# Key lesson plan Fraction operators

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```					                              HANDLING DATA                                YEAR 9               LESSON 1
HD1.1                         SPECIFY AND PLAN

Objectives                 Suggest a problem to explore using statistical methods, frame questions and raise
conjectures.
    Discuss how data relate to a problem; identify possible sources, including primary and
secondary sources.
    Design a survey or experiment to capture the necessary data from one or more
sources; determine the sample size and degree of accuracy needed; design, trial
and if necessary refine data collection sheets;
    Construct tables for large discrete and continuous sets of raw data, choosing suitable
class intervals; design and use two-way tables.

Starter             Suggest different cross-curricular problems.
Invite pupils to suggest conjectures. Such as;
Vocabulary
With physical education:
Conjecture                How far can people jump from a standing start?
Hypothesis                To what extent does a run-up help?
Hypothesis                Does practice improve the distance?
Prediction                Are Year 9 pupils able to jump or throw further than Year 7 pupils of the same height?
Resources                 Possible conjectures could be:
Your height and the length of your run-up are likely to affect how far you can jump.
OHT with cross-           A moderate run-up is useful, but the effect will diminish after a certain point.
curricular problems
With science
What effect does engine size have on the acceleration of a car?
Possible conjectures could be:
In general more powerful engines produce the greatest acceleration.
The addition of a turbo unit increases the acceleration of a car.

Main activity            Discuss how data relate to the enquiry and identify possible sources, including primary and
secondary sources.
Vocabulary
Ensure that pupils are aware of how relevant data might be obtained, eg:
survey, questionnaire,      a questionnaire or survey of a sample of people;
experiment, data,           printed tables and lists;
statistics,                 the Internet;
grouped data, class         other computer databases.
interval, tally, table,
frequency, data           Pupils working in groups design data collection sheets.
collection sheet,
database,                 For example:
sample, primary source,       Plan how to conduct a survey into long jumps or throws with different lengths of run-up.
secondary source, data        Identify magazines and books with information on engine sizes of cars and acceleration
log, two-way table,            times for 0–60 mph
discrete, continuous,         Plan how to conduct a survey into leisure activities at a sports centre
raw data,                     Plan how to conduct a survey into shopping trends, TV viewing or radio listening
representative, bias,
census
Resources
engine size and
acceleration.

Plenary              Select a data collection sheet from a group off pupils and discuss whether it does capture the
relevant data needed. Discuss sample size and degree of accuracy needed, and identify any
necessary refinements.
For example:
   Investigation of jumping or throwing distances
Check that the data collection sheet is designed to record all factors that may have a
bearing on the distance jumped or thrown, such as age or height. Decide the degree of
accuracy needed for each factor. Recognise that collecting too much information will slow
down the experiment; too little may limit its scope.
   Survey of acceleration data for popular cars
Check that the published data contain what is expected. Round published engine sizes to
the nearest 0.1 litre to eliminate unnecessary accuracy in data such as 1428 cc and 1964
cc.

Remember      Do not collect information that is not relevant to this survey.
   Remember to make the questions clear and unambiguous
   Make sure that the collection sheet is easy to use
   Make sure that the sample size is sufficient to ensure that the results are meaningful
HANDLING DATA                                YEAR 9                LESSON 2
HD1.2                            PROCESS AND REPRESENT

Objectives                   Find summary values that represent the raw data, and select the statistics most
appropriate to the problem.

Starter                Data CD, M3.4 Photos: Use the ‘children’ and ‘Sumo wrestlers’ photos of groups of people.
Estimate measures (mean, median and range) of chosen variables, e.g. height, weight, age,
Vocabulary                   income, time to run 200 m. Compare groups using key vocabulary. Consider effect of moving
mean, median, range          individuals between groups or combining entire groups.
and variable                 Compare mean weight of ‘children’ and ‘Sumo wrestlers’.
Resources                       What would happen to the mean weight if the groups were combined?
Y8 slides 1 Powerpoint       Estimate mean income of ‘children’. Consider adding footballer to group.
Note: Slide 15 has the
   How will the mean change?
groups singly; for
comparing the groups
the Powerpoint slide is
16

Main activity               Remind pupils how to calculate the mean, median and range.
Work through the example below identify a missing data item given a statistic (reverse
Vocabulary                   statistic)
statistic, interval…
A competition has three different games. Jane has played two of the games.
range, mean, median,
mode, modal class/group,
average…                                    Game A       Game B       Game C
distribution…stem-and-leaf
diagram…
raw data, estimate of the        Score         62           53            ?
mean/median, cumulative
frequency…
To win, Jane needs a mean score of 60.
Resources                    How many points does she need to score in game C?
Activity sheet HD 9.1        Pupils repeat this activity in groups. See HD 9.1
Questions are taken from the Framework Supplement of examples pages 260 to 261.
Questions 1 to 4 are Year 7, Questions 5 to 7 are Year 8, Questions 8 to 10 are Year 9 and
Question 11 is Year 9 more able. Teachers should adapt the questions to suit the ability of the
pupils if appropriate.

