# Exam topics

General recommendations:

• Look for patterns (especially in quiz questions)
• What hasn't been assessed yet? (compare review sheet to quizzes)
• Think about what the class found difficult. This might be assessed again to measure improvement.
• Remember that definitions are important in mathematics
 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
 "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
 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
 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