T E C OOL H IGH S CHOOL
I
NTERNAL
A
SSESSMENT
R
ESOURCE
S CIENCE D EPARTMENT
Physics 1.1: 90935 Carry out a practical physics investigation that leads to a linear mathematical relationship, with direction
Resource Title: The Bouncing Ball
Credits: 4
T EACHER GUIDELINES
The following guidelines are supplied to enable teachers to carry out valid and consistent assessment using this internal assessment resource.
Teachers need to be very familiar with the outcome being assessed by Achievement Standard Physics 90935. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it.
Achievement
Carry out a practical physics investigation, with direction, that leads to a linear mathematical relationship.
Achievement with Merit
Carry out an in-depth practical physics investigation, with direction, that leads to a linear mathematical relationship.
Achievement with Excellence
Carry out a comprehensive practical physics investigation, with direction, that leads to a linear mathematical relationship.
This will involve:
 developing a method for collecting the data
 collecting primary data, with units, relevant to the purpose, based on the manipulation of the independent variable over a reasonable range and number of values
 drawing a graph, based on the data
 writing a conclusion that links the processed data to the identified trend on the graph
This will involve:
 controlling the variable(s) that could have a significant effect on the results
 using technique(s) that increase the accuracy of the measured values of the dependent (and independent, if appropriate) variable
 drawing a linear graph, valid for the data
 writing a conclusion that states the equation of the relationship
This will also involve writing a discussion that validates the conclusion. The discussion may include as appropriate:
 a justification for the accuracyimproving techniques used
 a reason that there is a limit to either end of the value chosen for the independent variable
 a justification why a variable needs to be controlled.
 a description of any difficulties encountered when making measurements and how these difficulties were overcome
 a link between investigation findings and applicable physics ideas
 a description of any unexpected outcomes of the processing of the results and a suggestion of how these outcomes could have been caused and/or the effect they had on the validity of the conclusion
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C ONTEXT / SETTING
This assessment activity requires students to collect, process, and interpret data for a practical physical linear relationship. The sample context for this resource is the relationship between the drop height of a ball and its rebound height.
‘With direction’ means that the teacher provides general instructions for the investigation in the form of a purpose (investigating the relationship between the drop height and rebound height of a ball), method (demonstrating the set-up of the practical experiment) and the equipment from which to choose.
Providing a method means that students are to be given direction (i.e. “you will be changing the height from which you drop the ball”) about the overall approach they should take; they are required to develop a procedure for carrying out the investigation.
The purpose of this activity is to investigate the relationship between the height a ball is dropped from and the height it rebounds up to. It is assumed, in theory, that if E p
= mgh, and all the energy is transferred from the dropping ball to the rebounding ball, then mgh drop
= mgh rebound
. As such, the rebound height (as the mass of the ball and the force of gravity acting on the ball remain constant) will equal the original drop height. However, in reality the ball will lose energy to heat transfer due to the effects of friction, and the ball will not regain the original height. The method is to drop the ball from a range of heights and measure how far back up the ball rebounds.
This activity requires students to complete the following tasks:
 Develop the procedure for collecting primary data relevant to the purpose i.e., the relationship between the drop height and the rebound height. The students should be given the opportunity to trial their procedure. A detailed stepby-step procedure must be included in their final report. This procedure must be based on the manipulation of the independent variable over a valid range of values with repetition to show reliability. Variables that could have a significant effect on results must be controlled and techniques used to increase the accuracy of the measured values of the variables.
 Collect and record data following their written procedure.
 Process and interpret results to enable a conclusion to be drawn. This may include averaging or using a graph.
 Draw a conclusion from the processed data that links to the purpose of the investigation, justify the choices made to increase accuracy and relate their findings to theoretical physics ideas.
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C ONDITIONS
The assessment task will take place over the time frame as follows:
Day 1 – introduce the task, read through the task sheets and model the experiment.
Day 2 – students independently develop their procedure.
Day 3 – students trial their procedure and make any necessary changes to their plan.
Day 4 – students carry out the procedure and collect their raw data.
Day 5 – students independently process the data and write up the report.
As this activity occurs across a period of time, student work should be collected after each lesson and returned to them as required to ensure authenticity. An NCEA Assessment Task Cover Sheet should also be completed by each student on completion of their investigation.
R ESOURCE REQUIREMENTS
Students will need to be provided with the materials and equipment required for trialling and carrying out the investigation. Each workstation will require as a minimum:
 two metre sticks
 masking tape
 one tennis or squash ball
P RIOR TEACHING
It is anticipated that this investigation will be part of a wider unit of work, which would include learning about the energy changes that occur in falling objects, the equation E p
= mgh, use of equipment and appropriate use of vocabulary, symbols and conventions.
