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Common Assessment Task, Learning Sequence 1, 2015Subject: Mathematics

Year Level: 7

Student Name:

This COMMON ASSESSMENT TASK will be used to measure your achievement against the skills and understandings that we studied during this learning sequence.

You are required to complete each part of this assessment, and finish within the timeline allocated.

You need to work through the assessment from beginning to end, using the scaffolds and instructions included within each part of the task.Use your rubric and feedback from your teacher to guide you from one part of the assessment to the next. Make sure you evaluate the accuracy and success of each part before moving on to the next. After you complete your own checking, you need to show your teacher who will advise you if your work is at the expected level.

This is an independent task but you may ask questions to clarify the requirements of the task. Remember that your teacher will NOT do the work for you; he/she will help you with the thinking you need to employ to complete the work.

Remember to organise your time appropriately so you can complete as much of the assessment task as possible in the time given.

You are permitted to bring the following to class during this assessment task:

Common Assessment Task Overview

Task 1: Calculating the mean, median, mode and range for a mathematics class test results and for the height and foot lengths of students in a mathematics class.

Constructing graphical representation to represent data.Task 2: Explaining and commenting on the mean, median, mode and range of the foot lengths of a

class of students and their visitors. Investigating and identifying a possible title for a stem and leaf plot. Commenting on the similarities and differences on the range, mode and median of two stem

and leaf plots.Task 3: Analysing the heights of a sample of students in 1914 and another a sample of students in

1996. Discussing the four measures of central tendency of the heights of students in 1914 compared

to those in 1996.

Student Declaration:I declare that this assessment is my individual work after seeking and receiving feedback from my peers and teacher. I have not copied from another student’s work or from any other source, except where due acknowledgement is made explicit, nor has any part being written or completed for me by another person.Student Name:Student SignatureDate:

Turn to next page for details and scaffolds for each part

Y7 Mathematics – Statistics

Task 1Task 1 has two questions: Question 1 and Question 2 and each question is comprised of other questions.

In Task 1 you will be applying your knowledge of the meaning of, and demonstrating your skill in calculating the value of the following mathematical terms: mean, median, mode and range.

You will also be demonstrating your skill in representing data in various graphical formats.Question 1 Year 7 Mathematics classes have collected the foot lengths of students. Table 1 represents the foot lengths of thirty students randomly selected from all Y7 Mathematics classes. The Mathematics teachers would like your help in calculating some statistical facts about these students.

Table 1Foot lengths (to nearest centimetre)

12 21 15 19 25 14 18 32 15 30

20 32 32 14 28 25 25 13 31 25

24 19 14 33 18 27 32 31 28 19

How well can you manipulate the data above? Complete the tables and graphs below based on the Data in Table 1

Step 1:

Frequency Table

Length Tally Frequency

10-

15-

20-

25-

30-

Step 2: Construct a column graph to display the information in table

Step 3:

Complete a stem and leaf plot of the data from Table 1

Key= |

STEM LEAF

Step 4: Construct a dot plot from the data from table 1

10cm- 15cm- 20cm- 25cm- 30cm- 35 cm-

Mathematics Y7 Statistics Common Assessment Task p 2 of 13


A sample of 30 students foot length from year 7

Step 5

Complete a pie graph based on the data from table 1

#Hint For each pie in the graph use the following formula

Frequency/Total × 360º

Using these foot lengths marks:

Q1.1 Calculate the mean (average) foot length from the data in Table 1. You will need a calculator

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Q1.2 Calculate the mode foot length(most common score) from the data in Table 1 .

_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Q1.3 Calculate the median ( middle number) foot length. (Hint n+1/2)

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Q1.4 Calculate the range.


Colour on the Pie Graph

Students foot length in cm

Frequency

10-

15-

20-

25-

30-


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Question 2 Give examples of the different categories of data in the table below:

Task 2This is the second part of your assessment task. Congratulations for being here. It means you have checked with your teacher and with the rubric for this assessment, and you are ready to move on. Well done!

Task 2 has two parts: Part 1 and Part 2.

In Task 2 you will be:

* Analysising the effect of adding new values to your data set

* explaining and commenting on the mean, median, mode and range of the foot lengths of your class;

* investigating and identifying a possible title for a stem-and-leaf plot; and

* commenting on the similarities and differences on the range, mode and median of two stem-and-leaf plots.

Analysing data

The following questions refer to the foot length data as shown in Table 1. Remember to show ALL working out.

