Applied Academics

In Dog Pounds

Animal Health Technologist
Applications of Mathematics 10

Lesson Idea by: Van McPhail, Okanagan Mission Secondary School,
Kelowna, B.C.

"Animal health technologists (AHTs) are referred to as the 'right hand' of a vet," says Cathy Hall-Patch, an AHT and instructor at Cariboo College's animal health technology program. "Technologists take X-rays, blood work, collect samples, set up IVs and catheters, prep animals for surgery, induce anesthesia and often assist the vet in surgery."

"It's very diverse," says Hall-Patch. "We're a radiologist, lab technician, surgical assistant and medical nurse all rolled into one … it's an exciting and challenging career."

Animal health technologists need mathematical skills to do their jobs and help their patients, notes Hall-Patch. "We use it for drug calculations, determining dilutions, fluid flow rates for IVs, calculating the nutritional needs of an animal and in research (statistics are required to figure out probabilities and rate distributions)."

It's very important to do these calculations properly -- an animal could die if you make a mistake. This is especially true when an animal health technologist is preparing anesthesia for an animal about to go into surgery.

With the class, discuss all the ways an animal health technologist would use math. Why is using math important for them? Brainstorm answers to the following questions:

  • Would it be important for an animal health technologist to know an animal's weight?
    Why?
  • Do they ever need to convert a number from imperial measure to metric?
    Why?
  • Is there any reason for a large dog to be treated differently medically than a small dog?
    Give some examples.

In an emergency, animal health technologists must be able to do some fast calculations in their heads. Try a few on your own.

Complete the first column in Chart A below. (Take your pulse, weigh yourself and measure your height.)

Review methods of converting values from the English (imperial) units into metric units, and vice versa. (See Cord Applied Mathematics Unit 3: Measuring in English and Metric Units.)

For example: to convert miles into kilometres, you must use a conversion unit that will allow you to cancel away the old unit and be left with the new, desired unit.

The conversion unit should be written this way:
Desired Unit
Existing Unit

For example, to convert 6 kilometres to miles, multiply it by the conversion unit. In this case the conversion unit is 0.62 miles per one kilometre.

6 km (0.62 mi. / 1 km.)

The two kilometre units cancel each other, and you are left with miles as the unit. Now do the multiplication.

6 (0.62 mi.)
= 3.72 mi.

6 kilometres is equivalent to 3.72 miles.

Do the conversions with your own personal data.

Chart A
MEASURE
CONVERT TO
pulse for 10 sec. pulse rate per min.
pulse for 15 sec. pulse rate per min.
pulse for 20 sec. pulse rate per min.
your mass in kg weight in pounds
  mass in g
  mass in mg
your weight in pounds mass in kg
your height cm height in m
  height in in.
  height in ft.

Back to the veterinary clinic. A woman has brought her border collie in for surgery. The vet has asked you to prep the dog and induce anesthesia. According to the owner, the dog named Hobbes weighs about 45 pounds. The anesthetic your clinic uses is called Pentothal. It comes in a powder form. You've already mixed it to create a two per cent solution. (Some clinics use a different dilution; it can range from two per cent to five per cent.)
20 mg
ml

To effectively anesthetize an animal, you need to give it 10 to 12 mg of Pentothal per kilogram of its weight.

Your clinic generally goes with a ratio of 12 mg
  kg

You've weighed the dog yourself to ensure his weight is 45 pounds. How many millilitres of solution do you need to give Hobbes? (Hint 1 pound = 0.45 kilograms)

Additional Calculations:

1. If the solution is mixed at a five per cent, how much of it is required?

2. Create a graph that shows the amounts of Pentothal needed for dogs ranging from 1 kg to 80 kg. Plot both the two per cent and five per cent solutions on the same axis.

3. Using the graph, calculate how much each of these dogs will need of either solution:

  • 8 kg
  • 27 kg
  • 46 kg

4. A dog food manufacturer recommends that you feed your dog 60 g of their food for every 5 kg the dog weighs. Create a graph comparing the dog's mass to the amount of food recommended.

Course/Grade: Applications of Mathematics 9/10
Curriculum Organizer(s):
- Problem Solving
- Applying mathematics to solving problems in other disciplines		 Curriculum Sub-organizer(s):
Patterns and Relations
- use properly annotated graphical representations to model data from physical situations.
- interpolate, extrapolate, and draw conclusions from graphs representing naturally occurring data
Prerequisites:
Math 9		 Resources:
None

Solution to Practice

  • Convert Hobbes' weight from pounds to kilograms:

    1 pound = 0.45 kilograms
    45 pounds = ? kilograms
    45 x 0.45 = ? kilograms
    20.25 kg

    Hobbes weighs 20.25 kg.

  • How many ml of solution do you need to give Hobbes?
    To anesthetize an animal requires 12 mg, so  
      kg  
    20.25 kg x 12 mg    
    kg = ? of mg of anesthesia required  

    243 mg of Pentothol is required.

  • The Pentathol is made up into a two per cent solution (20 mg/ml), so how many ml of solution is needed?
    243 mg  
    (20mg/ml) = amount of solution required

    12.15 ml of the Pentothol solution is required to adequately anesthetize Hobbes for his surgery.

"It's very important to think it through logically and do it step by step," says Hall-Patch. It's hardest to figure out the amount of solution that is required. "My students often stumble at that step."