Topics to study for exam 1 (all or almost all problems will be of the sort described below. Most but not all of these sorts of problems will appear on the exam)

Section 1:

• CCSS practice standards 1, 2 4 and Polya's problem solving steps. You may be asked to explain how a lesson or activity addresses the practice standards or to explain how Polya's problem solving steps apply to a problem or problem solving process. You will not be responsible for the exact wording of the standards.
• Finding patterns: you may be asked to solve a set of problems about a sequence such as those in the Spotting Numbers problems, or you may be asked how such a problem fits with the standards or problem solving process as in the first bullet.
• You may be asked to write or analyze true/false equations or missing number problems
• You may be asked to rewrite incorrect equation-like things to make them into a set of correct equations.

Section 2:

• You may be asked to identify some of the things students have to learn when learning to count and/or to identify some common errors children make when learning to count.
• You may be asked to identify the CGI problem type of a given addition or subtraction word problem
• You may be asked to write a word problem of a given addition or subtraction CGI type
• You may be asked to describe the typical process for solving a problem by direct modeling for problems of type JRU, JCU, SRU or CDU.
• You may be asked to identify which CGI problem types are easier or more difficult than others (of the problem types whose difficulty is clearly easy to compare)

Section 3:

• You may be asked to identify the CGI problem type of a given multiplication or division word problem
• You may be asked to write a word problem of a given multiplication or division CGI type
• You may be asked to describe the typical process for a child solving a problem by problem by direct modeling (multiplication grouping, measurement division grouping, partitive division grouping)
• The vocabulary terms for the 4 operations may be used without further explanation in any question (so you should study the terms well enough that you would understand a question such as: "what would be a good strategy to use to solve a subtraction problem where the subtrahend is 1, 2 or 3").

Section 4:

• 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 solve a problem/compute a math fact using a specified strategy*
• You may be asked to identify a strategy* from a description of solving a problem
• You may be asked to show several different ways of solving a single problem
• You may be asked to tell what facts a given strategy* is efficient for, or you may be asked to tell what strategies would be efficient for a given fact.
• 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)

*The strategies you should study are:

• 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