Plenary                Choose one of the last three questions on the activity sheet and ask pupils to demonstrate their
solutions.
If there is time and you feel that this activity will be useful:
Ask pupils to solve this question:
Find five integers where the mean is 6 and the range is 10.
You may want to use mini-whiteboards to record solutions. Take feedback from to identify that
there is more than one solution!
If appropriate you may want to discuss advantages and disadvantages of the types of average.

Remember                      Range is the difference between the smallest and the largest data item
    Mode is the most common value – there can be no mode or there can be 2 modes
    Median is, when the data is arranged in order, the one in the middle – if there are two
values in the middle, then calculate the mean of the two values
    Mean is the sum of all the values divided by the number of items
HANDLING DATA                                  YEAR 9               LESSON 3
HD1.3                   PROCESS AND REPRESENT

Objectives              Construct and use two-way tables.
   Select, construct and modify, on paper and using ICT, suitable graphical representation to
progress an enquiry, including:
- line graphs for time series;
- scatter graphs to develop further understanding of correlation;
identify key features present in the data.

Starter           Display Two-way table OHT and ask pupils to write their solution to the following question
(from a Year 8 Optional test) on a whiteboard.
Vocabulary              On World Book Day, each pupil in Year 7 chose one book to read. Some pupils chose a
two-way table           fiction book. Some chose a non-fiction book.
(a)     The two-way table shows that:
Altogether, there were 142 pupils.      68 were boys.
Resources                       77 pupils chose a fiction book.        36 boys chose a non-fiction book.
Complete the two-way table
Whiteboards
Two-way table
Use OHT of Two-way
table
Boys            Girls              Total

Fiction                                                    77

Non-fiction book           36

Total                 68                                  142

Main activity          At the end of this lesson pupils will be able to process and represent data using the following
techniques:
Vocabulary
bar chart         bar-line graph          frequency chart          frequency diagram
Axese                   pie chart         stem & leaf diagram     two-way table            distance-time graph
Discrete                line graph        scatter graph
Continuous
You will need to establish which statistical diagrams pupils are secure in and therefore do not
Grouped
need further practice, and those that need further work during this lesson.
Frequency
Interval                Pupils should appreciate that:
Distribution               A table usually gives all the data that can be retrieved.
Correlation                A graph, chart or diagram representing the data highlights particular features that a table
Resources                   does not.
   Data shown in a graph, chart or diagram are often in an aggregated form that does not
Year 9 Statistical          allow the original data to be extracted.
Diagrams                   Calculated statistics are representative values of data sets.
PowerPoint Handling
Data                    Please refer to: Examples of Year 9 Statistical Diagrams
Handling Data Booklet

Plenary            Discuss appropriate selection of each statistical diagram. PowerPoint Handling Data and the
Handling Data Booklet are useful resources.

Remember                A table usually gives all the data that can be retrieved.
   A graph, chart or diagram representing the data highlights particular features that a table
does not.
   Data shown in a graph, chart or diagram are often in an aggregated form that does not
allow the original data to be extracted.
   Calculated statistics are representative values of data sets.
HANDLING DATA                                     YEAR 9                  LESSON 4
HD1.4                    INTERPRET AND DISCUSS

Objectives                Interpret graphs and diagrams and draw inferences to support or cast doubt on initial conjectures;
have a basic understanding of correlation.
   Compare two or more distributions and make inferences, using the shape of the distributions, the
range of data and appropriate statistics.
   Communicate interpretations and results of a statistical enquiry using selected tables, graphs
and diagrams in support, using ICT as appropriate.

Starter            Discuss differences in crime patterns between two areas. What can we deduce from these diagrams?
What can’t we deduce from these diagrams?
Vocabulary

Pie chart
Sector
Proportion
Resources
OHT Crimes

Main activity           Task 1 (whole class): Developing explanations
The teacher leads the class through the process of composing an explanation to a selected question.
Vocabulary               Preliminary step
In some questions the ‘explain’ part is presented towards the end. Where this is the case it would be
Whiteboard               useful to work through the preceding parts, dealing with any misunderstandings, before starting this
activity on composing explanations. This might be done in an earlier lesson.
Resources                Explaining stage
Focus on the ‘explain’ part of the selected question. Emphasise that pupils should not think of this as a
Handling data question
test question. They are to imagine that they are putting the chart and the requested explanation into a
bank                     magazine article. The explanation should be about three or four sentences long.
The following steps may be ordered differently to suit a particular class.
1 Model how to compose a written explanation, explaining your thinking aloud and pointing out key
features such as correct use of technical vocabulary or appropriate use of words such as
1
whereas, though, while, unless, however, equally and also.
2 Ask pupils to work in pairs to compose one written explanation (perhaps on a whiteboard).
3 Select a response to the chosen question (either from your class or from the CD-ROM). Show it
to the class and together with the pupils, analyse, annotate and perhaps revise the response.
(Examples of annotated scripts are available on the CD-ROM to illustrate what this step might
look like.)
4 Ask pairs to review their own explanation in light of the whole-class discussion. 1 For more
guidance on the use of connectives for contrast or comparison, see Literacy across the
curriculum module 2, Literacy in mathematics (available on the Key Stage 3 website from
January 2004).
When using the Handling data question bank please select questions appropriate to the level of the
pupils. The pupil’s produce their own written explanations to the question bank.

