Maths test scores

Maths test scores

Pencil and paper
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This task is about recording data on a stem-and-leaf graph.
The Year 8 students at Kaimoana School sat a maths test. The teachers wanted to compare the test scores for two classes on a back-to-back stem-and-leaf graph.
 
a)
Your teacher will read out the scores. You are to display this data as you hear it onto the back-to-back stem-and-leaf graph below.
The stem of the graph has been done for you.
  

Room 5
   Room 7
 
 

b)
 
Now complete the back-to-back stem-and-leaf graph below by ordering the numbers in each of the 'leaves' from part a). Make your graph as neat as possible.     
 
Room 5
   Room 7
 
 
 
Use your graph to answer the following questions.
 
c) 
i)  What is the median score for Room 5? __________
 
ii) What is the range for Room 5? __________
 
d)
i)  What is the median for Room 7? __________
 
ii) What is the range for Room 7? __________
Task administration: 
This task is completed with pencil and paper only.

Students need to record the data into a back-to-back stem-and-leaf graph in the order that it is read out.
They then need to re-order each of the leaves onto a second graph.

Teacher Reads:

The Year 8 students at Kaimoana School sat a maths test. The teachers wanted to compare the test scores of two classes on a back-to-back stem-and-leaf graph. I am going to read out the scores. I want you to display this data as you hear it onto the back-to-back stem-and-leaf graph in a) below. The stem of the graph has been done for you.
I will read out the Room 5 scores first, then the Room 7 scores. I will read each number twice and pause to give you time to record your answer.

Read out:

  • Room 5: 76, 37, 43, 58, 79, 98, 64, 68, 83, 71, 50, 23, 12, 55, 58, 91, 77, 95, 87, 24, 92, 86, 35.
  • Room 7: 21, 59, 63, 92, 99, 15, 95, 87, 51, 42, 38, 64, 79, 88, 49, 35, 10, 44, 84, 75, 28, 73, 54.

NOTE: When trialled we read the scores out using the following wording: "The first score is 21, (3-5 second pause) 21, (3-5 second pause). The next score is 59, (3-5 second pause) 59, (3-5 second pause). The next…" etc.

Level:
4
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
composite graphs, graph construction, graph interpretation, bi-variate data, stem-and-leaf graphs
Description of task: 
This practical task requires students to record data, which is read out to them, on a back-to-back stem-and-leaf graph. The leaves are then ordered into a second graph and the graph interpreted.
Curriculum Links: 
This resource can be used to help to identify students' ability to plot and re-order a back-to-back stem-and-leaf graph.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a)
All leaves recorded in the order shown below.

An error in recording includes a

•   missing data point.
•   extra data point.
•   transposition.
Leaves are presented in single-digit format.

b)
All leaves recorded and in numerical order on Room 5side.
All leaves recorded and in numerical order on Room 7 side.
NOTE: Accept errors if the numbers on this graph are the same as those
used for the graph drawn in a) but are still ordered correctly.

Numbers on both sides of the graph are vertically aligned neatly.

c)

Room 5: median: 68 - range: 86

d)

Room 7: median: 59 - range: 89
Diagnostic and formative information: 
  

Common error

Likely reason

c)

64

Knows about median but counts to it from left to right rather than from the stem out.