## SDS Topics in Numerical Order

VISUAL PROBLEMS: 1000 – 1170
1000visual problems
1007networks, tracing
1008pattern completion (visual)
1009counting shapes in shapes
1010visual sequences, linear
1015visual sequences, 2-dimen.
1020geometry, informal
1026tesselation
1027partitions
1030connecting dots
1040trees in rows, planting
1050pennies, arranging
1060toothpicks
1070grabbers, trick quest, cheap shots
1080optical illusions
Three-Dimensional Problems: 1090 – 1095
1090three-dimen. problems, elem.
1093geoblocks
1094two-dimen. versions of 3-d prob.
1095missing faces of solids
Problems With Numbers, non-computational: 1100 – 1170
1100number patterns (cf. 2530, 2850)
1110numbers in patterns, arranging
1120cross-number puzzles
1130magic squares
1140pails and measuring
1160crypt-arithmetic
1170money/coins: change; value (cf. 1350, 2480)
LOGICAL DEDUCTION: 1180 – 1290, 3750 (Formal)
1180logic, analysis (classic brainteasers)
1190time, incl. calendars
1192calendars
1200rank ordering
1210hats: who has which hat on
1220sorting: Canadian owns the wombat
1230sorting, misc.: which is which
1232incomplete information charts
1240river crossing
1245Jeep problems
1250false coins (2-pan scales)
1255scales, two-pan
1260handshake problem
1270pigeonhole principle
1280liars/truthtellers
1290venn diagrams (cf. 2030)
ARITHMETIC: 1300 – 2022
Arithmetic with Whole Numbers: 1300 – 1342
1300numerals, writing; digits (pl. value, cf. 1720)
1305odd-even numbers
1307consecutive integers
1310adding and subtracting (cf. 1140)
1320multiplying and dividing (incl +, -) (cf. 1140)
1322remainders
1330squares & square roots (cf.1670)
1331squares (cf. 1670)
1332square roots
1333higher powers & roots
1334powers, higher
1335roots, higher
1340counting (how many)
1342counting: how many ways
Arithmetic with Real Numbers: 1350 – 1450
1350decimal arithmetic, incl. \$ (cf. 1170, 2480)
1360rational numbers
1365fractions (numerical)
1367fractions, equivalent
1368rational number arithmetic
1370percent, numerical (cf. 2410, 2290)
1380integers
1385integer operations
1390irrationals
1400rationalization
1410exponents, arithmetic using (cf. 2100)
1412exponents, laws of
1420approximation
1430arithmetic means, numerical (cf. 2452, 2860)
1440geometric means, num. (cf. 2454, 2870, 3590)
1450harmonic means, num. (cf. 2456, 2880)
Calculator use: 1460 – 1480
1460calculator, use of
1465calculator, broken key
1470calculator: heavy calculations
1480calculator pattern discovery
Pre-Algebra Word Problems: 1490 – 1550
1490bargains (cf. linear programming 2220)
1510living life (1/8 as boy , 1/4 as..)
1520wages
1530word problems, whole #'s (typical)
1540word problems, hard but (typical)
1550word problems: soft-core algebra
1560pickanumba
1600prime numbers
1610factors
1620prime factorization
1630factor, greatest common
1640divisibility
1650multiples
1660multiples, least common
1680factorials
1690diophantine equations
1700number bases
1710sums of integers
1720place value, prob about (cf.1300)
1730number theory proofs
1740modular arithmetic
1800measurement, elementary
1810dimensional analysis
1900flow charts
2010real number system, structure
Complex Numbers: 2020 – 2022
2020i
2021complex numbers
2022complex number operations
SYMBOL MANIPULATION: 2030 – 2390, 2745, 4100
2030sets (cf. 1290)
2040operations, prop. of ("new math")
2050numerical expressions: order of op.
2070formulas, inventing (alg. expr.) (cf. 2530, 2580)
2080symbol manipulation (cf. 2110)
2090linear expressions
2100exponents, algebraic expr. with (cf. 1410)
2110polynomial manipulation
2120factoring, misc.
2122factoring, cubics and higher
2130absolute value (cf. 2285)
2140ratio
2150rational expressions
2152rational expressions, evaluating
2160fractions, complex
2162fractions, continued
2190reciprocals
Equations and Inequalities, Linear and Quadratic: 2200 – 2288
2200equations, linear & rational
2210inequalities, linear, incl. abs. values
2211inequalities w/ abs. value
2220linear programming (cf. bargains 1490)
2250rational equations
2260cubics & higher degrees (cf.2680)
2285equations with absolute value (cf. 2130)
2288equations, misc.
2290proportions (cf. 2560)
2300equations, exponential
2305exponential growth
Systems of Equations: 2310 – 2340
2310equations, systems of, linear
2315equations, systems, 3 or more variables
2320equations, systems of, non-linear
2330equations, systems of, trig.
2340equations, systems of, misc.
2350inequalities, misc.
2360matrices, determinants
2361matrices
2365determinants
2370identities, algebraic
2380binomial coefficients
2385Pascal's triangle (cf. 2890)
2390binomial expansion
WORD PROBLEMS NEEDING ALGEBRA: 2400 – 2500
Translating among Words, Equations, Diagrams: 2405 – 2408
2405translating words to equations
2407translating words to diagrams
2408word prob. w/ diagrams
Standard and Unusual Word Problems: 2410 – 2500
2410percent, algebraic (cf. 1370)
2412percent from Henle
2420rates
2430valves
2440distance, rate, time
2442distances upstream/downstream
2445perimeter & area & volume
2447area (cf. 3410-3450)
2448volume (cf. 3650)
2450means arith, geom, harm (cf. 2860-80)
2452arithmetic means, algebraic
2454geometric means, algebraic
2456harmonic means, algebraic
2460ages
2465ages, complicated problems
2470profit and loss
2480money (cf. 1170, 1350)
2485pre-calc text alg. probs.