Plenary             Discussing and revising
Pupils evaluate each others’ explanations.
   Select an appropriate question. Ask pairs of pupils to write their joint explanation on whiteboards,
and then join with another pair to discuss and evaluate the two responses. Guidance on The role of
the review partner (CD-ROM) will help here.
   Tell the four to agree a final form of the explanation in the light of their discussion.
   Select one or two examples, discuss the explanations with the class and ask pupils to explain how
their discussions improved their writing.
HANDLING DATA                                YEAR 9               LESSON 5
HD1.5                   INTERPRET AND DISCUSS

Objectives               Interpret graphs and diagrams and draw inferences to support or cast doubt on initial
conjectures; have a basic understanding of correlation.
   Compare two or more distributions and make inferences, using the shape of the
distributions, the range of data and appropriate statistics.
   Communicate interpretations and results of a statistical enquiry using selected
tables, graphs and diagrams in support, using ICT as appropriate.

Starter            Interpret data in a compound bar chart.
For example:
Vocabulary
Compound bar chart
Prediction
Resources
OHT of compound bar
chart (pg 268
Framework Supp.)

How has the method of travel changed over the last 20 years? Using the data in the graph,
predict what the results will look like for this year.
What about next year? In 10 years?

Main activity          Assessing explanations:
Pupils assess other people’s answers in test conditions.
Vocabulary
Select a question and six brief explanations written under test conditions from RE test
responses (CD-ROM). Display or distribute these to the class. Explain that three answers
would gain full marks and three would not. One of each is already identified.
Resources
Together with the pupils, ‘mark’ the remaining answers, showing why some are deficient and
RE Review Partner       how they should be improved. Correct and incorrect responses are identified for teacher use
OHT of RE Annotations   on RE correct responses (CD-ROM).
(pdf)

Plenary            Discussing and revising
Pupils evaluate each others’ explanations.
 Select an appropriate question. Ask pairs of pupils to write their joint explanation on
whiteboards, and then join with another pair to discuss and evaluate the two responses.
Guidance on The role of the review partner (CD-ROM) will help here.
 Tell the four to agree a final form of the explanation in the light of their discussion.
 Select one or two examples, discuss the explanations with the class and ask pupils to
explain how their discussions improved their writing.
HANDLING DATA                                 YEAR 9               LESSON 6
HD1.6                   INTERPRET AND DISCUSS

Objectives               Interpret graphs and diagrams and draw inferences to support or cast doubt on initial
conjectures; have a basic understanding of correlation.
   Compare two or more distributions and make inferences, using the shape of the
distributions, the range of data and appropriate statistics.
   Communicate interpretations and results of a statistical enquiry using selected
tables, graphs and diagrams in support, using ICT as appropriate.

Starter            Interpret data in a population pyramid. For example, discuss differences in the male and
female populations of different countries.
Vocabulary
Population pyramid
Resources
OHT of population
pyramid (Pg.269
Framework Supp.)

Main activity          Continue with:

Vocabulary              Assessing explanations:
Pupils assess other people’s answers in test conditions.
Select a question and six brief explanations written under test conditions from RE test
Resources               responses (CD-ROM). Display or distribute these to the class. Explain that three answers
RE Review Partner       would gain full marks and three would not. One of each is already identified.
OHT of RE Annotations   Together with the pupils, ‘mark’ the remaining answers, showing why some are deficient and
(pdf)                   how they should be improved. Correct and incorrect responses are identified for teacher use
on RE correct responses (CD-ROM).
During this lesson provide an A3 copy of one A4 page of the pupil’s scripts. Their
annotations in large writing will be used in the plenary.

Plenary            Review of lesson 6 followed by a review of the unit. This should take approximately 20
minutes.
Display Handling Data Cycle poster. Ask pupils for their ideas about each part of the cycle and
why the process is cyclical. Refer to Specify, plan and collect, what activities did we do?
Take feedback and discussion. Display pupil’s work and encourage them to explain the key
features. Repeat for Process and represent. Choose some good examples of the A3
annotations, and display and discuss.
Explain that we will return to this topic area after the SATs. We will be doing a Handling Data
Project in preparation for our Year 10, KS4 coursework.

Remember             Handling data is described by the cycle shown in the diagram.

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