IB Laboratories
Student Guide for Laboratory Reports
& IB Internal Assessment
From Mr. Collins
Quick Guide to Lab Report Sections
 WRITE ON ONE SIDE OF PAPERS ONLY! NO BACK-TO-BACK!
 SHEETS ALL SAME SIZE (8-1/2 X 11) WITH ONE STAPLE!
 USE THE HEADINGS AND SUB-HEADINGS SHOWN BELOW AND
ASSEMBLE IN ORDER
I.
LAB COVER SHEET with all handouts originally provided to you.
II.
DESIGN






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Research Question: define the problem.
Hypothesis: prediction of what should happen and why (theory)
Variables: identify & explain
Apparatus & Materials: list and/or diagram; rationalize quantities used.
Method / Procedure: how experiment was conducted & data collected
Control of Variables: how were key variables controlled?
Safety Considerations
III
DATA COLLECTION AND PROCESSING
 Data Tables: quantitative data and qualitative observations. Clear, legible,
includes units and uncertainties.
 Calculations of results: show and explain all equations & calculations.
 Graphs (if applicable): titles, axes labeled with units, best-fit lines/curves.
 Error Analysis and Uncertainties: For quantitative result labs
IV
CONCLUSIONS AND EVALUATION
 Conclusions: was hypothesis supported? compare w/literature values
 Limitations to the Conclusions: how reliable?
 Limitations to the Experiment: identify key sources of error & limitations
 Suggestions for Improvement
From Mr. Collins
How is IB Lab Work Graded? (IB Internal Assessments)
1. Your final IB score (1-7) in the IB Chemistry course is based upon how you perform on two
kinds of assessments: the end-of-course IB exam (called an “external assessment” because it
is made up and scored by IB) and your performance throughout the course on laboratory work
(called “internal assessments” because they are scored by your teacher). The end-of-course
exam will count toward 76% of your final score; the labwork 24%.
2. Your teacher will assess your lab reports using very strict IB criteria, which are used by all IB
science teachers world-wide. To make sure that everyone is following the rules and applying the
criteria correctly, all schools must send samples of student lab reports to IB for monitoring. If a
teacher is being too hard or too soft, that teacher’s marks which were awarded to students
will be adjusted accordingly—up or down.
In late March of your senior year, IBO will randomly select students by name for
sampling. If you are selected, we must send in your lab portfolio for evaluation by an
IB moderator. So you must make sure that your lab portfolio binder is kept up to date,
with no missing reports.
3. All IB science lab reports are graded using five criteria. They are:
Design
Data Collection & Processing
Manipulative Skills Personal Skills
Conclusions & Evaluation
4. Most labs will require you to write up only two or three of the report sections. Only a few
labs will require a write up and assessment of all five criteria.
5. Each of these criteria is further divided into two or three parts. When your teacher grades
your lab report, he/she will determine whether you met each aspect completely, partially, or not
at all (c, p or n). This will then determine what numerical score (0 up to 6) you will receive
for the criterion (see the IA Internal Assessment Matrix found on the last pages of this guide).
6. In the spring of your senior year, your teacher will review your portfolio and the marks you
have achieved against each of the five criteria. For Design, DCP, and C&E your top two scores
from all your labs (12 pts max each: 36pts max total) will be added together to your score
from MS (0 – 6) and PS (0 - 6). This will give you your mark for the Internal Assessment.
The highest possible lab score you can achieve is 48. Your scores will be recorded on a special
IB form (the PSOW/4 form) which will be maintained in the front of your portfolio.
From Mr. Collins
How is My Laboratory Work Graded ?
(Continued)
7. In addition to this formal IB Internal Assessment scoring system, your lab work will also be
graded for your regular course grade using the Prince William County scale. So you will also
receive a second score on each lab report for this grade. Your teacher will inform you how many
points each lab will be worth toward your regular course grade, along with tests, quizzes,
homeworks, etc.
8. The following pages show you in detail what is contained and expected in each section of the
lab report, and what you are required to do against each of the eight criteria. The bold-faced
underlined labels show you how to organize your reports. Your teacher will discuss these with
you frequently as the course goes on.
Refer to the following pages often throughout the course as you write your
laboratory reports. They will help you tremendously!
From Mr. Collins
TIPS AND SUGGESTIONS FOR WRITING UP DESIGN
Research Question