2490probs. w/ ans. a range of values
2500probs. misc. (consecutive integers)
FURTHER TOPICS IN ALGEBRA: 2510 – 2745, 2840 – 2990
2510operations, made-up, e.g. 2*3
2520relations
Functions: 2530 – 2630
2530functions, informal (cf. 2580, 2630, 2070)
2540domain, range
2542domain
2544range
2560variation, direct (cf. 2290)
2570variation, inverse
2580f(x) notation
2585functions, graphs of
2590absolute value function (see 2130, 2285)
2600greatest integer function
2610composite functions
2615functions, recursive
2620inverse functions
2630equations, functional
2640equations, polynomial
2650polynomials, real roots of
2660polynomials, complex &/or real rts.
2670remainder theorem
2680cubics (cf. 2260)
2700sequences & series (cf. 2860-80)
2701sequences
2702series
2710functions, exponential
2720optimization
Logarithms: 2730 – 2745
2730logarithms: manipulations
2735log to exp. form & v.v.
2740logarithms: change of base
2745equations, logarithmic
ANALYTIC GEOMETRY: 2750 – 2840, 3680 – 3723
2750coordinate plane
2760coord. geom: slope, dist, midpt. &c.
2761slope of line
2762distance formula
2763midpoint formula
2770lines on coordinate plane (cf. 3680)
2780conic sections
2782parabolas
2784ellipses
2786hyperbolas
2788circles (equations)
2790coordinate space: 3-d analyt. geom.
2800spheres (analytical)
2810graphing techniques symm, asymp.
2820polar coordinates
2840DeMoivre's theorem
2850sequences (progressions)
2860sequences, arithmetic (cf. 1430)
2870sequences, geometric (cf. 1440, 3590)
2880sequences, harmonic (cf. 1450)
2890Fibonacci numbers (cf. 2385)
2900series
2950induction
2970vectors
2980limits
2990probs. w/ (seemingly) insuff. info
INFORMAL GEOMETRY: 3000 – 3080
3000geometry, informal (for geom. class) (cf. 1020)
3004four-color problem
3050geometry: early (segments, angles)
3060points in plane
3065points in space
3070suppl., compl. angles
3071complementary angles
3072supplementary angles
3080separation (regions, counting)
EUCLIDEAN GEOMETRY: 3100 – 3650, 3750 – 3850
Triangles: 3100 – 3250
3100triangles and congruence
3140three-dimen. prob. w/ cong. triang.
3150triangles, elementary: general
3160triangles, isosceles
3170triangles, equilateral
3180triangles, right
3190triangles, right, 30-60
3200triangles, right isosceles
3210inequalities, geometric
3220optimization, geometric
3230median, alt, angle bis, &c.
3231medians of triangles
3232altitudes of triangles
3233angle bisection of triangles
3234perpendicular bisection of sides of triangles
3235midline of triangles
3240Menelaus's theorem
3250Ceva's theorem
3260parallel and perpendicular lines
3261parallel lines
3262perpendicular lines
3270parallel &perp. lines & planes
Polygons: 3300 – 3390
3300polygons
3305polygons, regular
3310polygons, angles of
3320inscribed & circumscr. polyg. (cf.3570)
3321inscribed polygons
3322circumscribed polygons
3330convexity
3340trapezoids
3350parallelograms
3360rectangles
3370rhombi
3380squares
3390other polygons
3400perimeter
3405area and perimeter
3410area (cf. 3420-3460)
3420polygons, area of
3440circles, area of
3450area, surface
3460area in coordinate plane
3470Pythagorean theorem
3475Pythagoras in 3 dimensions
Circles: 3500 – 3572
3500circles
3510arcs and angles
3520chords and angles
3530tangents
3540secants
3550circumference
3560power of a point
3570inscribed & circumscribed circles
3571inscribed circles
3572circumscribed circles
3580similarity (proportion)
3590means, geometric, in geometry (cf. 1440, 2870)
Solid Geometry: 3600 – 3650
3600solids
3601patterns of solids
3602sections of solids
3610cubes
3615rectangular prisms
3618cylinders
3620pyramids
3625cones
3630tetrahedrons
3640spheres
3650volume
3680analytic geometry: lines (cf. 2770)
3685analytic triangles
3687lattice points
3690analytic geometry: circles (cf.2780)
3695analytic problems in 3-dimensions
3700analytic geometry: spheres (cf. 2800)
3720reflections, rotations, translations
3721reflections
3722rotations
3723translations
3750logic, formal
Proof: 3752 – 3755
3752proofs, geometric
3754proofs, algebraic
3755proofs, phony
3800constructions
Locus: 3850
3850locus
TRIGONOMETRY: 4000 – 4340
4000trigonometry, basics
4040trigonometry functions, graphs of
4050trigonometry on triangles
4060sin(x + y)
4080cos(x+ y)
4100identities, trigonometric
4120functions, inverse trigonometric
4140law of sines
4160law of cosines
4200trigonometry probs, juicy numerical
4220trigonometry, spherical / 3-d probs
4300combinatorics
4340trigonometry on polyhedra, numer.
PROBABILITY: 4400 – 4420
4400probability (cf. 1340)
4410combinations
4420permutations
EVERYTHING ELSE: 5000 –
5000SAT for algebra 1
5200SAT for geometry
5300SAT for algebra/trig and beyond
5400achievement level 1
5500achievement level 2