Consecutive Numbers
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Approach:  One to one
ACCESS
Level: Year 8
Focus: Patterns, relationships, generalisations; verifying and proving  
Resources:
Card, calculator, recording book
213kb
Questions/instructions:  

Consecutive numbers are numbers that follow each other in order, like 1, 2, 3 or 9, 10, 11.
Hand student the Consecutive Numbers card.
Here is a card showing some sums with three consecutive numbers. Some people say that to add three consecutive numbers, you multiply the middle number by 3.
Hand out recording book, pencil, calculator.
Some people say that to add three consecutive numbers, you multiply the middle number by 3.
9 + 10 + 11 = 30
19 + 20 + 21 = 60
99 + 100 + 101 = 300
 
% responses
2009 ('05)
y4
y8
1. Do you think this would always happen? yes   73 (68)
  no   27 (32)
2. Explain to me why you think that. generalisation   10 (13)
(middle number is always 1 less than biggest number and 1 more than smallest number, so multiplying the middle number by 3 will always give the same result as adding all three numbers together) some explanation using one or more    
examples to justify   13 (11)
some verification (e.g. written/oral) but not clear   36 (34)
mathematical error justifying “no” as response to question 1   7 (15)

Total score:
 4
  10 (13)
3
  13 (11)
2
  36 (34)
1
  15 (11)
0  
26 (31)
Subgroup Analysis [Click on charts to enlarge] :
Year 8
Commentary:
While about three quarters of the year 8 students agreed that the sum of three consecutive whole numbers will always be the same as three times the middle number, only about one quarter could clearly explain why they gave that answer. On average, Pasifika students scored substantially lower than Pakeha and Mäori students.