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GlOSSARY

Absolute value The absolute value of a x Completing the When you add the same is the distance from x to 0 on the number line. quantity to both sides of a quadratic equation Absolute zero The temperature for which the vol­ (and make a perfect square), you are complet­ ume (of gases) would be zero--the lowest pos­ ing the square. sible temperature. Complex number A complex number cannot be Acute angle An angle whose measure is less than shown on a number line. It requires a two­ a right angle. dimensional number plane. Acute triangle A triangle that contains three acute Compound inequality An inequality that contains angles. more than one inequality symbol. Adding zero Adding the same quantity to both Constant A term having no variables. sides of an equation, or to the plus and minus Constraints A constraint is a condition necessary area on a workmat, is the technique of adding when solving an equation. zero. Conversion factor In the case of unit conver­ Area The size of a surface expressed in square sion, tbe proportionality constant (the number units. by which you multiply) is the conversion Arithmetic In an arithmetic sequence factor. the difference between consecutive terms is Coordinates In the Cartesian coordinate system, always the same. It is called the common the in an ordered pair, i.e., (x, y) are difference. used to locate a point on a plane. Associative Law For all real numbers a, b, and c, Degree of an expression The degree of an expres­ Addition: a + (b + c) = (a + b) + c., i.e., sion, in terms of the Lab Gear, is the lowest quantities can be grouped in any way. dimension in which you can arrange the blocks. : a· (h ·c) = (a· b) ·c., i.e., Density Density is equal to weight per unit of factors can be grouped in any way. volume. Average speed The total distance traveled divided Discriminant The discriminant is the quantity 2 by total travel time. b - 4ac that appears under the radical in the Axis In the Cartesian coordinate system, the hori­ quadratic formula, sometimes written as the zontal number line is the x-axis. The vertical Greek letter delta, 6. number line is they-axis. Distributing the minus sign When you write an Axis of symmetry If the graph of a parabola is equivalent expression without parentheses you folded so that its two sides coincide. the line on are distributing the minus sign. which the fold occurs is the axis of symmetry. Distributive Law For any real numbers a, b, Bounce ratio The bounce-height to drop-height and c, ratio. of multiplication over addition: a(b + c) = Cadence The pace of pedaling (a bicycle). ab + ac and (b + c)a = ha + ca. Cartesian coordinate system The Cartesian of multiplication over subtraction: a(b - c) = coordinate system is the technique of using ab - ac and ( b - c )a = ba - ca. horizontal and vertical axes and graph points Domain (of a function) The set of values that the to make geometric representations of algebraic input can take. equations. It is named for Descartes, the French Dynamic Dynamic rectangles have the mathematician and philosopher. property that half of such a is similar Chunking The process of grouping bits of infor­ to the whole. mation into a single piece of information. Also Equivalent equations If equations in two treating an entire algebraic expression as one variables have the same graph on the Cartesian variable. coordinate system, they are called equivalent Coefficient In a term, the coefficient is the equations. numeric factor of the term or number that is Euclidean distance The straight-line distance multiplied by the variable. between two points. Commutative Law For any real numbers a and b, Evaluating expressions When you evaluate an Addition: a + b = h + a. expression, you replace each variable in it by a Multiplication: ah = ba. given value and then simplify the result.

