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Year 7 Maths Unit

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					Mathematic Unit
     “Data
Measurement for
 Everyday Life”
  Year Seven




                  1
            QCT
       STANDARDS: 1,
         2, 3 and 4.




Introduction
This unit has been specifically designed for a mixed gendered year seven class.
The unit ‘Data Measurements for Everyday Life’ has been planned according to
the Australian Curriculum, Assessment and Reporting Authorities National
Curriculum draft. The topic for this four-week unit will be Statistics, more
specifically Data Measures.

Links to Other Subjects

 This topic very easily links to other strands of math’s such as

      Number: being able to count and order the data accurately in ascending
       and descending order.

      Algebra: identifying the patterns that exist within a specific data set.

      Time: determining amount of time spent collecting data in order to collect
       an adequate amount

      Calculation: using mental and calculator strategies to determine mean,
       median and mode
                                                                                  2
Developments from K - 7

Data Measures is a new concept introduced in year seven however during
‘Summary of Statistics’ in year five students are first introduced to Median and
Mode. After this brief introduction, Data Measures do not arise again in the
curriculum until year seven. In order for students to effectively complete this
unit, there must be a certain degree of scaffolding in the prior years of schooling
during the teaching of Data Representation and Investigation. It is assumed that
there would be informal discussion during these topics on the range of particular
data sets, for example, which has the most or the least. This informal discussion
and early introduction in Year Five sets the scene for this unit.




                                                                                 3
Scope and Sequence of Unit
UNIT NAME: Data Measurements for Everyday Life                                  YEAR: 7

TIME LINE: Four Weeks / Twenty Lessons                                          CONTENT STRAND: Statistics – Data Measures

OUTCOMES AND ELABORATIONS                                BIG MATHEMATICAL IDEAS                       PRIOR KNOWLEDGE

Data Measures: Determine mean, median                    The big mathematical idea for this unit is   Students need to be able to
and range and use these measures to                      Central Tendency. By the end of this unit
compare data sets explaining reasoning                   students should be able to accurately              Construct, read and interpret graphs
including using ICT.                                     identify the middle score of a data set.            and other simple data displays using
                                                                                                             technology
Elaborations
                                                                                                            Identify misleading representations
      Understanding that summarizing data by
       calculating measures of centre and spread                                                            Interpret secondary data often
       can help make sense of data
                                                                                                             represented by the media
      Calculating mean, mode, median and range
       from listed data and from graphs that show
       individual data with and without technology

      Using mean, median and range to compare
       data sets and explaining how outliers may
       affect the comparison.

      Using dot plot or stem plot to identify
       outliers in a data set, that is the data values
       that seem to stand out from the majority of
       data values.




                                                                                                                                                4
                   KEY:                                                   Teacher Aide Lessons

                           Learning Objectives                           Worksheets

                           Lessons in Computer Room                      Collection of Assessment



       Monday                  Tuesday                 Wednesday                  Thursday                   Friday
Week   Scan prior              Scan prior knowledge    Introduction of Mean       Check List Assessment      Check List Assessment
       knowledge of            of graphing
One    graphing

       Concept Map on       Gather examples of         Explicit Explanation of    Discussion of examples     Revise Dot Plot, show
       Statistics           graphs from                Mean                       of mean found for H/W      students an example
                            newspaper, internet:
       Mix and Match Graph look at common              Discussion: where we       With teacher guidance,     Individually students to
       game – written up as features of different      see mean/average in        as a whole class           put collected data onto
       ‘Stats Glossary’ in  graphs                     real life situations       develop a question and     a dot plot, work out
       book                                                                       collect data using peers   mean
                            Develop graphing           Develop class definition
       H/W: List examples   checklist, written in      and example: put into      In pairs, sort and order   Collect all students
       of how graphs are    glossary                   glossary                   data.                      work for checklist
       used in real life.                                                                                    assessment
                                                       Worksheet #1

                                                       H/W: find two
                                                       examples of mean in
                                                       the media


                                                                                                                                     5
Week   Reintroduction of      Consolidate            Reintroduction of Mode   Practice use of             Introduction to types of
       Median                 knowledge of Median    and Introduction of      measurements using          surveys
Two                                                  Range                    ICT

       Quiz: Write down six   Word Map of            KWL Chart about Mode     Students to work            Word Map of idea’s
       things you know        knowledge of median    on butchers papers in    through BBC Website         about surveys: what,
       about median?          so far                 groups of four           on ‘Data Handling’          why and how.