This section of the report is a paragraph that discusses the objective or purpose of your
investigation clearly and specifically. It answers the question, “What problem was I given in
this lab, and how do I intend to solve it?” To assess Planning (a) in a lab, the teacher cannot
give you detailed information and guidance. Instead, you’ll be given a general, open-ended
problem such as “Investigate the factors that affect X”. You must do some thinking to
recognize the nature of the problem that has been set, the factors (variables) that will affect
the outcome, and how they affect it (the hypothesis). So if a general question has been
posed, make it more specific and relevant to your individual experiment. Discuss how you
intend to approach the problem. Note: If you simply paraphrase and repeat the problem
as provided by the teacher, you get a "not at all" for this section!
Hypothesis(es)

A hypothesis is like a prediction. It will often take the form of a proposed relationship
between two or more variables that can be tested by experiment: “If X is done, then Y will
occur.” (Examples: “The pressure of an ideal gas will be inversely proportional to its
From Mr. Collins


volume if the temperature is held constant” or “The rate of the reaction should increase if the
temperature and/or the concentration is increased”).
You must also provide an explanation for your hypothesis. This should be a brief discussion
(in paragraph form) about the theory or “why” behind your hypothesis and prediction. For
example, why should raising the temperature of a reaction increase the rate? Why does the
pressure of the gas increase when the volume decreases? (Notice that if you omit the
explanation, you can only earn a score of “partial” on this second aspect).
Include balanced chemical equations if necessary to explain your hypothesis.
Variables

Variables are those factors that might influence the outcome of the experiment. You should
identify and list all reasonable variables, and briefly state why each one is relevant. Then
identify which variable(s) is/are independent variables (ones that you will manipulate and
change) and which are the dependent variables (the ones that will respond to what you did).
The remaining variables must be controlled.
Apparatus and Materials
You can do one of two things, (or combine both), depending on the experiment:


Make a diagram or sketch of your experimental setup, and label the items. Be as specific as
possible. (Example: “50 mL beaker” instead of “beaker”).
List the materials (chemicals, solutions) you used. The lab might require you to decide how
much of a substance or a solution to use. If so, you must state your reasoning or show the
calculations to justify your choice.
Method/Procedure
 Write the method (procedure) that you are going to use (or that you did use) in the
experiment. This might be in the form of a paragraph summarizing what you did.
Alternatively, you could make a bulleted list of step-by-step directions.

Provide enough detail so that another person could repeat your work by reading your report!
(But you don’t have to go into detail about standard, well-understood actions such as
measuring a temperature with a thermometer, weighing out a substance, etc.).

Don’t be repetitive! If you are doing several experiments using basically the same
procedure, don’t repeat yourself. Outline a basic procedure, then simply state what changed.

If you do something in your procedure to minimize an anticipated error, mention this as well.
(Example: “Carefully rinse the buret before filling it so water inside doesn’t affect the
concentration of the solution”).

In your method, clearly state how you will collect data. What measuring device will you use,
what data will you record, and when? Or what qualitative observations will you look for
(such as a color change) and what will you do when you see this happen?
From Mr. Collins

The procedure must allow collection of sufficient relevant data. This means that you should
consider doing more than one trial where appropriate. This is especially true when doing
things like titrations.
Control of Variables

Refer to the variables that need to be controlled. State clearly how each of these variables
will be controlled. (For example, if the temperature must remain constant, figure out how
you will do this and state it. Perhaps you might use a water bath that is maintained at a
certain temperature. Or perhaps the atmospheric pressure must remain constant. In this case,
you might read the laboratory barometer before and after the experiment, or do the
experiments all on the same day so atmospheric pressure doesn’t vary.
Safety
 List any safety precautions that must be taken or were taken during the lab. Examples:
o “Wear safety goggles throughout the experiment”
o “Be cautious in using strong acids/bases. Rinse off spills with water immediately.”
o “Don’t handle sodium metal with your fingers b/c it can react with moisture on skin”
o “Allow the crucible/test tube to cool after heating. Hot glass looks like cold glass.”
o “Avoid breathing vapors of the hydrocarbon liquids.”
From Mr. Collins
TIPS AND SUGGESTIONS FOR WRITING UP DATA COLLECTION AND
PRECESSING
DATA COLLECTION

The integrity of raw data is important from a scientific standpoint and from an ethical
standpoint! You must follow these procedures when recording data:
o Raw data and observations will always be recorded in a bound laboratory notebook.
o Data will be recorded in blue or black ink, not pencil. Errors can be lined out.
o Your instructor may require you to obtain his initials on your data sheets prior to
leaving the lab.

