Readiness Assessment

Add up the first few odd numbers and look for a pattern:

What pattern do you notice? Can you explain why this pattern happens? (Hint: try drawing dots in a square shape.)

Imagine cutting off each corner of a triangle with a straight line near each vertex. Draw what the resulting shape looks like.

How many sides does it have? What if you started with a square? A pentagon? A hexagon? Do you see a pattern?

You have a 4×6 chocolate bar (24 small squares) and want to break it into individual squares. Each break splits one piece into two pieces along a line.

What's the minimum number of breaks needed? Does the order or strategy of breaking matter? Why or why not?

Here's a sequence: 2, 5, 10, 17, 26, 37, ...

Take the differences between consecutive terms. Then take the differences of those differences. Keep going until you see something interesting.

What do you notice? Can you predict the next two terms of the original sequence? Can you find a formula?

The Fibonacci sequence adds the previous TWO terms. What if we added the previous THREE?

Write out the first 10 terms. The Fibonacci sequence has a famous property: the ratio of consecutive terms approaches ~1.618. Do the ratios in YOUR sequence approach something? What happens if you try different starting values?

Take a strip of paper and fold it in half repeatedly, always folding in the same direction. After each fold, unfold it completely and look at the pattern of creases (some fold up, some fold down).

After 1 fold, you get 1 crease. After 2 folds? 3 folds? 4 folds? How many creases after n folds? Do you notice any pattern in which direction the creases point?

(Actually fold paper if you can—it really helps!)

100 lights are in a row, all OFF. 100 people walk by:

After all 100 people pass, which lights are ON? Try small cases first (what if there were only 10 lights?). Look for a pattern—and try to explain why it happens.

Draw several connected graphs: dots (vertices) connected by lines (edges) with no crossings. For each graph, count:

Try at least 4-5 different connected graphs. Calculate V - E + F for each one. What do you notice? Do you think this always works?

An 8×8 checkerboard has two opposite corners removed, leaving 62 squares. You have 31 dominoes, each covering exactly 2 squares.

Can you tile the mutilated board completely with the 31 dominoes? Try it! If you think it's impossible, explain why—what's special about the removed corners?

Take any number and multiply its digits together. Repeat until you get a single digit. Count how many steps it takes—that's its "persistence."

Find the persistence of: 77, 123, 999, 277777788888899. Can you find a 2-digit number with persistence 4 or more? Is there any limit to how high persistence can go?

Start with any positive integer. If it's even, divide by 2. If it's odd, multiply by 3 and add 1. Repeat.

Try starting with 15, 27, and 31. What happens? Does every number eventually reach 1? (Nobody knows for sure!) Which starting number under 30 takes the most steps?

Three numbers are written on a board: (1, 2, 3). Each move, you pick two numbers, erase them, and write their sum and their absolute difference.

Your goal: get (0, 0, 0). Try some moves. Is it possible? Can you find something about the numbers that never changes no matter what moves you make?

Run this code in your head for inputs 1 through 6. What's it computing?

def mystery(n):
    total = 0
    for i in range(1, n + 1):
        total += i * i
    return total

# What pattern do you see?
# mystery(1) = ?
# mystery(2) = ?
# mystery(3) = ?
# ...

Calculate the outputs. Can you describe what this function computes in words? Bonus: Can you find a formula that gives the same answer without looping?

How would you explain to a 10-year-old what it means for a computer to "learn"? Don't use any jargon—use examples and analogies from everyday life.

Then: What's one important way that computers "learning" is different from how humans learn?

You want to build a program that predicts whether a movie will be a box office hit. What information about each movie would you collect?

List at least 6 things you'd want to know. For each one, explain whether it's a number, a category, or something else—and why you think it would help predict success.

These two functions LOOK almost identical, but one has a bug. Find it!

# Version A
def sum_list_a(numbers):
    total = 0
    for i in range(len(numbers)):
        total += numbers[i]
    return total

# Version B
def sum_list_b(numbers):
    total = 0
    for i in range(1, len(numbers)):
        total += numbers[i]
    return total

Test both with [10, 20, 30]. What's different about their outputs? Which one is "correct" and why might someone accidentally write the buggy version?

A hospital tests two treatments for a disease:

How is this possible? (Hint: think about how many mild vs. severe cases might get each treatment.) What lesson does this teach about analyzing data?

You've built a spam filter that blocks emails containing words like "FREE MONEY" and "CLICK HERE NOW". It works great!

But spammers are clever. Describe 3 different tricks they might use to get past your filter. For each trick, explain how you might update your filter to catch it.

A researcher finds that cities with more ice cream sales have more drownings. They propose banning ice cream to save lives.

What's wrong with this reasoning? What's actually going on? Can you think of another example where two things are correlated but one doesn't cause the other?

Imagine you have photos of handwritten digits (0-9) and want to teach a computer to recognize them. The computer can't "see" the way you do—it only sees a grid of brightness values.

Without just saying "use the pixels," describe 3-4 specific features a human might use to tell digits apart. Which pairs of digits would be hardest to distinguish, and why?

Someone wrote a function that's supposed to find the second-largest number in a list:

def second_largest(numbers):
    numbers.sort()
    return numbers[-2]

Come up with at least 3 different inputs that would cause this function to give wrong results or crash. For each, explain what goes wrong.

A video streaming site uses AI to recommend videos. It shows you videos similar to ones you've watched before. The more you watch a type of video, the more it recommends that type.

What problems might this create over time? Think about: (1) what happens to your recommendations, (2) what happens to content creators, (3) what happens to society if everyone uses this system.

An AI model was trained to detect skin cancer from photos. It worked great in the lab (98% accuracy!) but failed badly when used by real doctors.

Investigation revealed: the model had learned to look for rulers in the photos. Why might rulers have been in the training photos? Why would this cause the model to fail in practice? What should the researchers have done differently?

You've built a chatbot and want to know: "Can it actually understand what users mean, or is it just pattern-matching?"

Design a test with at least 3 specific questions or tasks that would help you answer this. For each test, explain: (1) what you'd ask/do, (2) what a "pattern-matching" bot might answer, and (3) what would prove the bot truly "understands."