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L INCOLN H IGH S CHOOL
Te Kura Tuarua o Waihora
I
NTERNAL
A
SSESSMENT
R
ESOURCE
S CIENCE D EPARTMENT
Physics 1.1: 90935 Carry out a practical physics investigation that leads to a linear mathematical relationship, with direction
Resource Title: The Bouncing Ball
Credits: 4
S TUDENT INSTRUCTION SHEET S
Introduction
This assessment activity requires you to carry out a comprehensive, practical physics investigation that leads to a linear relationship. The context for the investigation requires you to find the mathematical relationship between the height a ball is dropped from and the height that it rebounds to.
Achievement
Carry out a practical physics investigation, with direction, that leads to a linear mathematical relationship.
Achievement with Merit
Carry out an in-depth practical physics investigation, with direction, that leads to a linear mathematical relationship.
Achievement with Excellence
Carry out a comprehensive practical physics investigation, with direction, that leads to a linear mathematical relationship.
Purpose
You will develop a step-by-step procedure to determine the mathematical relationship between the
height a ball is dropped from and the rebound height it reaches; you will carry out your procedure, analyse or process the data, including stating the mathematical equation of the line of best fit and draw a conclusion from the data that links to the purpose of the investigation.
You need to justify any choices you made to increase the accuracy of your investigation and to justify your conclusion in terms of the processed data and the link between your findings and relevant principles of physics.
Method
You will be given the following equipment:
 two metre sticks
 masking tape
 one ball
This activity will be completed as follows:
Wednesday 18 th May – you will develop a step-by-step procedure to determine the mathematical relationship between the height a ball is dropped from and the rebound height it reaches.
Thursday 19 th May – you will be trialling your procedure and making any necessary changes.
Friday 20 th May – you will carry out your procedure.
Monday 23 rd May – analyse or process the data and draw a conclusion from the data that links to the purpose of the investigation.
Your teacher will collect all work in at the end of each lesson and return it to you as required. This is to ensure the authenticity of your work. In addition, one the last day you will be required to complete an
NCEA Assessment Task Cover Sheet.
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T ASK 1
D EVELOP A P ROCEDURE
Time Allowance: you have up to one class period on this.
Introduction
You are to develop a step-by-step procedure to determine the mathematical relationship between the drop height of a ball and its rebound height, using the equipment you have been provided with.
You will be given time to conduct trials to help you do this.
In this activity, you will need to review the equipment provided by your teacher and consider the key variables involved in this experiment.
Write down:
 the independent variable (the variable that is to be changed);
 the dependent variable (the variable that will be measured);
 how you will control any other variables (significant or relevant variables that will need to be kept the same to make your results more reliable).
Decide and record:
 how you will measure the dependent variable;
 any techniques you will use to make your results more accurate and/or reliable.
Write up your plan on the “investigation plan sheet” ( RESOURCE 1).
T ASK 2
C
OLLECT
& R
ECORD
R
ESULTS
Time Allowance: you have up to one class period on this.
Introduction
Carry out your procedure to collect data and record the results in a table, or other systematic way.
Remember to record any changes to your procedure and the reasons for the changes e.g., to increase accuracy or reliability.
Set up the equipment provided by your teacher. Using your method, collect data.
Record:
 your data, with units;
 any modifications you make to your method;
 any difficulties you encounter while gathering the data and how you try to overcome them. (These difficulties should not relate to mistakes you may have made when setting up or using the equipment.
If you make such mistakes, just fix them and carry on.)
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Do not throw the ball as you drop it. If you exert a force on the ball other than the force of gravity making it fall your experimental results may be invalid.
If you find that you need to change your plan then you must also change what you have written on your
investigation plan sheet.
T ASK 3
P
ROCESS
R
ESULTS
, I
NTERPRET
I
NFORMATION
& P
RESENT A
R
EPORT
Time Allowance: you have up to one class period on this.
Introduction
Process your results in ways that will help you reach a conclusion that is linked to the purpose of the investigation. This will usually involve some calculations (e.g. averages) and/or graphing to establish a relevant pattern.
Carry out your procedure to collect data and record the results in a table, or other systematic way.
Remember to record any changes to your procedure and the reasons for the changes e.g., to increase accuracy or reliability. Present a report on your investigation. This will include:
 your step-by-step procedure, including any changes made during your investigation
 the recorded and processed data, with relevant units
 a conclusion based on the processed data that links to the purpose of the investigation
 justification of the choices you made to increase accuracy during the investigation
 justification of your conclusion in terms of the processed data and the purpose of the investigation
 relating the findings of the investigation to applicable physics ideas
 using appropriate physics vocabulary, symbols and conventions throughout your report
Prepare your data as necessary to draw a graph with appropriate axes and plot the data.
Draw a line of best fit on your graph and calculate its gradient.
Using information from the graph, state the equation of the relationship between the independent and dependent variables.
Compile the information you have recorded into a report. Your report should include:

