# Expected Skills

Expected Skills

Campers at C&! come from different backgrounds and have a broad range of knowledge and skills. This is great — it keeps the camp dynamic and keeps the faculty on their toes!  Nevertheless, since we are presenting highly advanced material, campers will need to have certain background knowledge prior to camp in order to thrive.

There are three levels of “knowledge” we expect:

• Fluency — Campers should be able to perform these tasks effortlessly, without interrupting the flow of a more complex task.
• Competency — Campers can correctly perform these tasks, but it may require some thought and organization.  A camper with great organizational skills can get by with competency where others need fluency!
• Familiarity — Campers have seen many of these concepts before and perhaps were competent in the past.  They will be able to quickly pick these up with some reminders or practice.

Fluency skills will be expected of all campers.  The other expectations will vary according to age.

### Fluency

Campers need to be fluent in

• Basic arithmetic: multidigit addition, subtraction, and multiplication.  One-digit
into multi-digit division.
• The place value system and decimals.
• Adding and multiplying fractions.  Quick, what’s $-(\frac{7}{5} \times \frac{5}{4}) + 1$?
• Converting between fractions and decimals.
• Using exponents and roots.

### Competency

Campers should competently:

• Work with several variables represented by letters or names (not just x)
• Manipulate variables and expressions arithmetically.
• Use coordinates to specify a position on a plane or in 3D.
• Understand the meaning of “solving an equation” and be able to do it, at a minimum for simple one-variable equations.  Solve $5x + 10 = 25$. Or $x^2 + 9 = 25$.
• Use common geometric vocabulary.

### Familiarity

Campers should be familiar with most of the  following:

• Solving systems of linear equations ($3x + 4y = 25$, $4x + 3y = 24$)
• Graphing functions.
• Working with inequalities.
• Factoring polynomials with integer solutions. (What are the factors of $x^2 + 7x + 12$?)
• Finding the prime factorization of an integer (Write the prime factorization of 516.)
• Using a ruler and compass.
• Translating between expressions in English and algebraic expressions.
• Questioning why a mathematical process works.
• Reasoning logically, for example, solving logic puzzles.

If campers aren’t familiar with some of these, that is fine.  We do expect that they will be able to pick them up readily, with some practice.