Your lab report must contain the original hand-written data sheets that you recorded in
the lab. If necessary, tape the sheets to a standard-sized sheet of paper before assembling
your lab report so that all sheets in the report are the same size.

There are two aspects to Data Collection. You must collect and record raw data accurately.
But equally important—you must present the raw data so the reader can easily interpret it.
This means it must be organized and legible.

The best way to collect and present data is by using Data Tables. If Data Collection is being
assessed in a lab activity, your teacher will normally require you to make a data table before
you begin the lab. You might use one Table, or more than one.
From Mr. Collins

Give an identifying title to each Data Table.

Qualitative observations are just as important as quantitative measurements! Make sure you
take note of and record the physical characteristics of substances or solutions involved in the
reactions, their color changes, the evolution of a gas, whether something got hot or cold, etc.
Some researchers like to organize these qualitative observations in a separate Data Table—
intermingling them with quantitative data is often confusing and hard to read.

A measurement without units is meaningless! Make sure you include them: g, cm, mL, kPa,
etc. If you show the units in a column heading of a Data Table, you do not have to write
them again after each number in the table.

All measurements have uncertainties and you must indicate them in your Data Tables. This
is best done by paying attention to significant digits, and by using the “plus-or-minus”
(+/-) notation. Examples:
o Mass of a penny on a centigram balance: 3.12 g (+/- 0.01 g)
o Temperature using a typical lab thermometer: 25.5 oC (+/- 0.2 oC)

Just as for units, in a column of data you can show the uncertainty in the column heading and
then you don’t have to keep re-writing it for every measurement in the table.

The precision (+ or -) of common laboratory equipment is shown in a table near the back of
this handbook.
DATA PROCESSING
This is the part of the report in which you take your raw data and transform it into results that
answer (hopefully!) your research question. Here you will show the calculations that give you a
numerical result. Or it may involve making a graph of some type to show a trend or a
relationship. It might involve both of these. But just as in Data Collection, there are two
important aspects: processing the data correctly, and also presenting the processed data
effectively and legibly so the reader can clearly see the results.
Calculations of Results

You will often have to show calculations. Use plenty of room; make sure they are clear and
legible.

To make your calculations easy to follow, precede each calculation with a phrase that states
what you are doing. (For example: “Calculate the molarity of the solution:”, then show the
actual calculation). Show the units and the formulas of substances in all calculations.

Pay attention to significant digits! Don’t lose accuracy by carelessly rounding off.
From Mr. Collins

Identical, repetitive calculations do not have to be repeated. Show one sample calculation
(labeling it as such) and then you don’t have to repeat it for all the trials but only show the
results obtained.

When calculating an average value from repeated trials, don’t average the raw data. Instead,
calculate a result from each trial. Then average the end results from each trial to get your
final experimental average.
From Mr. Collins
Experimental Errors and Uncertainties

When the objective of the lab is to obtain a numerical result, you must also compare your
experimental result with the literature value and determine the percent error. You then must
analyze whether the error is due to random error alone, or whether systematic error in your
experiment was also present. This process is called error analysis.

A self-teaching lesson for dealing with uncertainty in measurements and conducting error
analysis is contained in the back pages of this guide.
Presentation of Results

There are many ways to present and display results. Tables and line graphs are used very
often in science. But in some situations, other techniques might also be good. Consider the
use of bar charts, pie graphs, or histograms.

Graphs must be done on graph paper—either hand-drawn or done with computer assistance.
In all cases, the axes of graphs must be clearly labeled with the variable and the units used.
Additionally, each graph must have a title that states what the graph depicts. (Examples:
Rate of reaction vs Concentration of Reactant; Pressure vs Volume of Carbon Dioxide).
o Line graphs may show the degree of uncertainty in plotted points by using error bars.
o Your teacher will give you further instructions on graphing techniques.
From Mr. Collins
TIPS AND SUGGESTIONS FOR WRITING UP CONCLUSIONS/EVALUATION
Conclusions

One (or more) paragraphs in which you draw conclusions from your results, and whether or
not your conclusions support your hypothesis. Your conclusion(s) should be clearly related
to the research question and the purpose of the experiment. You must also provide a brief
explanation as to how you came to this conclusion from your results. (In other words, sum
up the evidence).

