Kapa haka festival

Kapa haka festival

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This task is about using ratios to answer questions.

  

At a kapa haka festival different rōpū performed and supported each other.
a)
In one rōpū the ratio of performers wearing red to performers wearing black was 3 : 5. There were 45 perfomers wearing black.
 
How many performers were wearing red?  __________
 
b)
In another rōpū, the ratio of performers to kaiawhina was 15 : 6. There were 35 performers.
 
How many kaiawhina were there?  __________
 
c)
A kapa haka rōpū were grouped into three sections: waiata, poi and haka, in the ratio 1 : 2 : 5. There were 40 poi performers.
 
 
i)
 
ii)
How many were singing the waita?  __________
 
How many were performing the haka? __________
 
d)
Another kapa haka rōpū were grouped into three sections: waiata, poi and haka, in the ratio 4 : 14 : 22. There were 33 haka performers.
 
 
i)
 
ii)
How many were singing the waiata? __________
 
How many were performing the poi? __________
 
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Keywords: 
Description of task: 
Students use given ratios to determine the number of people at the movies.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y10 (03/2004)

a)   27 moderate
b)   14 moderate
c) i)
ii)
20 and
100
moderate
(for both correct)
c) i)
ii)
6 and
21
difficult
(for both correct)
Diagnostic and formative information: 
 
Common error Likely calculation Likely misconception
a) 15 1/3 of 45   
a) 75 45 × 5/3 Inverts ratio.
a)
b)
c) i)
d) ii)
43
26
15
25
45 – (5 – 3)
35 – (15 – 6)
33 – (22 – 4)
33 – (22 – 14)
Assumes differences in ratios are equivalent to differences between absolute amounts, i.e., sees 3 : 5 as 43 : 45, 15 : 6 as 35 : 26, and
4 : 14 : 22 as 15 : 25 : 33.
c) ii) 200    Uses ratio 1 : 2 : 10.
c) ii) 50    Uses ratio 2 : 4 : 5.