Your Investigation Plan Sheet altered to include any changes.

The aim of your investigation (to find the mathematical relationship between the height from which a ball is dropped and its rebound height);

Your method of gathering the data;

Your data, graph, and any working used to calculate the gradient;

The equation of the relationship that the graph line has established;

A discussion of this experiment.
The quality of your discussion and reasoning and how well you link this to the context will determine the overall grade. Your discussion should validate your conclusion. For example, your discussion could include:

A statement that explains why the particular accuracy improving techniques you used were necessary;

Reason(s) for your choice of the range of values for the independent variable (for example, why the range for the independent variable had an upper or lower limit);
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
For each controlled variable, a reason why control was necessary;

A description of any difficulties you had when making measurements and what you did to try to overcome these difficulties;

A description of any unexpected issue that arose when processing the data and how you dealt with the issue;

A link between your findings and relevant principles of physics.
M
ARKING
G
RID
Developing
a procedure
Collecting, recording and processing data
Judgements for Achievement Judgements for Achievement with Merit
A simple method is written Method states the accuracy improving techniques used
A range for independent variable is stated
Dependent variable stated
A valid range for independent variable is stated
Data is collected
Data is accurate
Key variables are controlled
Sufficient data is collected
Repeat data is collected and averages calculated
Judgements for Achievement with Excellence
Accuracy techniques are justified
Analysing data
Graph is plotted
Conclusion is given
Suitable graph is plotted with line of best of fit
Gradient of the graph calculated
Conclusion includes the mathematical relationship of graph
Discussion
Discussion statements relate analysing data with respect to related physics ideas
Discussion statements relate to developing method
Discussion statements relate gathering information
Grade N
All criteria within a column must be met
A M E
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Physics 1.1: 90935 Carry out a practical physics investigation that leads to a linear mathematical relationship, with direction Credits: 4
Resource Title: The Bouncing Ball
Resource 1: Investigation Plan Sheet
What is the purpose (aim) of the investigation?
Fair Test.
(a) Which variable will you be changing? (this is the independent variable)
(b) How will this variable be changed?
(c) Give a suitable range of values for this variable.
Fair Test.
(a) What will you measure (or observe) in order to get some data in the investigation? (This is the
dependent variable).
(b) Describe exactly how will you measure or observe this.
What other variables do you think are most important in this investigation and will have to be controlled to make it a fair test?
Variable How will it be kept the same, measured or controlled?
How will you ensure that your results are reliable?
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Use the information in the previous questions to write a detailed step by step method for carrying out your investigation.
Changes made after the investigation started.
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Results Table: Neatly record your results into a labelled table below.
Graph of your results: Draw a graph of your results on the graph grid below.
Mathematical relationship: Use your graph of results to calculate the mathematical relationship between the height of the dropped ball and the rebound height in the box below.
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Interpretation and Conclusion: Summarise the pattern or trend(s) of your results and say how this relates to the purpose of the investigation.
Evaluation:
Discuss the following:
 A link between your findings and relevant principles of science.
Discuss the following:

The reliability of your results. Do you think your results are reliable? Explain why.