Glossary 5094 Experiment An example of an experiment would comes out. Each table has a rule that allows you be one roll of a pair of dice. Each different pos­ to get y from x. sibility of a result is an outcome. An event is Any positive or negative whole number one or more outcomes. and zero. Involves repeated multiplica­ Intercepts of graphs tion by a number. x-intercept: The point where it crosses the or Raising to a power The opera­ x-ax1s. tion of multiplying a number by itself repeat­ y-intercept: The point where it crosses the edly. The number multiplied is the base. The y-axis. number of factors is the exponent. Intercept form: y = a(x - p )(x - q) Extrapolation When you know data points and Interpolation When you know data points and use use them to predict data values at a later or ear­ them to determine data values between those lier time, the process is called extrapolation. points, the process is called interpolation. Eyes The points of intersection of the grid lines Inversely proportional You can say that y is inside a polyomino are eyes. inversely proportional to x if the product of Factor (noun), Common A common factor x andy is constant. Algebraically, xy = k or divides each term in a polynomial evenly. y = kla for some constant k. Factor (verb) To write as a product. Iterating functions To iterate a function means to Fair A game is fair if each of the players is equally use its output as a new input likely to win. Lattice line A line having equation x = b or Family (of functions) A group of functions that y = b, where b is an integer. share a certain attribute. Lattice point A point on the Cartesian plane Fixed point If an in-out line is horizontal, its input having integer coordinates. is a fixed point. Legs The two sides of the right angle in a right Focus Point where all in-out lines meet, if extend­ triangle. ed to the left or right. Like terms Terms whose variable factors are Function A relation that assigns to each member the same. of its domain exactly one member, its range. Linear combination The equation obtained by Gear The gear ratio multiplied by the diameter of adding constant multiples of two equations the rear wheel (of a bicycle). together. Gear ratio The ratio of the number of teeth on the Magnification In function diagrams that have a chainwheel (of a bicycle) to the number of teeth focus, changes in y can be found by multiplying on the rear sprocket. the changes in x by a number, called the magni­ Geometric sequence In a geometric sequence fication. Also called rate of change. each term is obtained from the previous term by Mean The average of a set of values. multiplying by a constant amount, the common Median The middle value of a set of values. ratio. Numbers The ratio of the longer to the shorter Rational: A rational number is any number that side of a is the golden ratio. can be expressed as the ratio of two in Golden rectangle A golden rectangle satisfies this the form alb where b * 0. property: If you cut a square off one end of the Irrational: An is a real num­ rectangle, the remaining rectangle is similar to ber that cannot be written in the form alb where the original rectangle. a and b are integers. Group A set of elements, together with an opera­ Natural: Natural numbers are the numbers we tion, that satisfies certain rules. count with: I, 2, 3, 4, ... etc. Hypotenuse The side of a right triangle that is Real: Real numbers include all rational and opposite the right angle. i1Tational numbers. Identity An equation that is true for all values of Observed probability Can be represented graphi­ the variables. cally by the slope of the line through the origin Inequalities An inequality is a mathematical and the corresponding data point. sentence that contains an inequality symbol Obtuse angle An obtuse angle is greater than a between two expressions, e.g. 2 < 6, x + 4 > S, right angle. Input-Output Tables In such tables, xis the num­ Obtuse triangle An obtuse triangle contains an ber that is put in, andy is the number that obtuse angle .

.4.510 Glossary Order of operations A rule for the order in which Quadrant In the Cartesian coordinate system, the operations are to be done. axes divide the system into four parts, called 1) Compute within grouping symbols; quadrants. Quadratic formula A formula for finding the 2) Compute powers; 2 3) Multiply aud divide in order from left solutions of a quadratic equation ax + bx + c to right; . -b + ,tb~ - 4ac = 0. The formula 1s x = 4) Add and subtract in order from left to right. 2a Origin The point at which the axes of a graph cross; Quadratic function A second-degree polynomial point (0. 0) in the Cartesian coordinate system. function. Parabola The graph of a quadratic equation Radical 2 ax + bx + c = 0; a * 0 is a parabola. Radical sign: The symbol Parameter A constant or variable in a mathemati­ Radical expression: An expression written cal expression which distinguishes specific under the radical sign. cases. In y = a + bx, a and b are the Range (of a function) The set of values the output parameters. can take. Perimeter The perimeter of a figure is the distance Rate of change of a function The rate of change around it. of a function is the ratio between the change in Pi Pi, 1t, is approximately equal to the number y and the change in x. 3.1415926536. The formula for the area of a rate of change =change in y/change in x circle is 1t?. (r is the radius of the circle.) It is often called magnification. Plaintext The text of a message, before it is Ratio of powers law It states that x"lxb = x"-bas encoded. long as x * 0. Polycubes You can create polycubes by joining Rational expression The quotient of two polyno­ cubes together face-to-face. Polycubes are the mials. three-dimensional equivalent ofpolymninoes. Rationalizing the denominator Simplifying a Polynomial function A function of the form y = radical expression so fhat fhere are no radicals a polynomial. in the denominator and only whole numbers or Polynomials A polynomial is a monomial or a variables in the radicand. sum of monomials. Reciprocals Two expressions are reciprocals if Monomial: An expression that is the product of their product is one. Also called the multiplica­ numerals and variables. tive inverse. Binomial: A polynomial having two terms. Relative frequency The relative frequency of Trinomial: A polynomial having three terms. successes is the ratio of successes to trials. Polytans Shapes created by combining tans. Repeating A decimal in which the same Power A number that can be named using expo­ number or group of numbers repeats endlessly. nential notation. Right triangle A right triangle contains one angle Power of a product law It states that x'Y' = (xy)" of 90 degrees. as long as x andy * 0. Rise The units of altitude gained for every I 00 Power of a ratio law It states that x"ly" = (x/y )"as units moved in a horizontal direction (the run). long as x andy * 0. Run Distance moved in the horizontal direction Prime factorization Prime factorization occurs when dealing with grade and slope. when you write a whole number as a product of A number expressed as the prime factors. product of a power of 10 and a greater An integer greater than one that than or equal to I but less than 10. has no factors other than one and itself. Sequence An ordered or expres­ Probability The probability of an event is inter­ sions, called terms. preted to mean the relative frequency with Similarity Two figures are similar if all the dimen­ which an event occurs if the experiment is sions of one can be obtained by multiplying repeated many times. the dimensions of the ofher by the same number. Product of powers law States that x" • .l = x" + " This number is called the ratio of similarity. as long as x * 0. Simple radical form Writing the square root of a Pythagorean theorem In all right triangles, if a whole number as a product of a whole number and b arc the lengths of the legs and c is the and the square root of the smallest possible length of the hypotenuse, then a2 + b2 = c2 whole number.

