Time to get to school
Key competencies
This resource involves interpreting a graph, and explaining why a person has a correct interpretation of the graph. This relates to the Key Competency: Using language, symbols and text.
Y7 (03/2010)  
a) 
Abby Statements that identify that most students take less than 30 minutes, for example: Only 3 take more than 30 minutes;

very difficult 
c) 
xaxis values should be numbers on a scale (continuous data), rather than intervals.

Distinguish between "most as mode" and "most as distribution".
Because Jason said that 8 people took the longest when Abby said 18 people.
Most children [take] 1019 minutes to get to school, but overall most children took less than 30 minutes to get to school.
Because 18 children took less than 30 minutes and 3 took 30+ minutes.
Because 18/21 came before 30 minutes.
Because 9 kids get to school in 09 minutes, 8 children took 1019 minutes and 3 took 2029 minutes so you then add then together and that makes most of the class.
Because she said most children took LESS than 30 minutes to get to school so that also includes the people who came in 09 mins and 1019 mins and 2029 minutes.
Looks at the "biggest chunk" of the distribution graphically.
Lots and lots of people made it to school under 30 minutes on the graph.
Because the graph says that the majority of the class took 030 mins to get to school.
Because there were only 3 people that took more than 30 minutes and all the rest took under 30 minutes.
Not much people came after 30 minutes.
 The big idea behind this question is the distribution of data. This is the shape that a graph of the data makes. Interpreting statistical graphics is far more than identifying specific features of a graph. Students should concentrate on what the graph is showing overall. In this case, students are asked to identify where most of the data lies, i.e. where "the biggest chunk of the data" is.
 Students need to move beyond identifying the mode of data. Students often interpret "most" as the single category with the greatest number of data points in it (i.e. the mode). Mode is better described as "most common" rather than "most". This looks at only a limited part of a graph and gives an idea where the middle of the data lies. It does not describe the overall shape and spread of the data. The word "most" does cause a tension in the meaning of the word. This is worth having a conversation about to stimulate thinking.
 This resource uses measurement data, which is sometimes known as continuous data. This means that the data (in this case time) can take on any value, not just whole numbers. For more information about, this click on the link, Types of data: Statistics.
These misconceptions indicate that the student is not yet performing at Year 7.
Common response  Likely misconception  
a) & b)  B  Jason 
Confuses mode with the distribution "largest part" of the data Visual comparison Because 1019 goes the highest. That bar is higher than the rest. Because 1019 has the biggest graph. I looked at the graph. Because I think the graph says that. Because the graph shows more on 10 to 19 minutes. Numerical comparison Correct comparison of the part to the whole for the mode only 
i) 
A  Nisha
C  Tim 
Assumes the bar that each of the four children are in is based upon the number stated by them in their speech bubble (e.g., Nisha takes 10 or fewer minutes, Jason takes 20 minutes, etc) Sees Nisha as taking least time or being closest to school On the graph most people took less than 10 mins to get to [school] and Nisha was the closest. (Student also misreads the graph) Because she made it the fastest. Because she was the person [who] took the least time to get to school. Because she was close. Because [s]he was on time for school. Other 
i)  A  Nisha 
Misreads the graph Because on the graph there is no one that took more than 10 minutes. Because the children did take less than 10 minutes. Cause on the graph it says 7 minutes and Nisha said less than 10min to get to school. (Confuses time and frequency) 
i) 
B  Jason E  All correct 
General stories about the students in the class Because he was the farsted [of] them. Because it has what time they had to be at school and Jason got there before everyone in room eight. Because some kids get to school late and early. 
These students need to see that "most" refers to all the children represented in the graph, not just the single category where most data is (the mode). Students need to see where the biggest chunk of the data is. Get them to put a circle around the part of the graph which has most of the data (i.e., 0 19, 029 or 039).
The student needs to see that while 1019 minutes is the most common range of times, that it contains well under half of the data.
There may be a need to have a discussion about the difference between "most" and "most common". "Most" talks about the overall shape or distribution, while "most common" is the idea of mode. Click on Mathematical classroom discourse for more on class discussions.
Assumes the bar that each of the four children are in is based upon the number stated by them in their speech bubble (e.g., Nisha takes 10 or fewer minutes, Jason takes 20 minutes, etc)
The students need to realise that each child in the question (Nisha, Jason etc.) is talking about the graph of the data and not about themselves. The most common explanation given is that Nisha is closer than the other children and will take less time. Once this is clarified, students should then attempt the question again.
Misreads the graph OR General stories about the students in the class
Either of these suggests that students cannot interpret the graph and most likely need significant work at constructing and interpreting graphs, in particular bar graphs on whole number data, as these are simpler than histograms. Use the keywords or click on the link graph interpretation OR graph construction.
Does not understand histograms
If the student does not understand histograms, then they need to be introduced to the idea, and then given simple histograms to construct. Use the keyword or click on the link, histograms. Histograms are very similar to bar graphs, but are used for measurement data, not discrete data.