Asaf Ferber

School of Physical Sciences

Math Club 24-25

Welcome to the 5th Grade Math Club!

Who We Are:
The 5th Grade Math Club is a fun and engaging space where students can explore the world of mathematics beyond the classroom. Led by Asaf Ferber, a math professor at UCI, the club focuses on building problem-solving skills, mathematical curiosity, and confidence in a collaborative environment.

Our Mission:
We believe that math is not just about numbers and equations—it’s about thinking critically, solving problems, and learning how to tackle challenges creatively. Our mission is to make math accessible and enjoyable for every student, no matter their skill level.

What We Do:

  • Weekly Math Challenges: Each week, students will tackle fun, interactive problems that push them to think outside the box. From puzzles to logic games, we cover a wide range of math topics.
  • Collaborative Learning: Students work together to solve problems, encouraging teamwork and communication.
  • Math Competitions (Optional): For those who are interested, we participate in local and national math competitions.
  • Supportive Environment: Our goal is to help students grow at their own pace, with guidance from experienced coaches and peers.

Meeting Information:

  • When: Every Tuesday from 2:30 PM to 3:30 PM
  • Where: Room D6

Join Us!
Whether your child is a math enthusiast or just beginning their math journey, the 5th Grade Math Club is a great place to learn, grow, and have fun with math. To join, please complete the permission slip and return it to me by email.

Volunteer Opportunities:
Parents, I’d love your help! If you’re interested in volunteering as a coach or assistant, please contact me.

 

A brief summary of our meetings:

Meeting 1 (September 10)

Competition Training We also practiced with problems from the 2016 Noetic Math Contest. You can find the file under: 2016f_grade5_all (password: noetic).

Infinite Memory Math Trick!

This week, we learned a fascinating math trick that makes it seem like we have infinite memory (ask your kids to show you!). The trick involves creating a set of cards labeled from 1 to 50 (or any other number), with each card having a seemingly “random” 8-digit number written on it. When someone picks a card and shares the label, we can instantly recall the 8-digit number—making it appear as though we have limitless memory!

Here’s the secret: instead of actually memorizing all the numbers, we use a clever encoding scheme that allows us to generate the 8-digit number in our heads on the spot! The idea is to use a simple mathematical rule to produce a number that looks random but is easy to compute mentally.

How it Works

Let’s walk through an example to demonstrate the trick. Say the chosen number is 23. We use the following steps to generate an 8-digit number:

  1. Multiply the chosen number by 4.
    For 23, this gives:
    23 × 4 = 92
  2. Reverse the digits.
    Reversing 92 gives:
    29
  3. Continue generating digits by summing the previous one or two digits, ignoring any tens (i.e., just use the last digit of the sum).
    So, starting from 29:

    • Next digit: 2 + 9 = 11 → write down the 1 (ignore the tens).
    • Next digit: 9 + 1 = 10 → write down the 0.
    • Next digit: 1 + 0 = 1 → write down the 1.
    • Next digit: 0 + 1 = 1 → write down the 1.
    • Next digit: 1 + 1 = 2 → write down the 2.
  4. Keep going until you have 8 digits.
    For 23, the final 8-digit number is:
    29101112

Now, when someone picks card 23 and asks for the 8-digit number, we can simply do this quick calculation in our head and confidently respond with 29101112—making it seem like we have memorized the number all along!

Example with a Different Number

Let’s try another example, say the number is 17:

  1. Multiply by 4:
    17 × 4 = 68
  2. Reverse the digits:
    68 becomes 86.
  3. Continue generating digits:
    • 8 + 6 = 14 → write 4.
    • 6 + 4 = 10 → write 0.
    • 4 + 0 = 4 → write 4.
    • 0 + 4 = 4 → write 4.
    • 4 + 4 = 8 → write 8.
  4. Final 8-digit number for 17:
    86440448

This simple method allows us to generate what looks like a random number, but it’s really just the result of a straightforward mental calculation. The trick is impressive because it appears as though we’ve memorized all these random 8-digit numbers, when in reality, we’re just computing them on the fly!