If a numerical value or result is the object of the lab, you must compare it with the literature
value and if possible, calculating a percent error.
Limitations to Conclusions

Considering how large are the errors or uncertainties in your results, how confident are you
in the results? Are they fairly conclusive, or are other interpretations/results possible?
From Mr. Collins
Limitations of the Experimental Procedure

Identify and discuss significant errors and limitations that could have affected the outcome of
your experiment. Were there important variables that were not controlled? Were there flaws
in the procedure you chose which could affect the results? Are measurements and
observations reliable? Is precision unknown because of lack of repeated trials?

Your emphasis in this section should be on systematic errors, not the random errors that
always occur in reading instruments and taking measurements. You must identify the source
of error and if possible, state how it probably affected your results.
o Acceptable Example: “Because the simple calorimeter we used was made from a tin
can, some heat was lost to the surroundings—metals conduct heat well. Therefore,
the value we obtained for the heat gained by the water in the calorimeter was lower
than it should have been.”
o Unacceptable Examples: “The test tubes weren’t clean” “Human Error”
Suggestions for Improvement

Suggest improvements or fixes for the weaknesses you identified in the previous section.
These suggestions should be realistic, keeping in mind the type of equipment normally found
in high school or college general chemistry labs. Suggestions should focus on specific
pieces of equipment or techniques you used. (Vague comments such as “We should have
worked more carefully” or “I should have been given a better calorimeter” won't cut it!
From Mr. Collins
Manipulative skills will be be assessed for certain experiments that require you to come up with
a numerical result, or to identify an unknown. Obviously, your score in this area will be largely
determined by whether you “hit the mark”. It is also determined by your safety considerations.
A student who must be constantly reminded to wear goggles, for example, will not achieve high
scores in this area! Horseplay or fooling around in lab will also earn a lower score in this area.
From Mr. Collins
Your personal skills will be subjectively assessed by the teacher (and your classmates)
during Group IV:
From Mr. Collins
Precision and Uncertainties for Common Lab Equipment
When you record a scientific measurement, the last digit that you record is understood to have
some uncertainty, and to be your best estimate. When reading non-electronic devices such as
rulers, thermometers, and glassware, the general rule of thumb is to "read between the lines"!
This means that you can estimate one more digit or decimal place than the device is marked.
But this rule does NOT APPLY to electronic equipment (such as a balance or electronic
thermometer) which gives you a direct digital readout. For these digital devices, your teacher
will provide you the precision of the instrument.
The following uncertainties apply to careful measurements made by a trained observer:
Length (common metric rulers): +/- 0.01 cm (or 0.1 mm)
Mass (electronic balances): always +/- one unit in the last digit. This means that a common
centigram balance is +/- 0.01 grams; a milligram balance +/- 0.001 grams.
Volumetric Glassware
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
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
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10 mL graduated cylinder:
25 mL graduated cylinder:
100 mL graduated cylinder:
500 mL graduated cylinder:
50 mL buret:
10 mL graduated pipet:
Fixed volume pipets (glass):
+/+/+/+/+/+/+/-
0.02 mL (always record to 2 decimal places)
0.1 mL (always record to 1 demical places)
0.5 mL (always record to 1 decimal place)
5 mL
0.02 mL (always record to 2 decimal places)
0.01 mL (always record to 2 decimal places)
0.2 % of the capacity (Ex: 25 mL = +/- 0.05 mL)
Beakers and Flasks: Approximately 5% of the capacity. (But of course, you would never use
one of these to measure a precise amount of liquid, would you?)
Thermometer
 (alcohol or mercury):
 TI CBL temperature probe:
+/- 0.2 oC
+/- 0.1 oC
pH Measurements


pH paper:
+/- 1 pH unit (pH paper gives a "quick and dirty" estimate)
TI CBL pH probe:
+/- 0.1 pH units (even though it reads out to 0.01).
pressure

TI CBL pressure probe: +/- 2 kPa (even though it may read out to decimal places)
From Mr. Collins
Treatment of Error and Uncertainty in Chemistry Measurements
How to do an Error Analysis—a self-teaching guide
1. In science, we are always seeking to better understand the world around us. We do this by
designing and carrying out experiments according to the scientific method. And in these
experiments, we are often concerned with measuring something—coming up with a numerical
value for some property or behavior we observe. Eventually, if we can interpret and make sense
of all these measurements, we might propose a scientific law that allows us to predict the values
in future cases without actually having to conduct the experiment each time.
2. But it takes work and effort, often trial and error, to design good experiments. And even in a
well-designed experiment, it is impossible to make absolutely perfect measurements. There are
two types of error or uncertainty that will always limit the precision and the accuracy of our
results. The two types are called random error and systematic error.