       Discussion of          Find examples of     Explicit demonstration        a) Collecting Data       Examples of
       Answers                median using,        of Range
                              newspaper, magazines                               b) Representing          1. Cross sectional
       Explicit explanation   and internet         Develop class definition         Data
       of median                                   and example for both                                   2. Longitudinal
                              Develop class        and add to glossary           c) Averages
       Discussion: using                                                                                  3. Time series
                              definition and                                  Students to choose one
       graphs, what does      example: put in      In pairs, using a group
                                                                              activity from A, B and C:   Discuss how questions
       the median tell us?    glossary             of 50 randomly                                         will vary for each type
                                                   coloured paddle pop        revise, complete the
       Worksheet #2                                                           activity and take the       of survey
                              Worksheet #3         sticks or counters will
                                                   work out range and         test.                   Individually choose
                                                   mode. Specific colours     ‘Low Achievers’ to work type of survey and
                                                   should be given a          with Teacher Aide       develop a relevant
                                                   particular value.                                  question

                                                                                                          H/W: use constructed
                                                                                                          survey on family
                                                                                                          members and friends




                                                                                                                                    6
Week    See where the gaps     Explanation of           Introduction of Outliers   Identifying Outliers        Identifying Outliers
        in students            Assessment                                                                      using dot plots
Three   knowledge are

        Revision of ways of    Discuss task and         Students use               Each student is given a     Look at dot plots
        working for each       explain criteria         dictionaries and           page out of the local       constructed from
                                                        internet to search for     newspaper, they have        previous lesson:
        Card Game              Break students into      definition                 to cut out an article and   identify Outliers
                               groups (speaker,                                    highlight a paragraph
        Worksheet #4           director, manager)       Using students heights                                 Work out mean and
                                                                                   which is eight lines
                                                        as data set, collect       long.                       mode, median of
                               Run through data         measurements                                           collected data
                               collection procedure –                              Table of alphabet and
                               visit tuck shop to       Spot the outliers          tally of how many times     Evaluate: How do the
                               practice                                            the letters arises in the   outliers affect the mean
                                                        H/W: How do outliers                                   and mode? What does
                                                                                   paragraph.
                                                        affect data?                                           this mean for data sets?
                                                            Group One to          Students to organise        How do dot plots help
                                                             Tuck Shop             data and put onto dot       us identify outliers?
                                                                                   plot
                                                                                                                   Group Three to
                                                                                       Group Two to                Tuck Shop
                                                                                        Tuck Shop


Week    Relationships       Sorting and sharing of      Use ICT to create pie      Work out mean,              Completion of
        between percentages collected data from         chart of results           median, mode and            Assessment Task
Four    and pie graphs      Tuck Shop                                              range for data set

        Explicit explanation   In data collection       ‘How to’ Power point        Students work            Finishing touches: title
        and examples of how    groups, students sort                               individually and silently and contents page to be

                                                                                                                                      7
percentages work       out their data.            Students have a go at     to work out               added to report
with pie graphs                                   putting their
                       As a class, students       information into pie            Mean               Type up justification
Discuss formula        construct a                graph
                       representation on the                                      Median             Complete any
Develop a definition   white board that will      Students will also work                             unfinished elements of
and example for                                                                   Mode and           the report
                       best collect their         out their percentages
glossary               shared data                for each, showing all           Range              All students to hand in
                                                  working out
Work Sheet #5          Each group presents                                                            assessment.
                                                                            Write up justification
    Group Four to     their data to the class,                             for the data they have
     Tuck Shop         adding to the                                        found
                       representation on the
                       white board                                          ‘Low Achievers’ to work
                                                                            with Teacher Aide.
                       Students add
                       representation to
                       workbook

                       (please note, this
                       lesson needs to take
                       place after lunch so all
                       data can be collected)

                           Group Five to
                            Tuck Shop




                                                                                                                                8
Resources                                   Literacy Demands                              Mathematical Language

Computer Rooms: Internet, Macintosh         This unit requires students to translate            Mean
Word and Excel,                             information often from a worded problem
                                            into mathematical terms and symbols. It             Median
Classroom Computers                         also requires students to justify their
                                                                                                Range
Newspapers, Magazines                       mathematical answer with a worded
                                            explanation. Students need to be able to            Mode
‘Mix and Match’ A4 cards                    comprehend the questions in order to give
                                            appropriate answers.                                Data Sets
Novelty Card Pack
                                                                                                Outliers
‘How To’ power point
                                                                                                Skewed
Work Sheets
                                                                                                Reasoning
Coloured paddle pop sticks or counters