With practice, this trick becomes quick and effortless, and your kids can amaze their friends and family by appearing to have “infinite memory.”

Meeting 2 (September 17)

In this meeting, we enjoyed some pizza while working on math!

Competition Training  We focused on problems from the Math Olympiad for Elementary and Middle School (MOEMS). Specifically, we solved all the problems from Contest 1 and the first three problems from Contest 2 (2021). You can find all these problems in the following file: MOEMS 2021

Meeting 3 (September 24)

Competition Training In this meeting, we continued working on problems from the 2021 MOEMS and solved all five exams from that year. The kids did well overall, and I introduced them to solving systems of equations with two variables. You can create some examples at home to let them practice!

Math Trick In this meeting, I taught the kids how to construct an n×n magic square for odd values of n. A magic square is a square grid of numbers where the sum of each row, column, and diagonal is the same. This sum is called the “magic number.”

We also turned this into a fun magic trick, and here’s how you can recreate it or let your kids practice:

  1. Build a Magic Square:
    First, create a magic square using the “Siamese method” (or “de la Loubère method”) for odd n. The Siamese method allows you to fill an n×n grid with numbers in such a way that the sum of each row, column, and diagonal is the same—the magic number M. (An example of how to construct the square is included below).
  2. The Trick:
    Once you’ve built the magic square, the magic number M will be known. Now, here’s the “magic” part of the trick:

    • Ask someone to pick any number x they like.
    • Then, follow these steps:
      1. Multiply the chosen number x by 2.
      2. Add 4 times the magic number M (since you know M, you can quickly calculate 4M).
      3. Multiply the result by 5.
      4. Divide the obtained number by 10.
      5. Subtract the original number x.
      6. Divide the result by 2.

    Amazingly, at this point, the result will be the magic number M! You can then reveal to the person that no matter what number they chose, the sum of all rows, columns, and diagonals in the magic square will be equal to M—making it look like you’ve read their mind!

Example:

Suppose we create a 3 × 3 magic square, and the magic number M=15.

Now, let’s walk through the trick:

  • The person picks a number, say x=7.
  • Multiply 7×2=14.
  • Add 4M=4×15=60, so 14+60=74.
  • Multiply 74×5=370.
  • Divide by 10: 370/10=37.
  • Subtract the original number: 37−7=30.
  • Divide by 2: 30/2=15.

Voilà! The result is the magic number M=15, which is the same number that every row, column, and diagonal in your magic square sums to.

This trick cleverly combines the construction of a magic square with some basic arithmetic manipulations, allowing you to “predict” the result and amaze everyone!

Steps to Build an Odd-Order Magic Square:

  1. Start Position:
    Begin by placing the number 1 in the middle of the top row.
  2. Move Up-Right:
    After placing a number, move to the square above and to the right. If the move takes you outside the grid:

    • If you move above the top row, wrap around to the bottom row.
    • If you move right of the rightmost column, wrap around to the leftmost column.
  3. Occupied Square Rule:
    If the square you move to is already occupied, instead of moving up-right, move directly below the last number you placed.
  4. Repeat:
    Continue filling the numbers using these rules until the square is complete.

Example: 5×5 Magic Square

  1. Place 1 in the center of the top row.
  2. Move up-right to place 2. Since it’s outside the top, wrap around to the bottom row.
  3. Move up-right to place 3.
  4. Move up-right to place 4, but since the position is already occupied, place 4 directly below 3.
  5. Continue this process until the square is complete.

This method will work for any odd n, and the sum of each row, column, and diagonal will always be the same (the “magic constant”).

Question: The magic number of a magic square is the number M (for magic!) that represents the sum of each row, column, or diagonal. Can you find a formula for M that works for every magic square?

Meeting 4 (October 1)

Competition Training In this meeting, we continued solving problems from previous MOEMS contests. We solved exams 1 and 2 from the files below.