Did the method work alright? How did it allow you to get valid results or data?
 The difficulties (if any) that you encountered and how you tried to overcome them.
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L INCOLN H IGH S CHOOL
Te Kura Tuarua o Waihora
I NTERNAL A SSESSMENT R ESOURCE
S CIENCE D EPARTMENT
Physics 1.1: 90935 Carry out a practical physics investigation that leads to a linear mathematical relationship, with direction
Resource Title: The Bouncing Ball
Credits: 4
M
ARKING
S
CHEDULE
Judgements for Achievement
Student lists steps or gives a reasonable description of how the experiment was carried out, with units. i.e. the method could be followed by most students and collects sufficient data – it doesn’t have to be perfect.
Units may be found from the table of results.
Independent variable is stated in the method or implied in results, with a range of at least three values given. i.e. the independent variable is the height the ball was dropped from. Units are cm or m.
Dependent variable stated in the method or implied in results
i.e. rebound height of ball. Units are cm or m.
Judgements for Achievement with Merit
Method states the techniques used to increase accuracy and evidence of accuracy improving techniques can be found in the results table. i.e. averaging repeated trials; parallax error correction; using significantly more than 4 height dropped values.
The results table has repeated data and averaged results.
Independent variable range provided is five or more, and is made of constant increases. i.e. the independent variable is consistent, e.g. 15cm 30cm 45cm
60cm 75cm 90cm etc.
Key variables that are required to be controlled are listed and how they are controlling is stated. i.e. Same ball used throughout the experiment is stated.
Judgements for Achievement with Excellence
As for Merit, plus at least one justification in the choices made to increase reliability is given. e.g. repeating and averaging removes impact of outlying results; OR viewing the investigation from the side reduces parallax error and the misreading of the ruler.
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At least 1 value of dependent variable is given for each independent variable value, including relevant units. i.e. at least one rebound height value has been provided for each drop height completed. Units are cm or m.
Measurements are reasonably accurate.
i.e. rebound values are all within 1.5cm of each other
Independent variable is plotted on one axis, dependent on the other. Axes are labelled with variable name and unit (evidence of units can come from above tabulated data).
Data is mostly plotted accurately.
Graph line drawn, relevant to the plotted data. i.e. Drop height is plotted on one axis, rebound height on the other.
Axes are labelled with variable name and unit (evidence of units can come from above tabulated data).
Data is mostly plotted accurately.
Graph line is straight and relevant to the plotted data.
Range of inputs used gives at least 4 useful values for dependent variable spread over a range that is reasonable for the equipment given. i.e. at least four drop heights over a constant, large range have been used.
Essential derived values are calculated. i.e. repeats have been recorded, and an average calculated for
each of the drop height values.
Graph also contains:
Drop height on x-axis, and rebound height on y-axis.
Appropriate scales that are easy to read, plus the graph covers a reasonable proportion of the graph paper.
A straight graph line is drawn that accurately fits the plotted points
A conclusion is given. Minimum evidence required is a statement that as the value of one variable increases, the value of the other also increases. i.e. Minimum evidence r equired is that e.g. “as the drop height increases, the rebound height increases.”
Gradient of the graph is calculated, using a valid method, with value given to a reasonable number of significant figures.
A conclusion is given and includes a correct mathematical relationship. Accept the equation if the intercept has not been included. i.e. rebound height = 0.57 x drop height (or whatever gradient has been calculated as)
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At least three discussion statements are given. Each statement should relate to a different bulleted point in the discussion section of the student instructions and should be a high quality statement that contains detail equivalent to that given in the evidence statements in the example below.
If any of the individual statements do not meet the quality requirement, two slightly lesser quality statements (not necessarily for the same bullet point) can be accepted in its stead.
Developing a method e.g. Need parallax minimisation when measuring the height because not possible to have the ball bounce along the scale of the ruler. OR Do lots of measurements because each bounce is hard to see and will have reaction time error.
Gathering information e.g. Minimum height was <e.g. 20cm> because height less than this gave bounce too small to be measured accurately.
Maximum height was <e.g. 200cm> because greater height would hit the roof or damage the floor or was greater than the two rulers combined, so could not be accurately measured. OR
Same ball used each time because different balls bounce different amounts. OR Bounce height hard to measure because of difficulty identifying peak height, line of be st fit didn’t go through origin but should have done because zero height gives zero bounce – ignored the intercept because it must have been
caused by inaccuracies.
Analysing data
Report explores related physics ideas (theoretical relationship vs. experimental findings) and validates or justifies variances. e.g. It is expected that the response for a collision with the floor will be linear and proportional to starting potential energy, where
PE = mgh. There will be some energy lost/work performed in deformation of the ball and the ball will not bounce up to exactly
the same height as the start point.
Grade N
All criteria within a column must be met
A M E
Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard. Evidence for each criterion may be presented anywhere in the report.
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