: He Whakamäramatanga Pängarau
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Approach: One to one  
Focus:   Demonstrating understanding of number operations
Resources:  Ngä käri e 7, kia 25 ngä mataono rite
Kupu:
Questions/instructions: 
E whä aku pätai pängarau hei whakamärama mäu.
Whakatenatena i te äkonga ki te whakamahi i ngä mataono rite, ki te whakamärama
hoki i ana whakautu.
 
% responses
Whakaaturia ngä käri 1a me 1b.
4 + 2
  
2 + 4

1. He örite te otinga o te 2 täpiri i te 4, me te 4 täpiri i te 2? Whakamäramatia mai.
Whakamahia ngä mataono hei äwhina i tö whakamärama.

Pätai äwhina:
Whakamäramatia mai, he aha i pënä ai tö whakautu?
Whakamäramatia mai ö whakaaro.
 

same

100

any other response

0
Strategy:

only 6 cubes, conceptual
didn’t see the need to rearrange; argues that the number of blocks doesn’t change however they are arranged

13

only 6 cubes
rearranges order and argues that order doesn’t affect number of blocks

18

only 6 cubes
(rearranges order and focusses on answer (counts 6 each time))

47

12 cubes
(argues that they are mirror images (switched around), so are the same.)

16

12 cubes and counts 6 each time

7

doesn’t use cubes at all
argues clearly that if you had piles of 2 and 4 cubes the total would stay the same however the piles are organised.

0

doesn’t use cubes, physically or conceptually
says 2 + 4 = 6 and 4 + 2 = 6

0
Whakaaturia ngä käri 2a me 2b.
4 – 2
  
2 – 4
 

2. He örite te otinga o te 4 tangohia te 2, me te 2 tangohia te 4? Whakamäramatia mai. Whakamahia ngä mataono hei äwhina i tö whakamärama.

pätai äwhina:
Whakamäramatia mai, he aha i pënä ai tö whakautu?
Whakamäramatia mai ö whakaaro.
 

different

80

any other response

20
Strategy:

uses 4 cubes
(explains, without physically removing cubes; that you can take 2 from 4 but you can’t take 4 from 2)
9

uses 4 cubes
(shows that you have 2 left when you take 2 from 4, but that you cannot take 4 from 2 ( or -2))
58

uses 6 cubes
(sets out piles of 4 and 2; takes 2 away from pile of 4, leaving two; tries to take 4 away from pile of 2, can’t do it (or -2))
7

doesn’t use cubes at all
says that 4 - 2 is 2, while 2 - 4 is 2 (same)
4

doesn’t use cubes at all
says that 4 - 2 is 2, but 2 - 4 you can’t do (or -2)
2
Whakaaturia ngä käri 3a me 3b.
3 x 4
  
4 x 3
 

3. He örite te otinga o te 4 whakareatia ki te 3, me te 3 whakareatia ki te 4?
Whakamäramatia mai. Whakamahia ngä mataono hei äwhina i tö whakamärama.

pätai äwhina:
Whakamäramatia mai, he aha i pënä ai tö whakautu?
Whakamäramatia mai ö whakaaro.
 
same
95
Strategy:

uses 12 cubes
sets out 3 groups of 4 cubes; says that the same thing can be seen two ways: as 3 groups of 4 or as 4 groups of 3; therefore the same.
31

uses 12 cubes
sets out 3 groups of 4, rearranged into 4 groups of 3; says must be the same
36

uses 12 cubes
sets out 3 groups of 4 cubes; counts12; rearranges into 4 groups of 3 cubes, counts 12
7

uses 24 cubes
sets out 3 groups of 4 cubes; sets out another 12, in 4 groups of 3 cubes; shows number of blocks are the same
4

uses 24 cubes
sets out 3 groups of 4 cubes, counts 12; sets out another 12, in 4 groups of 3 cubes, counts 12
9

doesn’t use cubes
says 3 x 4 is 12; 4 x 3 is 12, therefore same.
0
Whakaaturia te käri 4.
2 – 4

Käore e whakamahia ngä mataono mö tënei o ngä pätai.
4. He aha tëtahi tau, mënä ka täpirihia atu ki te 8, ka tangohia ränei i te 8, ko te 8 tonu te otinga?
 

gives 0 (number used in addition or subtraction)

58
5. He aha tëtahi tau, mënä ka whakareatia te 8 ki taua tau, ka wehea ränei te 8 ki taua tau, ko te 8 tonu te otinga?
 

gives 1 (number used in multiplication or division)

53

Commentary:
 Overall, students performed very well in questions 1-3 of this task which required an understanding of how the commutative property applies to addition, subtraction and multiplication. Just over half of the students were successful in questions 4 and 5.

 
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