Q3.1 If Israel Folau (37cm) and five members of the Australian Winter Olympic team Torah Bright, Belle Brockhoff, Ludia Lassila, Anna Segal and Michelle Steele (all 23cm) joined your class and had their foot length measured.

a) How does this change the range of the foot lengths? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________



_________________________________________________________________________________________________

b) How does this change the mode of the foot lengths? _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Q3.2 Explain the reasoning behind your decision ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Q3.3 Three of the Australian Winter Olympic team have other commitments and don’t turn up to school on the day of measuring their foot lengths.

a) How would this affect the median? ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b) How would this affect the range? _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Q3.4 Explain the reasoning behind your decision _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

The following two questions refer to the Table 1

Q3.5 Four students are removed from the data set, so that the mode number of the foot length stays the same and the median changes.

a) Who could they be, giving reasons for your choice?



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Q3.6 Four students are removed from the data set, so that the mode number of foot length changes and the median stays the same.

b) Who could they be, giving reasons for your choice?_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Back-to-back stem-and-leaf plots

Back-to-back stem-and-leaf plots can be constructed on either side of a central stem, as shown below.

TITLE 1:______________ TITLE 2:_________________

Q4.1 What does the highlighted area in the stem and leaf plot represent?__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Q4.2 As there is no title/heading on the stem and leaf plot we do not know what it represents.

a) What do you think the data could possibly represent? __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b) Suggest a title that you think could represent each side of the central stem.

Title 1: ____________________________________________________

Title 2: ____________________________________________________



Q4.3 Comment on similarities and differences between the two data sets, discussing the following features: Range Mode Median __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Analysing a newspaper article1 featuring a statistical reference to the word ‘median’.You will use the information circled in Figure 3 to analyse its statistical content. The article gives the author’s opinion on how to measure the impact of the National Disability Insurance Scheme.

This photo shows an extract from an article published in The Sunday Age, 16th February.

Q5.1 What is your understanding of this paragraph?

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1 “Disability care goes straight to the heart but needs a businesslike touch”, Liz Kelly, The Sunday Age, 16 th February 2014Mathematics Y7 Statistics Common Assessment Task p 7 of 13

Things to consider as you read this article

A person with a disability might include a person who has a physical disability, a psychiatric disability or an intellectual disability.

“Gross personal income per week means” means the total amount of money a person receives each week.


Q5.2 Construct a stem-and-leaf plot of the median gross personal income per week for people aged 15 to 64 with reported disabilities. You should show at least seven other possible values of the gross personal income per week.

Q5.3 Construct a stem-and-leaf plot of the median gross personal income per week for people aged 15 to 64 with no reported disabilities. You should show at least seven other possible values of the gross personal income per week.

Q5.4 Can you predict whether a person with a disability will have enough money to live on?

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Task 3Congratulations on your achievement of getting this far! You have reached the third and final part of your assessment.

Task 3 has two parts: Part 1 and Part 2.



In Task 3 you will be:

* interpreting two data sets; one representing the heights of 175 students attending a school in 1914 and the other representing the heights of 143 different students attending the same school in 1996; and

* justifying your interpretation of a comparison of the differences in heights between these two groups of students.

THE DISTRIBUTION OF HUMAN HEIGHT TASK

Here are two pictures of students attending a school taken in 1914 and 1996.

Analyse and compare (Find mean, median, mode and range) the differences between the two groups. Explain your findings.

Figure 3

Figure 3 shows 143 students attending a school in 1996, lined up according to their heights. The heights are measured using the imperial system (feet and inches) and have been converted to the nearest centimetre in Table 3.

1996 students – 143 students

height in cm 152 155 157 160 163 165 167 170 172 175 178 180 183 185 188 191 193 196

number of students

5 5 7 7 11 13 18 14 11 13 13 9 12 7 2 3 1 3



Table 3 represents the heights and numbers of the 143 students shown in Figure 3.

Figure 4

Figure 4 shows 175 students attending the same school in 1914, lined up according to their heights. The heights are measured using the imperial system (feet and inches) and have been converted to the nearest centimetre in Table 4.

1914 students – 175 students

height in cm 147 150 152 155 157 160 163 165 167 170 172 175 178 180 183 185 188

number of students

1 0 0 1 4 5 5 15 16 15 18 12 10 11 2 3 1

Table 4 represents the heights and numbers of the 175 students shown in Figure 4.Q6.1 Discuss the four measures of central tendency (mean, median, mode and range) of the height of each group of students in 1914 compared with 1996. (Use “a format to support students in writing an explanation” in answering this question).



A format to support students in writing an explanation.

Opening Statement

Write what you are going to explain in at least one sentence.

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Explanation Sequences

Write what you were thinking before you started calculating the four measures of central tendency.

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Write how you calculated the four measures of central tendency.

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Describe your observations of any differences between 1914 and 1996 measures of central tendency.

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Write the challenges you faced.

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Write how you worked your way through these challenges.

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Concluding Statement

Write an interesting sentence describing what you have explained in the Explanation Sequences.

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End of Common Assessment Task


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