Colour of lunch boxes
Y4 (06/2009)  
a) b) 
D and
Any 1 of:
[Do not give credit if the student responds with D but reasons"A, B, and C are correct, so D must be wrong."] 
Both correct  very difficult 
 Because … there were 9 in that column and 17 in the other columns.
 Because I added the dots and colours [of the lunch boxes and these] had more than people with no lunch boxes.
 Because 5, 6, 4 and 2 add up to more than 9
 Because there are 26 children in the class and half of 26 is 13 and only 9 children had no lunch box.
 Because I counted the number of coloured boxes and I counted the number of people that hadn't bring (sic) their lunch box and the numbers weren't equal.
 ... because I counted no lunch boxes, then I counted green, yellow, blue, and red and there were more lunch boxes.
 Because if you stacked up all the other colours but no lunch box the colour would be taller.
Common error  Likely misconception  
a) 
Emma
All correct 
Confuses "Most common" with "More than half"
Sees "No lunch boxes" as the most common, rather than blue or that blue is the second most common colour.
Sees that blue as the most common colour (a correct conclusion), but then thinks that "No Lunch Boxes" is more than half because it is the most common frequency. 
a)
b)

Noah and "Emma, Jack, and Maya correct so D must give an incorrect statement." 
Difficulty finding a half & the sample size from graph
Uses the information on the individual bars of the graph for Emma, Jack, and Maya, but not for Noah.

a)
b)

Noah Any 1 of

Cannot write down their reasoning
The student may be able to correctly select Noah, but cannot write down a reason.

 You could ask "What colour is more common that blue?" Students may respond "No lunch box." You could then respond "What colour is that?"
 You could ask "Which is more common, having a lunch box, or not having a lunch box?" This can be done visually (estimating), or by counting.
 Students may then need to explore if Noah is correct or not. This needs them to understand "half" and how to find the sample size on a dot plot.
Difficulty finding a half & the sample size from graph
 Ask the student(s) "How many students were in the class?"
If they cannot do this, then they will need experience in constructing and understanding dot plots. Click on the link or use the keyword, dot plots.
 If they can answer the question (i.e., "There are 26 students), then ask them:
 "How many have lunch boxes?" or "How many do not have lunch boxes?" "Is this more than half?" or "Is this less than half?"If they cannot answer this, then they need to work on recognising fractions greater than or less than a half.