Glossary 5114 Simultaneous equations Two or more equations of the shortest path between them that consists for which you must find a common solution. of only horizontal and vertical segments. Slope A number telling how steeply a line slants; Terminating decimal A decimal that can be the ratio of rise to run. written in decimal form with a finite number Slope-intercept form y = mx + b of digits. Solving an equation When you find all the values Terms An expression that is the product of numer­ of a variable that make an equation true, you als and variables. are solving an equation. Theoretical probability Can be represented 2 Standard form equation ax + bx + c = 0 graphically as a line through the origin. Step function May be shown by a graph. The end Translations (of groups) A graph obtained by points of the steps may be filled in (closed cir­ shifting the location of a given graph without cles) or hollow (open circles). changing its shape is called a translation of the Subjective probability Subjective probability is original graph. assigned to an event according to a person's Variable A letter or other symbol used to represent own knowledge, beliefs, or information. a number or numbers. Surface area The surface area of a figure (for Vertex of an angle The "comer" of a geometric example. a ) is the number of unit figure is the vertex. The plural is vertices. it would take to cover all its faces. Vertex form of quadratic function The quadratic Tan In the world of geometric puzzles, a tan is half function y = (x ~ H)2 + V in vertex form. a unit square (cut along the diagonal). Volume of solids The volume of a solid is the Tangent A line that touches a graph at only one number of unit cubes it would take to build it. point is tangent to the graph. Zero product property It states that when the Taxicab distance The taxicab distance between product of two quantities is zero, one or the two points in the Cartesian plane is the length other quantity must be zero.

4512 GlossarJ N D E X

A B Common ratio, 200, 398 Absolute value, 329, 45 l, 465 Banking, 82-83, 118 Commutative exponentiation, 269 Absolute zero, 435 Base, 56 Commutative group, 241 Acute angle, 331 negative, 317-319 Commutative law, 117 for addition, 4 7 , Acute triangle, 331 Base period, 426 for multiplication, 50 Addition, 27 , 273 associative law for, 47 Binomial, 172 Comparing commutative law for, 47 multiplication of, 173 ages,224 function diagram and, 6 7-68 squares of, 251-252 algebraic expressions, 225 length model of, 52 numbers, 224-225 Blood alcohol concentration populations, 303-305 linear, 52 formula for, 432 rational expressions, 231 of opposites, 88 graphing, 432-433 Completing the square, 471-472. 500 order of operations and, 28 Bounce ratio, 398-399 of radicals, 338 Complex number, 503 Boundary dot, 157-158 solving linear equations with, 221-223 Complicated area, 157-158 Bracket, 209 of zero, 46, 48 Compound inequality, 161,270-271 Braking distance, 148 Algebra, of moves, 198 Compound interest, 312, 346 Building-block number, 186-188 Algebraic expressions, comparing. 225 Condition. See Constraint Business application, 468 Alice in Wonderland, 236 Constant. ll-13 Angle c Constant difference graph, 230 acute, 331 Cadence, 443 Constant perimeter, 458-460 obtuse, 331 Calculator right, 331 Constant product, graphing, 169-170, 176 area of circle and, 357 Angstrom, 32 Constant product function, 169- J 71 division with, 145 Constant ratio graphs, 230 Angstrom, Anders, 32 exponentiation with, 272 Constant sum, graphing. 