Collaborative Problem Solving & STEM TASKS

Day 1

Collaborative Problem Solving

Znorlian Numbers

Student Work

The Unusal Baker's Cake

The Baker charges $10 for the entire cake.
How much should the Baker charge based on the size?

Student Work

Day 2

Bridge Engineering

Engineers use math to predict how strong a bridge will be by looking at how its thickness and length affect how much weight it can hold. They create graphs and equations to show that thicker bridges can hold more weight, while longer bridges usually hold less. By testing and modeling with numbers, engineers can design bridges that are both safe and strong before they are even built

Increasing the thickness of a bridge significantly increases its strength, allowing it to hold more weight.
There is a strong positive relationship between thickness and breaking weight (Graph 1 & 2).
As the length of the bridge increases, its strength decreases, meaning longer bridges are more prone to breaking under weight.
The relationship between length and strength is negatively correlated, and the effect becomes more pronounced at greater lengths (Graph 3 & 4).
Both variables — thickness and length — have a measurable and opposite impact on bridge strength, with thickness enhancing and length reducing the load-bearing capacity.

Day 3

Collaborative Problem Solving

1001 pennies

Student Work

Tax Collector

Tax Collector is played like this: Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose. The tax collector must receive payment after every move. If you have no moves that give the tax collector a paycheck, then the game is over and the tax collector gets all the remaining paychecks.

The goal is to beat the tax collector.

Example:
Turn 1: Take $8. The tax collector gets $1, $2 and $4.
Turn 2: Take $12. The tax collector gets $3 and $6 (the other factors have already been taken).

Turn 3: Take $10. The tax collector gets $5.

You have no more legal moves, so the game is over, and the tax collector gets $7, $9 and $11, the remaining paychecks.

Total Scores:
You: $8 + $12 + $10 = $30.
Tax Collector: $1 + $2 + $3 + $4 + $5 + $6 + $7 + $9 + $11 = $48.

Questions:

Is it possible to beat the tax collector in this $12 game? If so, how? What is the maximum score you can get?

Bonus: What if you played the game with paychecks from $1 to $24? How about $1 to $48?

Student Work