Use the paediatric dosage formulae (Fried's rule for infants, Young's rule by age and Clark's rule by weight) and the IV flow-rate formula to calculate doses and drip rates by substitution

What this dot point is asking

Medication dosage is the real-world setting NESA uses to test one skill: can you substitute into a given formula? Adult medicines are tested on adults, so a child or infant needs a smaller dose, scaled down to fit their size. Standard rules do that scaling, and you are given the rules. The marks come from choosing the right one, putting each number in the right place, evaluating carefully, rounding sensibly and writing the answer with units. There are three rules for children and infants (the word for these is paediatric, meaning "for children"). The only decision you make is which rule matches the information you are given: Young's rule when you know the child's age in years, Clark's rule when you know the child's weight, and Fried's rule for an infant whose age is in months. A separate flow-rate formula handles intravenous (IV) drips, which feed fluid straight into a vein. It turns a volume of fluid and a time into a number of drops per minute. The deeper idea is that every one of these formulae is just the adult dose times a fraction that is less than one. Young's rule multiplies by $\text{age}/(\text{age} + 12)$, Clark's by $\text{weight}/70$ and Fried's by $\text{months}/150$, so each gives a child a sensible fraction of the adult amount. Marks are lost in three predictable ways: picking the wrong rule for the information given, forgetting to change the IV time from hours to minutes, and rounding a drip rate to anything other than a whole number of drops.

The answer

The four formulae, and what each symbol means

NESA gives you three rules for children and infants, plus one for IV drips. Read them as "the adult dose, scaled down".

Every symbol must be read correctly, because using the wrong rule or the wrong units is the fastest way to lose the marks:

• adult dose is the normal full dose for an adult, the quantity printed on the packet. It can be a mass in milligrams (mg) or a volume in millilitres (mL); the child's dose comes out in the same units.
• age in Young's rule is the child's age in whole years. It is used for children roughly $1$ to $12$ years old, and it appears in both the top and the bottom of the fraction.
• weight in Clark's rule is the child's mass in kilograms. The fixed number $70$ is an average adult mass in kilograms, so the fraction $\text{weight}/70$ is the child's share of a full adult dose. (You may see an older imperial form of Clark's rule, $\text{dose} = \dfrac{\text{adult dose} \times \text{weight in pounds}}{150}$, which uses a weight in pounds and divides by $150$ instead; the HSC uses the metric kilograms-over-$70$ version above, so use that unless a question gives a weight in pounds.)
• age in months in Fried's rule is used for an infant, where an age in years would be too coarse. The fixed number $150$ plays the same scaling role that $70$ plays in Clark's rule.
• volume in the flow-rate formula is the amount of fluid to be infused, in millilitres (mL).
• drop factor is a property of the giving set (the tube and chamber), measured in drops per mL; common values are $15$, $20$ and $60$. It is given in the question.
• time in minutes is the duration of the infusion. Infusions are usually prescribed in hours, so you almost always have to multiply by $60$ first.

Every result is a calculated dose, not a guarantee of safety: in real life a pharmacist or doctor checks it against the drug's own guidelines. For the exam, you choose the rule, substitute and evaluate.

The callout below maps each symbol of Young's rule to its meaning. The same idea applies to the other rules: identify what each pronumeral stands for before you substitute.

Choosing the right rule

The whole skill is matching the rule to the information given, then substituting. A quick decision guide:

• The question gives an age in years ($2$ to $12$ or so): use Young's rule, the only rule with $\text{age} + 12$ on the bottom.
• The question gives a weight in kilograms: use Clark's rule, the only rule with $70$ on the bottom.
• The patient is an infant and the age is in months: use Fried's rule, with $150$ on the bottom.
• The question is about an IV drip, giving a volume and a time: use the flow-rate formula, and convert the time to minutes.

Once the rule is chosen, the method is identical for all three child rules: write the formula, substitute the adult dose and the child's measurement, work out the top and the bottom, then divide. Keep full precision until the end and round only at the final step.

Working out an IV drip rate

An IV drip delivers fluid one drop at a time. The flow-rate formula turns the order (a volume over a time) into a setting the nurse can count: drops per minute. The schematic below shows the three quantities that feed the formula. The volume comes from the bag, the drop factor is stamped on the giving set (the tube and chamber), and the time is the duration ordered. The formula combines them into drops per minute.

For the bag in the diagram, $1000$ mL is to run over $8$ hours through a set with a drop factor of $20$ drops per mL. The time in minutes is $8 \times 60 = 480$, so the flow rate is $\dfrac{1000 \times 20}{480} = \dfrac{20\,000}{480} = 41.6\ldots$, which rounds to $42$ drops per minute. Because a drop is a whole thing, a drip rate is always rounded to a whole number of drops.

How exam questions ask about medication dosages

The wording tells you which formula to use:

• "Use Young's rule to find the dose for a child aged ...", or any dose question that gives an age in years, means substitute into Young's rule.
• "Use Clark's rule ...", or a dose question that gives a weight in kilograms, means substitute into Clark's rule.
• "Use Fried's rule ...", or a dose question about an infant with an age in months, means substitute into Fried's rule.
• "Calculate the drip rate / flow rate in drops per minute" means use the flow-rate formula; first convert the time to minutes, then round the answer to a whole number of drops.
• "A child is given a dose of ... ; find the child's age (or weight)" is a back-solve: put the known dose and adult dose into the formula and solve the equation for the remaining unknown.
• "To the nearest milligram / millilitre" is a rounding instruction; carry full precision and round only at the end.

Working out a drip rate stage by stage

The drip-rate calculation is short, but it is the one most students get wrong, because of the hidden unit conversion. The four stages below take the saline infusion from the worked example, $1000$ mL over $8$ hours with a drop factor of $20$ drops per mL, through to a whole-number flow rate. The key decision is converting the time to minutes before substituting.

Stage 1, list the three quantities. Read them straight from the question and the giving set: volume $= 1000$ mL, drop factor $= 20$ drops/mL, time $= 8$ hours. These are the bag, the chamber and the clock in the schematic above.

Stage 2, convert the time to minutes. The formula divides by the time in minutes, but infusions are ordered in hours, so multiply by $60$:

Stage 3, substitute and evaluate. Put the volume, drop factor and time-in-minutes into the formula, working out the top first:

Stage 4, round to whole drops. A drop is a whole thing, so a flow rate must be a whole number; $41.6\ldots$ rounds to $42$ drops per minute. If you had forgotten Stage 2 and divided by $8$ instead of $480$, you would have got $2500$ drops per minute, an impossible rate, which is the built-in check that you remembered to convert.

Why each rule gives a fraction of the adult dose

It is worth seeing why these formulae behave sensibly, because "explain" questions ask exactly this. Each rule is the adult dose times a fraction less than $1$. In Young's rule that fraction is $\dfrac{\text{age}}{\text{age} + 12}$. For a small child the top is much smaller than the bottom, so the fraction is small and the dose is a small slice of the adult amount. As the child grows older the fraction creeps towards $1$, so the dose nears the full adult dose. In Clark's rule the fraction is $\dfrac{\text{weight}}{70}$. This compares the child's weight with a $70$ kg average adult (the reference), so a child half that weight gets half the dose. Fried's rule, $\dfrac{\text{age in months}}{150}$, does the same job for the first months of life, when weight and age in years are both poor guides. Seeing the rules this way also explains why Young's and Clark's rules can give slightly different answers for the same child. One scales by age and the other by weight, and a child of a given age may be lighter or heavier than average.