Giant Protractor
Tape Measures

Catering for Diverse Learners               Teacher Aide Support                          Assessment Opportunities

Visual Impairments will be catered for by   Teacher Aide hours are first period every     Throughout this unit there are two
being seated up the front of the class,     second Thursday. For this unit, Teacher       opportunities for assessment. Firstly there
worksheet will have bigger font and all     Aides will work specifically with low level   is an assessment at the end of week one, to
computer work will have the view of the     achievers, helping them mostly with           determine any gaps in the basics of data
screen enlarged by 100%. For lessons        assessment pieces.                            representation: the unit will be altered
where being seated up the front may not                                                   slightly according to these gaps. Secondly
give the best vision, the student will be                                                 there is an assessment in week four so the

                                                                                                                                    9
given enlarged hand outs of what is             students can demonstrate the knowledge
happening, for example a power point.           and skills they have learned throughout the
                                                unit. This also will demonstrate if the
Auditory Processing Disability will be          students have reached the unit objectives
catered for by being seated up the front,       or not.
simple explicit language and hand signals
will be used when explaining content or
giving directions and directions on cue
cards card’s will be given out where
possible.



Unit Evaluation

How effective was my sequence?

Did I cater for my diverse learners?

Could I change my resources?

Overall, was my unit successful? Why/why not?




                                                                                        10
Lesson Plan A

Lesson: Measurement Card Game           Date:
Time: Week Three, Lesson Eleven         Year: 7


Unit Outcomes

Calculating Mean, Median, Mode and Range from listed data and from
graphs that show individual data with and without technology.

Learning Objectives

Throughout this lesson student‟s knowledge of how to measure data sets
will be consolidated and reinforced through the use of hands on
materials.

Students Prior Knowledge

Students will need prior knowledge of data sets and the ways of working
for mean, median, mode and range.

Resources

      A deck of cards per students (must bring in more incase some
       students don‟t bring in)

      A large set of novelty cards for demonstration

      Record Sheet (See Worksheets)

      Blue Tack

      Calculator and Pen per student

      Printed simplified rule cards for diverse learners

Lesson Procedure

Introduction (10 minutes)

   1. Students will be seated at their desks

   2. Discussion about ways of working for mean, median, mode and
      range. Concept map will be drawn up on board to help aid discussion
      and remind students throughout game.

   3. Record Sheets handed out
                                                                      11
Lesson Content and Procedure (30 minutes)

   4. Rules of game are explicitly taught: students are given a particular
      hand they must pull out of their deck of cards. From that hand,
      students will work out the measurements during allotted time
      frames. There are four measurements to work out: if correct
      student receives 5 points for each, if incorrect received 0 points.
      Students must show their working on the record sheet. The winner
      is the student with the highest number of points at the end of the
      four rounds.

   5. Value of picture cards and aces are written up on white board

   6. Using the novelty cards blue tacked to the whiteboard, show
      students the hand they must pull out of their deck.

   7. Allow 3 minutes for all except mean, which should allow 4 minutes.

   8. When all four have been worked through, work out correct answers
      and winner.

Conclusion (10 minutes)

   9. If time permits, play another round with a new hand.

   10. Get students to glue record sheets into workbook and hand in

   11. Pack up

Assessment/Evaluation

The student‟s work can be evaluated by looking at their working out of
each round. This evaluation will allow the content and teaching to be
adjusted in order to fill in the gaps of the student‟s knowledge.

Adaption’s for Diverse Learners

Visual Impairment – Student will be given a set of large playing cards and
the font will be enlarged to size 16 on the record sheet.

Auditory Processing Disability – Student will be given a laminated card
that has a set of simplified rules and instructions for the game.




                                                                          12
Teacher Reflection/Evaluation

Learning Objectives?

Did the students meet the objectives? Why or Why not?



What could be improved to enable students to meet objectives?



Self as a teacher?

Where my resources effectively used?



Did I cater for my diverse learners appropriately?



How was my classroom management during this learning experience?



