Bard Math CAMP 2024 Application
A Note for Parents

We welcome all interested students, encourage those who feel shy to join, andoffer scholarships to make attendance possible for students at all economiclevels. We value the diversity of our student body, especially with groups
traditionally underrepresented in the mathematical sciences.
∞February 29, 2024
Dear Parent,
Thanks for helping your child apply to our Creative and Analytical Math Program. We’ve
received the CAMP Interest Form. This packet is the formal application. Applications received by April 30th will receive full consideration. We expect to review all applications andinform you by May 15th whether your child is being invited.
Please print out this packet for your child and have them complete it by hand. They may
use additional pages, of course. When they are done, please scan1 and put together their work
into a single, neatly organized PDF document. Email it to us at <hello@bardmathcircle.org>.
Please do not help your child solve the problems!
But do make sure that they understand the instructions, including that we accept many
students who do not answer all the questions. Then leave the questions for your child topuzzle over. Taking a few days to ponder the problems is fine. What is more important indetermining suitability for the program is whether your child enjoys trying challenges or ifthey find them stressful or otherwise unpleasant.
If appropriate, you may include a note about how your child engaged with this packet,
and how you interacted with them throughout the process.
Sincerely,
BARD MAT H CIRCLE

1 We recommend that you use a scanning app such as TinyScanner. Such apps produce very readable PDF scans.

Bard Math CAMP 2024 Application
A Note for Students

February 29, 2024
Dear Student,
Thank you for submitting the CAMP Interest Form. Now it’s time for theMath Activity Packet, which is the formal application. Please print this out
and complete it by hand. You may use additional pages, of course. When
you are done, please scan and return it as a single, organized, PDF document.
Please solve the problems on your own! Use scratch paper andshow us your thinking!
You may ask your adult for help in clarifying the instructions. It is important to know that we accept many students who do not answer all thequestions. You may use a calculator on these activities, or write a computer
program if you know how. (Most CAMP students have no programming experience; that’s okay.) Take your time to puzzle over these problems. Taking
a few days to ponder is fine.
If you enjoy working on these problems, especially the parts that you can’t
answer in less than five minutes, then you will probably enjoy attending
CAMP this summer. If you don’t enjoy this application, then you might find
CAMP to be stressful or otherwise unpleasant.
Please consider asking your adult to write a note about how they were partof the application process for CAMP.
Sincerely,
BARD MAT H CIRCLE

Bard Math CAMP 2024 Application
Student Paragraph

Name:

Please tell us why you want to attend the Bard Math CAMP.
(Write 2–3 sentences, or more if you like. You may describe what math you have especially enjoyed figuring out, or
any information we should take into consideration.)Bard Math CAMP 2024 Application
Math Questions
Instructions: Solve the following problems, writing your answers clearly. We’re very interested in how you
solved them, so please write out your steps. Feel free to be creative, except don’t search the internet.
You may use a calculator and/or write a computer program. If you do, please let us know.
Feel free to use additional pages to write out your answers.

1. The numbers 3 and 5 are 2 apart on the number line and add to 8. What
two numbers are 2 apart on the number line that add to 5?

2. How many pairs of whole numbers, a and b, make the following equation
a true statement?
a+b=2024 2024+ab

For example, if you try a = 3 & b = 4, this would become
22024 2024+= 674 + 506
34
3
which is definitely NOT TRUE!
3+4=

List the pairs you find:a b

3. A bicyclist going downhill traveled 16 meters during the first second. For
the next 3 seconds, the distance covered was ¼ more than the distanceduring the previous second. They kept a constant speed for the rest ofthe ride. The total ride lasted 8 seconds. What distance did the bicyclisttravel?

4. A right triangle is a triangle in which one of the angles is a right (90◦ )angle. The sides of the triangle that form the right angle are called legs
and the side opposite the right angle is called the hypotenuse.

squareon leg 1

cut thesquares on legs
1 & 2 to forma square on
the hypotenuse

squareon leg 2

One way to state the Pythagorean
Theorem is that if you have a right triangle and build two squares whose side
lengths match the lengths of the twolegs, then they may be cut up and thepieces reassembled to form a square
whose side length is exactly the lengthof the hypotenuse.

Diagrams that show how to cut and reassemble the leg-squares are called“dissection proofs”. There are many ways to create them.
(a) Cut out the five shapes on the next page. (It’s okay to have someone
help you do the cutting).
On the page after that, there is a right triangle with squares drawn on
its legs and hypotenuse.
(b) Use the five shapes to build the large square that is on the hypotenuseof the right triangle. Trace and label the pieces with their numbers toshow how you formed the large square.
(c) Then use the same five pieces to build the squares on the legs. Traceand label them too.

2
1
3

45

90

Bard Math CAMP 2024 Application
Computer Science and Programming Experience

One of the great things about CAMP is the opportunity to write computer programs to further explore
mathematics. We understand that you may not have any previous programming experience, or you might bequite accomplished! Describe your Computer Science (CS) and Programming knowledge and background in
the following questions. If you don’t have any relevant experience, no worries! Just write “N/A” and leave
the rest blank. Or take a risk and fill in your best guesses. Please complete this section without checking
reference material, just use what you know in your head.

1. What programming languages have you worked with?

2. Describe your favorite programming achievement.

3. Variables. Feel free to respond N/A to the following questions if you are not sure, or if they do not apply:• What is a variable in CS?

• How do you declare a variable in your favorite programming language?

4. Write a short function to print out “Bard CAMP 2024” in your favorite
programming language.

Bard Math CAMP 2024 Application
Checklist

Applications received by April 30th will receive full consideration.
When you have completed this packet,□ Please organize your pages and scan them as one PDF document.
If you don’t have a flatbed scanner, we recommend a smartphone
app like Tiny Scanner, for both Android and iPhone. The results
are quite good.
□ Email the PDF to <hello@bardmathcircle.org>
Use the subject line:“2024 CAMP Math Activity Packet:<Student Name>”.

□ If things are going slowly and you won’t have this completed by April 30th, please send a friendly email to<hello@bardmathcircle.org>.