Exam topics

General recommendations:

Exam I

Alternate algorithms

  • partial sums
  • equal-addition subtraction
  • counting-up subtraction
  • Austrian subtraction
  • partial products
  • lattice multiplication
  • line multiplication
  • partial quotients (aka. big 7)

Estimation

  • front-end estimation
  • clustering estimation
  • estimating with compatible numbers
  • rounding

Mental math

  • mental math compatible numbers
  • balancing
  • tack on trailing zeros
  • front-end mental math

Problem solving

  • find patterns (e.g., pizza problem)
  • easier related problem (e.g., pizza problem)
  • Gauss's method (e.g., handshake problem)
  • working backwards (e.g., overlapping sets)
  • matrix logic (e.g., logic puzzles)

Venn diagrams

  • union of sets
  • intersection of sets
  • set complement
  • problems involving overlapping sets
Exam II

"Add to" problems

  • add to - start unknown
  • add to - change unknown
  • add to - result unknown

"Take from" problems

  • take from - start unknown
  • take from - change unknown
  • take from - result unknown

"Put together / take apart" problems (PTTA)

  • PTTA - total unknown
  • PTTA - addend unknown
  • PTTA - both addends unknown

"Compare" problems

  • compare - difference unknown
  • compare - bigger unknown
  • compare - smaller unknown

Level 1: Direct modeling strategies

  • making / counting all
  • taking away
  • matching (for compare problems)
  • trail & error (for start unknown problems)

Level 2: Counting strategies

  • counting on
  • counting down
  • repeated (skip) counting

Level 3: Decompose / recompose

  • make a ten
  • doubles +/- n
  • rearrange
  • commutative property
  • distributive property

Equal groups

  • equal groups - product unknown (multiplication)
  • equal groups - partitive division
    (# groups KNOWN; # per group unknown)
  • equal groups - quotative division
    (# per group KNOWN; # groups unknown)

Remainders

  • extra (round up)
  • leave off (round down)
  • remainder is answer
  • fractional part

Multiplication with arrays/area

  • array - product unknown
  • array - factor unknown
  • area - product unknown
  • area - factor unknown

Multiplicative comparisons

  • comparison - multiplier unknown
  • comparison - bigger unknown
  • comparison - smaller unknown
Exam III

Numbers and place value

  • base 5
  • Egyptian numerals
  • Roman numerals
  • Babylonian numerals
  • Mayan numerals
  • base blocks
  • place value and other bases

Arithmetic

  • base 5 addition
  • base 5 subtraction
  • base 5 multiplication
  • base 5 division

Error patterns (aka. buggy algorithms)

  • recreate error pattern
  • describe error pattern

Integer models

  • number line
  • chip model
  • negative × negative = positive
Post Exam III

Prime factorization

  • factors & multiples
  • factor trees
  • prime factorization
  • greatest common factor
  • least common multiple
  • how many factors?
  • unique factorization theorem (aka. fundamental theorem of arithmetic)

Properties of operations

  • identity
  • inverse
  • commutative property
  • associative property
  • distributive property of addition and multiplication