Overall, how did my lesson go?




                                                                   13
Lesson Plan B

Lesson: Pie graphs on ICT             Date:
Time: Week Four, Lesson Eighteen      Year: 7


Unit Outcomes (Curriculum)

Calculating mean, mode, median and range from listed data and from
graphs that show individual data with and without technology

Learning Objectives

Use ICT to create a pie chart which will effectively represent collected
data from the „Tuck Shop‟ Investigation

Resources

      Computer Lab

      Projector

      “How To” Power point

      USB Sticks

      Collected surveys and data from previous lessons

      Students work books

Students Prior Knowledge

Students will need prior knowledge of the data which will need to be
transferred onto a graph. They will also need knowledge of what they
want their finished pie graph to look like.

Lesson Procedure

Introduction (10 minutes)

   1. Students will be seated at individual computers in computer room

   2. Aim for lesson will be discussed: Students to put collected „Tuck
      Shop‟ data onto a pie graph using word.

   3. Explicit explanation how to make graph using word: power point is
      shown on projector
                                                                          14
Lesson Content and Procedure (45 minutes)

   4. Students told to log on

   5. Open „How To‟ power point on their individual screens

   6. Students to make their own graph following the prompts: teacher
      to be walking around room, answering questions.

   7. Work out percentages for each section of data using appropriate
      formula (See glossary of work book if cannot remember)

Conclusion (5 minutes)

   8. All students to either print completed graph or save to USB.

   9. Log off and pack up equipment

Assessment/Evaluation

The completed graph will be added to a portfolio that will be evaluated
and marked at the end of the unit.

Adaption’s for Diverse Learners

Visual Impairments - Students will be seated at the front of the
classroom and their individual computer screen‟s view will be increased.
The font will also be enlarged for them.

Auditory Processing Disability - Students will be seated up the front of
the class with a clear view of teacher. A simplified set of instructions
will be given out at the beginning of the lesson and a printed version of
the power point will be given to them.

Teacher Reflection/Evaluation

Learning Objectives?

Did the students meet the objectives? Why or Why not?



What could be improved to enable students to meet objectives?

Self as a teacher?

Where my resources effectively used?
                                                                            15
Did I cater for my diverse learners appropriately?



How was my classroom management during this learning experience?



Overall, how did my lesson go?




                                                                   16
Worksheet #1




 A farmer has his cows, sheep and chickens separated into a
 number of different paddocks. Help him work out the mean
                      for each animal.




                  18 18 15 18 18 14 4 21
                          Mean =



                  94 96 84 69 70 105
                          Mean =



                   23 1 31 18 10 7 3 17
                          Mean =

         How many animals does he have altogether?


           What is the mean of all the farm animals?
                                                          17
                        Assessment Tool A

                     Check List Assessment
Students can or cannot accurately complete each stage with appropriate working.

Students Collect Sort        Organ    Interp    Work    Comments
Names    Data    Data        - ise    - ret     out the
                             Data     Data      Mean of
                             onto               the
                             Dot                data
                             plot




                                                                             18
Worksheet #2




                             MEDIAN
Q1. The Smith Family Drove from Sydney to Cairns for their family
holiday. On the way they stopped seven times to fill up their car with
petrol. They paid $1.69, $1.99, $1.10, $2.05, $1.30, $1.23, $1.44. What
is the median price they paid??



Q2. The salaries of eight McDonald‟s employees are listed below. $30
000, $40 000, $32 000, $29 000, $43 000, $31 000, $35 500, $27 000.
What is the median salary?



Q3. A family of five members runs the Bridge to Brisbane 10 km event.
They do it in 55 minutes, 1 hour and 18 minutes, 38 minutes, 44 minutes
and 1 hours and 25 minutes. What was the median time for the family?



Q4. James is always being told he plays too much Xbox so he decides to
record how many hours he plays over a four week period.

8hrs, 3hrs, 1hr, 2hrs, 4hrs, 1hr, 6hrs, 4hrs, 4hrs, 3hrs, 1hr, 2hrs,
3.5hrs, 2hrs, 7hrs, 2.5hrs, 3.5hrs, 3.5hrs, 6hrs, 4hrs, 1hr, 1hr, 2hrs,
2.5hrs, 3hrs, 9hrs, 3.5hrs, 2hrs, 1hr, 4hr.

   a) What is the total number of hours he played during that month?

   b) What is the mean number of hours played?

   c) What is the median hour James played?


