down from 5 before the rocket blasts off “5, 4, 3, 2, 1, blast off!”
Tatau iho i te rima i mua i te pahūtanga o te waka tuarangi, “rima, whā, toru, rua, tahi, pahū!”
 
Watch for:
When children are counting do they say the standard list of counting words in order? Which parts of the sequence do they know? Which parts do they need help with?
When children are counting do they match each spoken number with one object? Do they move more than one object for spoken number? How do they coordinate spoken numbers with objects when counting?
Tatau Huinga
(Counting sets)
Use opportunites that arise in play to ask children to count the number of items in sets. Focus on the total number of items.
 
Matching sets activities, such as:
There are 3 teddy bears, how many porridge bowls will we need?  
E toru ngā tetipea. Nō reira kia hia ngā perēti mā rātou?
 
There are 6 paint pots, how many brushes will we need?
E ono ngā ipu peita, nō reira kia hia ngā paraihe (tētahi mā ia ipu peita)?
 
There are 5 cars, how many drivers will we need?
E rima ngā motukā, nō reira kia hia ngā taraiwa?
Encourage children to use numbers to compare sets rather than matching items one to one. Extend their thinking with questions such as:
How do you know you have the right number?
He aha koe i mōhio ai koinā te tau tika?
 
How many have you got?  
E hia ngā poraka?
E hia kei a koe? E hia kei a Hinewai?
 
How many more do you need?
Kia hia atu anō māu?
Kia hia atu anō māu kia rite ki ā Tamanui?
 
Follow up counting with questions that ask children to describe their thinking:
How do you know?
He aha koe i mōhio ai?
 
Why do you think that?
He aha i pēnā ai ō whakaaro?
 
Tell me about that.
Whakamāramatia mai.
 
Are you sure?
Kei te tika tēnā?
 
How could you check?
Me āta tirotiro.
Me pēhea e āta tirotiro ai?
Develop children’s awareness of numerals around them, for example on the clock or the calendar:
What number is this?
He aha tēnei tau?
 
How could we write the number 3?
Me pēhea te tuhi i te toru?
 
Other numbers to use include those on posters, dates of birth, birthday charts, sign-in sheets, books, puzzles, profile books, games, snakes and ladders, cards.
 
Watch for:
Do children need to recount to tell you how many are in a set? For example “Can you count these teddies for me?” then after they have counted “how many teddies are there?”
Do children need to match one to one to make sets of the same size or can they use numbers to make the comparison?
Tatau ake i te kotahi hei whakaoti rapanga tau
(Counting from one to solve number problems)
Use everyday situations which involve joining and separating sets to develop children's ability to count to solve number problems. For example:
 
How many cups are on the table? How many cups are on the tray? How many cups are there altogether? Let’s count to find out.
E hia ngā kapu kei te tēpu? E hia ngā kapu kei te paepae? E hia ngā kapu katoa? Tatauria e tātou.
 
How many jackets are hanging up? If 2 children put their jackets on how many will be left hanging up? Let’s count to find out.
E hia ngā koti e iri ana? Mēnā ka kuhu a Hana rāua ko Tīpene i ō rāua koti, ka hia e iri tonu ana? Tatauria e tātou hei whiriwhiri.
 
Follow up counting with questions that ask children to describe their thinking:
How do you know?
He aha koe i mōhio ai?
 
Why do you think that?
He aha i pēnā ai ō whakaaro?
 
Tell me about that.
Whakamāramatia mai.
 
Are you sure?
Kei te tika tēnā?
 
How could you check?
Me āta tirotiro.
Me pēhea e āta tirotiro ai?
 
Watch for:
Do children use counting to solve everyday number problems? Can they reliably produce an accurate result?
Tatau ake hei whakaoti rapanga tau
(Counting on to solve number problems)
Incorporate counting into children’s play. Encourage children not to count the first set of items but to count on or back from the largest number to solve number problems. For example:
 
There are five animals in this pen and the farmer adds three more sheep. Let’s count how many we have altogether as we put them in.
E rima ngā kararehe kei te pātiki. Mēnā e toru atu anō ka tāpirihia atu, e hia katoa ngā hipi? Tatauria i a tātou e tuku atu ana i ngā hipi ki roto i te pātiki.
 
There are 7 trucks on the road but these 2 pull over to park. How many trucks are left on the road? Let’s count to find out.
E whitu ngā taraka i te huarahi e haere ana. E rua ka tū ki rahaki. E hia ngā taraka ināianei e haere tonu ana?
 
Ask follow up questions which encourage children to describe their thinking:
Why did we start from 5?
He aha i tīmata ai i te rima?
 
How do you know?
He aha koe i mōhio ai?
 
Why do you think that?
He aha i pēnā ai ō whakaaro?
 
Tell me about that.
Whakamāramatia mai.
 
Are you sure?
Kei te tika tēnā?
 
How could you check?
Me āta tirotiro.
Me pēhea e āta tirotiro ai?
 
Watch for:
Do children start their counting from one, or can they count on or back from the largest number?