Batch 2 - Class 90 - Owls & Voles (Population Simulation), Squarable Numbers

• Mirror Maze

• Place 5 times as many voles in the meadow as there are owls in your family. Write this starting number of voles on the population tracking page next to "Month 1"
• Each month your family of owls eats some voles (Put those in your sandwich bag to eat later). Each owl can eat as many voles as you she likes. Any owl who does not eat at least one vole will die of starvation. Your family needs to eat as much as possible over time so that you can produce baby owls.
• After eating time, you should record the number of voles eaten, and subtract from starting count to get to voles remaining.
• Next, voles in the meadow have babies. Each pair of voles will produce one baby. Record those, and add to the vole count.
• Repeat the process for 6 months. Now owls reproduce as per the table provided in worksheet. Note that BOTH requirements must be met for any column.

• What hunting strategy did your group use?
• Did your entire family survive for six months?
• Instructor Notes: Look for examples where the family dies out, or can't reproduce. Invoke kids to answer why that is happening and what can they change to correct this. Kids should realize the trade off between starvation and reproduction.
• How many voles did you collectively eat over six months?
• How many voles were left in the meadow?
• How will you modify your hunting strategy for the next simulation. How can your family eat as many voles as possible over six months without destroying the food supply?
• Try your strategy and record again. What are the results?
• Suppose your family had 3 owls. What is the smallest number of voles that the meadow could contain to feed the family of 3 owls sustainably? What if the family had 4 owls? 5 owls? What is the pattern? Why?
• What if each owl had to eat 2 voles each months? 3 voles each months? Can you find a formula now basis size of family and number of voles required to be eaten per month?

• Use Excel sheet to model the simulation, so that it gives you the same answer as your worksheet.

• What differences do you think exist in the real world? Research the facts to enrich your model.
• Owls need to eat more than one vole each month (Typically 6 each night)
• How many voles are required using earlier formula to support 4 owls?
• Voles usually have more than one baby at a time (4-12 each month)
• Voles born this month are not old enough to have babies next month (takes 37-47 days to mature)
• Owls do not confine themselves to a meadow (hunting range for a barn owl is about 2.7 square miles)
• Owls can eat other animals if vole population is low (lizards, birds etc)
• Voles can be eaten by other animals besides owls (foxes, hawks, cats, snakes, etc)
• Animals can die of old age
• A meadow can support only so many voles before they run out of food (typically 50 voles/acre can be supported)
• Owls may not have voles sitting around for them to eat - hunting failures
• Its harder for owls to find voles in winters than in summers
• Implement those changes in your worksheet/ Excel model.
• Can you find strategies where the vole population remains stable, declines or grows rapidly?

• Which numbers are squarable? Is there an easy way to tell if a number is squarable or not?
• Can you see patterns and strategies to discover new squarable numbers?
• For the numbers that are not squarable, can you prove that they are not?

• Build a refined model for the Owls and Voles simulation on Excel
• (Alice - 78) The forgetful White Kinight - The White Knight told Alice about a trial where there were three defendants, and
• All three defendants knew who was guilty, and made statements to that effect
• The first defendant accused either the second or the third defendant, but the White Knight couldn't remember which one
• The second defendant claimed to be the guilty one!
• The third defendant either accused himself, or he accused the second defendant, but the White Knight couldn't remember which one
• The guilty defendant lied. Either one or both told the truth, and the White Knight couldn't remember which one

• Answer: We are given that the guilty one lied. If B were guilty, he would have told the truth when he accused himself; therefore, B cannot be guilty. If A were guilty, then all three of them would have lied (because A would have accused either B or C, both of whom were innocent; B would have accused himself, who was innocent; and C would have accused either C, who was innocent, or A, who is innocent). But we are given that not all of them lied, so A can't be guilty either. So C was guilty.