167-168, 176,230 Approximation, 272-273 radical expression and, 352 Area, 4-5 raising to a power \Vith, 56 Constant sum function, 167 of circle, 144-145,357-358 reciprocal on, 101 Constraint, 371, 373-374 complicated, 157-158 scientific notation using, 275 Continuous graph. 152-153 on geoboard, 36-37 square root using. 279, 334, 330 Conversion factor, 418-419 of geoboard square, 238-239 subtraction with, 44 Coordinate(s), 84 multiplication and, 27-28, 51, 88 Carroll, Lewis, 236 Cartesian, 84-85 ofpolyomino, 23,34-35,360-361 Cartesian coordinate system, 84-85 multiplication and, 85-86 of rectangle, 459. 461-462. 466-467 multiplication and, 85~86 finding distance from, 332 graphing, 14 Celsius temperature, converting to slope from, 294 of square, 358 Fahrenheit, 104, 140-141,390 Cover-up method. I 06-107 of stretched polyomino, 354~355 Celsius temperature scale, 103-104 Cube(s), 247 surface, 30~ 31 Centimeter. 8 in cubes, 257 of triangle, 74~ 75 units of, 8 cubic, 8 making squares from, 248 square, 8, 281 storing, 469-470 Area formula, 157~158 Charles, Jacques, 435 of sums, 260 Area function, 146-147 Charles's law. 435 ofx, 10 Arithmetic sequence, 193 Chunking, 239, 269 Cube problem, 257 A-, 485 Circle Cubic centimeter, 8 Associative law, 117,241 area of, 144-145,357-358 Cubic inch, 8 for addition, 47 circumference of, 144 Cubing, with table, 248 for multiplication, 50 closed, 154 Current, 506 Astronomical unit, 32, 277 open, 154 Cylinder, graduated, 137 Automobile accident taxicab, 328 l-for-10 rule and, 149 Circumference, of circle, 144 D 3-sccond rule and, 149 Closed circle, 154 Dahl, Roald, 237 Average, 195-196 Closure, 241 Data, equations from, 438 grade, 208 Decimal, 401-402 improving, 234-235 Coding function, 92 Coefficient. 19 as . 401-402 \Veighted, 220 fraction as, 40 I Combined function, I 09-111 Average speed, 151-152,439 repeating, 401 Axis Combining like terms, 19 terminating, 401 horizontal, 6 Common denominator, 490 Degree, 18-19 origin, 7, 84 Common difference, 193 of expression, 18-19 of symmetry. 464 Common factor. 181 higher, 19 vertical, 6 greatest. l81 of polynomial, 18-19, 129-130

Index 5134. De Morgan. Augustus. 229 Equation(s) Extrapolation, 427-428 Denominator from data. 438 Eyes, 72 common. 490 equivalent. 228~229. 376 rationalizing, 352 from graphs, 128 F zero in, 489 identities and, 215-216 Factor. 174 Density, 137-138 linear, 134, 389-390 common, 181 parameters for. 381-382 Dependent variable, 436-437 greatest, 181 solving, 21 !~213, 261 Descartes, Rene, 84 Factoring, 180-181 standard form of, 381-383 difference of squares, 255 Diagonal, on geoboard, 404-405 from patterns, 127 polynomials, 259 Diameter, area and, 144 with percents. 307 prime, 406 Dice game. 409-411 points and, 128 of third~degree polynomials. 175 Dicube, 31 quadratic, 476-478 of trinomials, 174-175 and, 490-491 Difference Fahrenheit temperature, converting to real number solutions for. 502 absolute value of, 329 Celsius, 104, 390 simplifying, 488--489 of perfect squares, 383 Fahrenheit temperature scale, l 03-104 solving, 261-263. 477, 497 factoring. 255 with zero product property, Fair, 409 Dimension, 5, 15-17 463-464 Family of functions, 449-450 finding, 4 79 standard form of, 496 Feet per second. 148 lowest, 18 sum of solutions of, 503 Fibonacci, 333 Diophantus, 229 x~intercepts for, 476~~477 , 59 Direct variation, 138, 146-147 recurrence, 445 Fibonacci sequence, 505 Discount, 2 J 7 simultaneous, 374,387-388.449 Finding x, 12 Discrete graph, 152-153 system of, 376-379 solving, 106-107,211-213 Fixed point, ! J 8, 289. 446, 460 Discriminant, 502 addition and subtraction and, Flip, 198 Distance. 