Math Trick We also spent some extra time discussing how to build a magic square and learned how to play the game of NIM. I’ll gradually teach the kids how to develop a mathematical winning strategy for NIM in the upcoming sessions.

I also showed few of the kids how to create a nice box from Origami.

2022 moem 4 2022 moem 3 2022 moem 2 2022 MOEM

Meeting 5 (October 8)

Please print the following files:

SR Math Club 2024 Week 5 Problem Set          SR Math Club 2024 Week 5 Match Problem Set

 

Meeting 6 (October 15)

Competition training In this meeting, we solved Exam 1 and part of Exam 2 from the most recent MOEMS contest.

Math Tricks We also learned a fun trick that brings us closer to earning the title “mathmagicians!” Here’s how it works:

  1. Ask someone to choose k numbers (for example, let’s use k = 3) and write them in a row.
    For instance, if they choose 2, 5, and 8, you write:
    2 5 8
  2. Then, ask the person to choose an additional k-1 numbers (here, 2 numbers) and write them as the first column, starting below the first chosen number.
    Suppose they choose 3 and 4. Now, the first column looks like this:
    2
    3
    4
  3. Fill in the rest of the k x k grid. In each row, the difference between consecutive numbers should match the difference between the corresponding numbers in the first row. So for this example, the grid would be:| 2 | 5 | 8 |
    | 3 | 6 | 9 |
    | 4 | 7 | 10 |
  4. Now, write down the sum of all the numbers on the main diagonal (top-left to bottom-right) on a piece of paper and hand it to the other person (no peeking!).
    In this case, the diagonal numbers are 2, 6, and 10, so you write 18 on the paper.
  5. Ask them to circle any number from the grid (say, 7), and then cross out all the other numbers in the same row and column as the circled number.
    For example, if they circle 7, you cross out 4 and 10 (from the same row and column).
  6. Continue this process until all numbers are either circled or crossed out.
  7. Once done, ask the person to sum all the circled numbers and tell you the total. Then, reveal the number you wrote earlier—TADAM! It matches!

Meeting 7 (October 22)

Competition training In this meeting, we solved the following exam from the NOETIC contest (password: noetic): noetic fall 23

The “Predict the Total” Trick

How It Works:

  1. Ask someone to think of any three-digit number.
    (For the trick to work, the first and last digits of the number must differ by at least 2. For example, 421 works, but 444 won’t.)
  2. Have them reverse the digits of the number.
    • Example: If they choose 421, the reverse would be 124.
  3. Subtract the smaller number from the larger number.
    • Example:
      421 – 124 = 297
  4. Reverse the result.
    • Example: The reverse of 297 is 792.
  5. Add this reversed number to the original result.
    • Example:
      297 + 792 = 1089

No matter what starting number they choose, the final answer will always be 1089! You can predict the result in advance and write it down on a piece of paper for a big reveal at the end.

Meeting 8 (October 29)

Competition training In this meeting, we solved the following exam from the NOETIC contest (password: noetic):

The “guess the missing digit” Trick

How It Works:

  1. Ask someone to think of any (say) 3 digit number.
  2. Have them add up all the digits of their number.
    For example, if their number is 527, they do 5 + 2 + 7 = 14.
  3. Ask them to subtract that sum from the original number.
    Using our example, 527 – 14 = 513.
  4. Ask them to choose any two digits from their answer. For example, assume they chose 5 and 3.
  5. Ask them to tell you the sum of the digits they chose. In our case, they will tell you “8”.
  6. Reveal the missing digit! Just say the smallest positive integer (can be 0) that if you add to the sum they gave you we get a multiple of 9. In our example, the missing digit is 1, becase 8+1=9.

Meeting 9 (Novermber 5): 

Heather took over this meeting.

November 12: No meeting. 

Meeting 10 (Novermber 19):

NOETIC contest!

During this meeting the kids will take the exam. Afterward, if you can allow them to stay a bit longer, I’ll go over the answers with them.