                                                                          19
Worksheet#3




                WORK OUT THE MEDIAN FOR
  a) 3, 6, 4, 14, 35, 7, 7, 5,

  b) 35, 76, 55, 45, 44, 56, 43, 48, 46, 46, 46, 46,

  c) 50, 87, 88, 130, 109, 126, 77, 87, 109, 109, 123

  d) 209, 405, 366, 560, 309, 299, 325,

  e) 687, 1098, 999, 789, 875, 545, 1001, 779




  f) Tim is travelling around the USA. He decides he is going to have
     the same burger: beef pattie, onion rings, cheese, lettuce, tomato
     with mustard and ranch sauce in all the 52 states he is visiting. The
     amount Tim paid for each burger is below:

     $4.50, $2.50, $3.00, $5.95, $5.00, $7.00, $6.05, $3.75, $2.50,
     $6.00, $1.95, $3.75, $4.50, $4.25, $6.00, $5.95, $4.80, $3.95,
     $4.50, $3.50, $6.50, $7.85, $9.05, $8.75, $3.80, $2.50, $4.25,
     $4.80, $5.60, $5.60, $7.80, $3.50, $5.25, $5.20, $6.80, $4.85,
     $5.00, $7.50, $3.75, $2.95, $7.20, $6.85, $5.30, $6.60, $4.45,
     $12.00, $2.95, $7.50, $6.85, $4.50, $4.50, $4.50

  1. What is the average price Tim paid?

  2. What is the median price Tim paid??




                                                                       20
Worksheet #4




               Record Sheet for Card Game…




Hand:




Working                                 Answer   Points
Mean




Median




Mode


Range


Total




                                                     21
                           Assessment Tool B




Question: The Tuck Shop is revising its menu and has decided it needs to
take out two items that are their lowest sellers. They cannot decide
between

      The sausage roll

      The baked bean jaffle

      The ham, mustard and onion sandwich

      The almond cookie

      The potato and green pea pie

Your job is to develop a formal report which includes

   1. Collection of the appropriate data: you will be broken up into
      groups of three and will spend one 10 minute period during the hot
      lunch time at the Tuck Shop surveying the items bought.

   2. Sort out data and share results so all members of the class have
      the same data

   3. Use ICT, to represent the collected data on a pie chart

   4. Work out the mean, median, mode and range. Identify any outliers
      and evaluate how they might skew the data.

   5. Write a justification about which items you believe need to be
      taken off the menu.

Reminder: Steps 1, 2 and 3 are to be done in groups, Steps 4 and 5 must
be done individually.




                                                                         22
A                        B                      C                     D                   E

Translated problem       Translated problem     Translated problem    Developed a         Little or no
into appropriate         into question and      into question and     survey. Collected   attempt to develop
question and             developed survey.      developed a survey.   and attempted to    survey. Collected
developed survey.        Collected data and     Collected data and    sort data using     data. Some
Collected data and
                         sorted using           sorted using          graphical           attempt to
sorted using graphical
                         graphical              graphical             representation.     represent data
representation: tally,
bar graph. Using ICT,
                         representation:        representation.       Using ICT           using ICT. Little or
correctly represented    tally. Using ICT,      Using ICT,            attempted to        no attempt at
data as pie chart and    correctly              represented data as   represent data as   working out mean,
converted data sets      represented data as    pie chart. Worked     graphical           median, mode and
to percentages.          pie chart. Worked      out mean, median,     representation.     range.
Correctly worked out     out mean, median,      mode and range.       Some attempt to     Justification was
mean, median, mode       mode and range         Justification was     work out mean,      not present.
and range using          using appropriate      present.              median, mode and
appropriate formulas.    formulas.                                    range. One or two
Justification was in
                         Justification was in                         sentences as
depth and referred to
                         depth.                                       justification.
data.



                                                                                                                 23
Worksheet #5

At the local high school, 60 year seven students were asked to choose
their summer sport.

The results were as follows:

Swimming                                      20

Cricket                                       15

Dance                                         12

Canoeing                                      3

Tennis                                        10



Draw a pie graph of the results. (Show all working in your exercise book)

Work out the percentage of the choices and don‟t forget to clearly label
the graph.




   a) Which sport had the highest percentage?

   b) Which sport had the lowest percentage?

                                                                        24
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