328-330 221-223 Focus, 289 Euclidean, 328-329 multiplication and division and, Formula finding from coordinates, 332 227-229 on geoboard, 279-280,334 area, 157-158 with squares, 264-266 Pick's, 158 skidding, 350 writing, 106 taxicab, 328-329 quadratic, 497-498, 500-501 Equidistant, 464 vs. speed, 126 speed by, 126 vs. time. 125-126, 156 Equivalent equations, 228-229.376 Fraction( s ), 40 J -402 Distributing, 189 Equivalent fractions, !15 combining terms involving, 452 the minus sign, 87 Eratosthenes. 274 complicating, 490 as , 401 Distributive law, 172-173 Estimating. 140~141 decimals as, 40 l-402 division and, 172-173, 220 population, 349 equivalent, 115 of division over addition and subtraction. Euclid, 328 lattice points and. 404 173 Euclidean distance, 328-329 quadratic equation'; and, 490-491 minus and, 87. 182-85 Euler, Leonhard, 76 radicals and, 352 multiplication of polynomials and, 99 Evaluating, 11-12 rationalizing, 352 of multiplication over addition and simplifying, 172~173, 488-489 subtraction, 52-53 Even number, 192 Fractional exponent, 348 Distributive la\v. radical expressions and. Event, 410 351 probability of, 413 frequency. relative, 412-413 Division Experiment, 409 Frown parabola, 178 distributive law and, 172-173, 220 Exponent, 56 Function(s), 6! function diagram and, 68 fractional, 348 area, 146-147 model for, l 0 I Jaws of, 314,322,349 coding, 92 multiplication and. 97-99 multiplication and, 276 combined, I 09 -1 I I of radicals, 337-338 negative, 317-319 constant product, 169~171 shortcut ! 02 112.348-349 constant sum, 167 solving linear equations with. 227-229 zero. 267-268 domain of. 342 by zero. 108 Exponential growth, 303,317-318 families of. 449-450 Division symbol, 97 midpoint of, 346 fixed point of, 1 18, 446, 460 Division table. 145 Exponential notation. 56 inverse, 11 0-l II linear, 296-298 Domain, 342 Exponentiation, 56 iterating, 445-447 calculator, 272 Domino, 4 opposite, 105 commutative. 269 Domino problem, 25 perimeter, 69-70 order of operations and, 129 Double negative, 84-86 polynomial, l29-130 Expression polyomino, 72-73 Downstairs block, 183 algebraic, comparing. 225 Dynamic rectangle, 485-486 quadratic, 177-179 degree of, 18 intercept fom1 of, 492-493 E evaluating, II-J 2 standard form of. 474, 493 radical, 335,351-352 Electron, weight of, 325 vertex of, 492-494 rationaL 231-2.13 x-intercepts of. 496-497 Equal pmver, 313~314 comparing, 231 range of, 342 Equal ratio, 121 equivalent, 231-232 reciprocal, 105 Equal Sf.JUares, 265,471. 499-500 simplifying, 209-210 representing, 44B-450

,4514 Index as, 200 of area function. 461-462 K square root, 340-343 of blood alcohol concentration. 432-433 Kasner, Edward, 281 step, 154 of inequality, 270-271 Kelvin temperature, conversion to surface area, 70-71 of parabola, 177-179 Celsius. 120 ofx.61 of rectangle area, 14 Kelvin temperature scale, 120 Function diagram, 61-63 Greater than or equal to symbol, 155 Kilo, 321 addition and, 67-68 Greater than symbol, 93, 155 combining functions and. I 09-110 Kilometer, square, 281 Greatest common factor, 181 division and, 68 focus of, 289 Group, 241 L magnification of, 289 commutative, 24 1 Lab Gear, 9-10 multiplication and, 67-68 Grouping symbol, 209 Lab Gear magic, 90-- 91 operations and, 67-68 Group theory, 241 Lab measurements, 137-139 parallel-line. 289 H , 272-274 parameters of, 291-292 using, 277-278 for recurrence equation, 445 Halfway growth factor, 348 I .attice line. 404 fur squares and roots. 340-342 Halfway measure. 346-347 Lattice point, 404,416 subtraction and, 68 Height time-distance, 64-65 as function of age, 286-287 Laws of exponents. 314. 322. 