In the interests of being reasonable, I have split the exam into two parts, which you can take at the same time or you can take separately on separate times/days. The time limit for part 1 is 1 1/2 hours, and the time limit for part 2 is 1 hour. I've tried to be generous with the time limits, so that this is easily enough time for you to answer all of the questions that you are prepared to answer. If you fine my time limits/estimates to be off by a significant amount, please let me know.

Exam 1 part 1:

- Know what Diens principle of perceptual variability, Vygotzky's zone of proximal development, and what flexible and inflexible knowledge is. You may be asked to make and explain connections between these principles and CGI research and how children learn the basics of addition, subtraction, multiplication and division.
- Know the formal (balance) meaning of the equals sign, and what sorts of errors students typically make that involve the equals sign. Specifically review missing number problems and problems where several equations are strung together in a way that is incorrect (what I refer to as run on equations). You may be asked to write problems, correct run-on equations, or explain students understandings and misunderstandings that involve the equals sign.
- Be able to identify addition, subtraction, multiplication and division problems using the CGI problem type structure. I will provide tables of the names in case you forget a term.
- Be able to write addition, subtraction, multiplication and division problems given a CGI problem type.
- Know and be able to describe and compare the typical ways that students direct model to solve the problem types that have identified direct modeling strategies: JRU, JCU, SRU, CDU, Multiplication, Partitive Divsion, Measurement Division.
- You may be asked to identify which CGI addition or subtraction problem types are easier or more difficult than others (of the problem types whose difficulty is clearly easy to compare)

Exam 1 part 2:

- Given an addition, subtraction or multiplication problem, be able to explain several
*counting*and*derived facts*(not direct modeling) strategies that could be used to compute that fact. Know which strategies are most efficient for a given math fact. - Given one of the addition, subtraction or multiplication fact strategies listed here, be able to describe the strategy, and tell which facts that strategy is considered efficient for.
- Addition
- count on
- use doubles
- use 10/make 10

- Subtraction:
- count back
- count up to
- back down through 10
- build up through 10
- use addition

- Multiplication
- skip count
- double (for 2), double twice (for 4)
- count up from a known fact
- break down into known facts (distributive law)

- Division
- skip count up to
- use multiplication

- Addition
- You may be asked to explain how one would use strategies in teaching math facts
- You may be asked to tell some of the goals that one might be trying to achieve when using strategies in teaching math facts.
- You may be asked to show how to show an addition or subtraction fact strategy* using a number line or ten frame (where appropriate)
- You may be asked to write a fact family for a given math fact
- You may be asked to explain the commutative or distributive law (in a way similar to the homework assignment)