Time to get to school

Time to get to school

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about reading information from a graph.

Question

Time children took to get to school
 
This graph shows the time it took the children in Room 8 to get to school one day. 
a) Which person made a correct statement about the graph?

    • Nisha

    • Jason

    • Tim

    • Abby

    • They all made correct statements

b) Explain why you decided on your answer.

Question 2Change answer

c)  What is one problem with the way this histogram has been set up?
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto-marking).
Level:
4
Curriculum info: 
Maths, Statistics, Statistical literacy
Key Competencies: 
Using language, symbols, and texts
Keywords: 
graph interpretation, distribution, histograms, work samples
Description of task: 
Students identify a correct statement about the overall distribution of a graph and explain their reasoning.
Curriculum Links: 
This resource can be used to help to identify students' understanding of identifying correct and incorrect statements about a data display. It uses the concept of distribution, which relates to "identifying patterns (Level 3), variations and spread (Level 4)" in the data.

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.

Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y7 (03/2010)

a)
b)

 Abby
Statements that identify that most students take less than 30 minutes, for example:
Only 3 take more than 30 minutes;

  • 18 out of 21 take less than 30 minutes;
  • 18 students take less than 30 minutes;
  • Under 30 minutes includes 0-9, 10-19, and 20-29 minutes.

very difficult
(both correct)
c)
x-axis values should be numbers on a scale (continuous data), rather than intervals.
  
Based on a representative sample of 208 students.
 
Examples of correct student responses
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] 10-19 minutes to get to school, but overall most children took less than 30 minutes to get to school.
Looks at the "biggest chunk" of the distribution numerically. 
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 0-9 minutes, 8 children took 10-19 minutes and 3 took 20-29 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 0-9 mins and 10-19 mins and 20-29 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 0-30 mins to get to school.

Looks at the small "tail" of the distribution numerically. 
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.
Teaching and learning: 
  • 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.
Diagnostic and formative information: 
​While most students at Level 4 (Year 7 and Year 8) are comfortable with the concept of the mode, ideas about the overall distribution are still under-developed. Only a few students in the sample we took (about an eighth) mentioned ideas of distribution early in Year 7, indicating it needs to be a focus of teaching and learning.

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 10-19 goes the highest.
That bar is higher than the rest.
Because 10-19 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
10-19 on the graph has 8 people and the other numbers are 7, 3, 2, 1, [so] 8 is the one with most people.
It couldn't be 20-29 minutes cause only 3 took that long and it couldn't be 0-9 because only 7 took that long so my answer is 10-19 cause 8 took that long.
Because there were lots of people that took 10-19 minutes to get to school.

Correct comparison of the part to the whole for the mode only
On the graph it shows that 8 people out of 21 students took 10 to 19 min to get to school.
Over 70% of students select Jason, and about two thirds of these gives explanation like the ones above.
i) A - Nisha

 


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
Because Nisha is in the 10-19 but Tim is in the 20 to 29 minutes.
On the graph it says 0 to 9 and it is less than ten.
Because 20 mins is a lot of time for people to get to school.
Because it would take 20 min to get to school because it depends how fast you walk.
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.
Next steps: 
Confuses mode with the distribution "largest part" of the data
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, 0-29 or 0-39).
The student needs to see that while 10-19 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.