Spike Prime + Wobbledogs STEM Worksheet: Pythagorean Theorem & AoPS Algebra for 15-Year-Olds

Instructions

You've decided to use your engineering and math skills to design the ultimate high-tech habitat for your Wobbledogs. Use your knowledge from Wobbledogs, your Lego Spike Prime set, and your AoPS math courses to solve the following challenges.

Part 1: The Triangular Play Zone

The main play area in your new habitat will be a right-angled triangle. One leg of the triangle is against a wall and measures 9 meters. The other leg is against a second wall and measures 12 meters. The third, longest side (the hypotenuse) needs a special laser fence that you will build and program.

1. Using the Pythagorean theorem (a² + b² = c²), calculate the exact length of the laser fence. Show your work.

Part 2: Spike Prime Gate Logic

The laser fence from Part 1 is controlled by your Lego Spike Prime hub. The hub runs a program to ensure only Wobbledogs with a high 'Stability' score (S) can temporarily disable the fence. The formula your program uses is S = 4(n + 3), where n is the number of legs a Wobbledog has.

1. The fence only deactivates if the Stability score S is greater than 36. Write and solve an inequality to find the minimum number of legs a Wobbledog must have to pass through the fence.

Part 3: Wobbledog Genetic Engineering

You've discovered a rare gene that gives Wobbledogs 'Lego-Compatible Paws,' which is very useful for your building projects. This gene has a 1 in 5 chance (or 20% probability) of being passed down from a parent.

1. You are creating a new 'Enrichment Food' that increases the original probability of the gene being passed down by 50% (of the original probability, not an additional 50 percentage points). What is the new probability, expressed as a percentage?


2. If you provide the 'Enrichment Food' to a group of Wobbledogs that then have 40 puppies, how many puppies would you mathematically expect to be born with 'Lego-Compatible Paws'?

Part 4: The Final Blueprint

Review your work from the previous sections. In the space below, sketch a simple diagram of your high-tech Wobbledog habitat. Be sure to label the triangular play zone with the correct dimensions you calculated in Part 1. Then, write one sentence describing another feature you would add and program using your Lego Spike Prime set (for example, an automated food dispenser, a ball launcher, etc.).

My Additional Spike Prime Feature:

__________________________________________________________________________________________________________________________________

__________________________________________________________________________________________________________________________________

Answer Key

Part 1: The Triangular Play Zone

1. Answer: The laser fence is 15 meters long.
   Work:
   • a² + b² = c²
   • 9² + 12² = c²
   • 81 + 144 = c²
   • 225 = c²
   • c = √225
   • c = 15 meters

Part 2: Spike Prime Gate Logic

1. Answer: A Wobbledog must have more than 6 legs, so the minimum whole number of legs is 7.
   Work:
   • The inequality is 4(n + 3) > 36.
   • Divide both sides by 4: n + 3 > 9
   • Subtract 3 from both sides: n > 6
   • Since the number of legs must be a whole number greater than 6, the minimum is 7 legs.

Part 3: Wobbledog Genetic Engineering

1. Answer: The new probability is 30%.
   Work:
   • Original probability = 20% or 0.20.
   • Increase amount = 50% of 20% = 0.50 * 0.20 = 0.10. This is a 10% increase.
   • New probability = Original probability + Increase amount = 20% + 10% = 30%.
2. Answer: You would expect 12 puppies to have the gene.
   Work:
   • Expected puppies = New probability * Total number of puppies
   • Expected puppies = 30% of 40
   • Expected puppies = 0.30 * 40 = 12

Part 4: The Final Blueprint

• The sketch should show a right-angled triangle with the two shorter sides (legs) labeled as 9 m and 12 m, and the longest side (hypotenuse) labeled as 15 m.
• The description of the additional Spike Prime feature will vary. Any reasonable idea, such as an automated toy, a sensor that measures food levels, or a programmable door, is acceptable.