Random error comes from the measuring device itself and depends upon its precision.
All measuring devices produce some uncertainty in the last measured digit. We cannot
eliminate random error totally. But we can minimize it by using good measuring devices
and more importantly, reading them carefully and skillfully to as many significant digits
as they allow.

Systematic error refers to errors or limitations that can be avoided. They might be due
to an improperly calibrated instrument. Or perhaps we are not reading the instrument
correctly. Finally (and most often), perhaps our experimental method was flawed and
can be improved by more careful experimental design.
3. How to Deal with Error and Uncertainty—follow these four steps:
a. When recording your data, also record the precision (+/-) for all measurements due to
random error, depending on the measuring device (See previous page). You can do this
either by writing the +/- value after each measurement or by including the +/- value in the
heading of a data table column.
b. Do your calculations to obtain your experimental result.
c. Using the uncertainties in each data element, calculate the percent uncertainty in your
result that is due to random error alone. (See para 4 below).
d. Now take the literature value of the result and calculate the percent error between your
value and the literature value.
e. Compare the results of steps (c) and (d) to decide whether random error alone can
account for how far you were off the literature value, or whether systematic error also
affected your results.
From Mr. Collins
4. Calculating the Uncertainty of a Numerical Result

When you add or subtract data, the uncertainty in the result is the sum of the
individual uncertainties. Convert this sum to a percentage.
Example 1:
Mass of crucible + product:
Mass of empty crucible:
Mass of product
74.10 g +/- 0.01 g
- 72.35 g +/- 0.01 g
1.75 g +/- 0.02 g
The individual uncertainties are added to give +/- 0.02 g for the result. Converting to a
percentage, (0.02 g / 1.75 g) x 100 = 1 %. This is the percent uncertainty due to random error.
Note that the random error introduced by a centigram balance is very tiny when you are
weighing quantities of about 5 grams or more. However, the random error of the balance begins
to contribute a large uncertainty if you try to weigh a very tiny quantity.

For multiplication and division of data, the percent uncertainty in the result is the
sum of the percent errors of each measurement.
Example 2: A student did an experiment to measure the density of a liquid. He weighed an
empty graduated cylinder, placed a volume of liquid in the cylinder, and then weighed it
again.. Her data is shown here:
Mass of empty graduated cylinder:
25.64 g +/- 0.01 g
Mass of grad cylinder with liquid:
28.02 g +/- 0.01 g
Volume of liquid:
3.00 mL +/- 0.05 mL
Since density = mass/volume, the student calculates the experimental density value:
2.38 g / 3.00 mL = 0.793 g/mL
Suppose the literature value for this density is 0.809 g/mL. Then the percent error between the
student’s result and the literature value is [(0.809 - 0.793) / 0.809] x 100 = 1.98 %.
Can random error alone account for this difference? To find out, we must calculate the percent
uncertainty that is due to random error.
The mass of the liquid is (28.02 g - 25.64 g) = 2.38 g +/- 0.02 g
(Notice that the mass uncertainty is now +/- 0.02 g because we had to subtract two mass values)
What % uncertainty in the mass is this? 0.02 g / 2.38 g x 100 = 1 %
Similarly, the % uncertainty in the volume measurement is 0.05 mL / 3.00 mL x 100 = 2 %
To find the overall uncertainty of this density value, we simply add 1% (the mass uncertainty) to
2% (the volume uncertainty), for a total uncertainty due to random error of 3%.
This percent uncertainty is larger than the student’s overall percent error! This means that
random error alone can account for the difference between the student’s value and the literature
value. We can say that the student got the same value as the literature value, within the
limitations of random error. Systematic error, if present, did not appear to affect the result.
From Mr. Collins
Example 3: A student performs a calorimetry experiment to determine the amount of heat
transferred in an experiment. He takes the following measurements:
Mass of water:
100.00 g +/- 0.01 g (negligible uncertainty)
Initial temperature of water: 23.6 +/- 0.2 oC
Final temperature of water: 27.4 +/- 0.2 oC
Change in temp (T)
3.8 +/- 0.4 oC
(11% uncertainty)
His calculation would be:
Q = (mass) (T) (Cp of water)
Q = (100.00 g) (3.8 oC) (4.184 J /g oC) = 1589.92 J = 1.6 kJ
How should the student report the result? What is his uncertainty?
The balance uncertainty is negligible, and there is no uncertainty shown in the Cp value for
water. The biggest source of random error is the thermometer. Since the T value can be plus
or minus 11%, the overall result must also be plus or minus 11%, which is the sum of the three
uncertainties in the heat transfer equation.
Since 1.6 kJ x 11 % = 0.18 kJ
So the student should report his result as 1.6 kJ +/- 11%, or 0.18 kJ.
Suppose the literature value is 1.7 kJ. Looking at the student’s value, the discrepancy can be
explained purely by random error. The student’s result is the same as the literature value within
the limitations of his measuring device, since his value can be plus or minus 11%.
But what if the literature value was 2.4 kJ?. In this case, random error alone cannot account for
the discrepancy. Therefore, some systematic error must have occurred. It is this error that the
student should seek to identify and make some suggestions for eliminating it next time.
From Mr. Collins
IB INTERNAL ASSESSMENT MATRIX FOR LAB REPORTS
CRITERION
ASPECTS
Identifies and clearly states a focused problem or research
question. The key variables (independent, dependent, and
controlled) are selected and identified. The hypothesis
(prediction) is directly related to the research question and it
is explained (quantitatively where appropriate).
Design (D)
c
Data Collection &
Processing (DCP)
n
A realistic method A method that allows for the
that allows for the collection of sufficient relevant
control of the
data and excludes the
variables is
collection of irrelevant data is
designed.
designed.
Appropriate
apparatus/materials
are selected;
(diagrams may be
acceptable)
c p n
c p n
Raw data (qualitative/quantitative) is recorded appropriately, The raw data is
Data/results are presented
including units and uncertainties where necessary.
presented clearly appropriately and effectively;
and processed
where relevant, errors and
correctly to produce uncertainties are taken into
results that help
account.
interpretation;
where appropriate,
error analysis is
included.
c
Conclusions and
Evaluation
p
LEVEL
p
n
c
p
n
A valid conclusion (based on the correct interpretation of the The procedure
results), with an explanation, is given; where appropriate,
(equipment and
results are compared with literature values.
method) including
limitations or errors
in manipulation is
evaluated.
(Discussion of the
limitations of data
analysis may be
included).
c p n
c p n
From Mr. Collins
c
p
n
Suggestions to improve the
investigation following the
identification of weakness(es)
are stated.
ccc 6
ccp 5
ccn cpp 4
ppp cpn 3
cnn ppn 2
pnn
1
nnn 0
ccc 6
ccp 5
ccn cpp 4
ppp cpn 3
cnn ppn 2
pnn 1
nnn 0
ccc 6
ccp 5
ccn cpp 4
ppp cpn 3
cnn ppn 2
pnn 1
c
p
n
nnn 0
IB INTERNAL ASSESSMENT MATRIX FOR LAB REPORTS
CRITERION
ASPECTS
Follows instructions accurately, adapting to new
circumstances (seeking assistance when required).
Manipulative Skills
(Summative)
LEVEL
Competent and
methodical in the
use of a range of
techniques and
equipment.
Pays attention to safety issues.
ccc 6
ccp 5
ccn cpp 4
ppp cpn 3
cnn ppn 2
pnn 1
c
p
n
Approaches the project with self-motivation and follows it
through to completion.
Personal Skills
(Group IV Only)
c
From Mr. Collins
p
n
c
p
n
Collaborates and
communicates in a
group situation and
integrates the
views of others.
c
p
n
c
p
n
Shows a thorough awareness
of their own strengths and
weaknesses and gives
thoughtful consideration to their
learning experience.
c
p
n
nnn 0
ccc 6
ccp 5
ccn cpp 4
ppp cpn 3
cnn ppn 2
pnn 1
nnn 0
From Mr. Collins