349 _v=b-x,84 weight as function of, 287-299 Legs, 331 G Hexomino, 4, 5 Length. units of, 8 Leonardo of Pi sa. 333 Gases, volume of, 435 Higher degree, 19 Less than or eyual to symbol, 155 Gauss, Carl Friedrich. 191 Home pm.ition, 197 Less than symboL 93, 155 Gear, 443 Hori.wntal axis, 6 Letter string, 159 Gear ratio, 442-443 HoriLOntallinc, 154-155 Light-year, 283 Gcoboard Hypotenuse, 293-294 area on, 36-37 I Like terms, 19, 39-40 diagonal on, 404-405 combining. 19 ldentity(ies), 215, 258-260 distance on, 279-280, 334 Line(s) equations and. 215-216 equivalent fractions on, 115 equations of, 389~390 graphs for. 215 slope on, 293-294 horizontaL 154-155 tables for, 215 Geoboard square, 238-240 intersections, 384-·386 Identity clement, 241 lattice, 404 Geoboard triangle, 74-75 Inch. 8 median-median, 429--431 Geometric sequence(s), 200 cubic. 8 points on, 146,384 sums of, 398-400 square, 8 relationships between, 405 Girth. 470 Independent variable, 436-437 in representations, 448 Goldbach's conjecture, 274 Inequality(ies), 93-96. 155 segment, midpoint of, 345 Golden ratio, 504-505 compound, 161,270 slope of, 296~297 Golden rectangle, 504 graphical solutions for, 218-219 stairs on. 403-404 straight, 328 , 273,281 graphing, 270-271 through points, 389-391 Grade, 293 rules of, 239 solving, 210 vertical, 154~155 Grade average, 208 Inequality sign, 93 Linear addition, 52 Graduated cylinder, 137 , 291 Linear combination, 379 Graph(s) for simultaneous equations, 37B-379 Inflation. 369 analyzing, 176 Linear equation, 134 In~out table, 61 constant difference. 230 parameters for. 381-382 constant product, 169-170, 176 Inside dot, !57-158 slope-intercept form of. 297-298 constant ratio, 230 Inside product, 189 solving, 211-213.261 constant sum, 167-168, 176.230 Integer, 503 addition and subtraction and, 221 -223 continuous, 152-153 Intercept, 131 multiplication and division and discrete, 152-153 of linear equation, 381 227-229 , equations from. 128 of parabola, 465 standard fonn of, 381-383 for identities, 215 Linear function. 296-298 intercepts of, 131 Intercept form, of quadratic function, 492-493 iterating, 445-447 intersections of. 131 from patterns, 127 Interest Linear growth. midpoint of, 345 poinb through, 131-132 compound, 3 12, 346 Linear subtraction, 52 of sequences, 192 simple, 312, 346 Longest perimeter, 7 speed by, 126 Interpolation, 427-428 Lowest dimension. 18 for squares and roots, 342-343 Intersection, of graphs, 131 , 59 tangents to, 262 Inverse action, 110 through origin, 132 Inverse element, 241 M V-shaped, 451-452 ~agnification. of function diagram, 289 Inverse function, II 0-111 Graphical analysis, 218 :Vlathcmatical model, 301-302 Inversely proportional, 432 Graphical solution, 264 in science, 435-437 Irrational number, 406-407 for inequalities, 218-219 Mcan(s), 195 Iterating linear function, 445-447 Graphing, 6-7 sums and, 195-196 Iteration, 446 lndex 5154, Measurement, units of, 8 power, 198 Parallel-line function diagram, 289 Measurement error, 140 scientific, 273-274. 356 Parameter(s), 230,291-292 Median. 195 small numbers in. 320 for linear equations, 381-382 using, 275-276 Median-median line, 429-431 Parentheses, 203, 209 symbolic, 398 Metric system. units in, 321 Pascal's triangle, 417 Number(_s) Pattem(s) Midpoint, 344-345 absolute value of, 451, 465 equations t'rom, 127 of exponential grov.·'th, 346 building-block, 186- I 88 finding, 58 of linear growth, 345 comparing, 224-225 graphs from, 127 of line segment, 345 complex, 503 from points, 127 of triangle, 363 even, 192 predicting and, 6 Miles per hour. 148 Fibonacci, 59 Pentomino, 4, 5 Million. 273 irrational, 406~407 perimeter of, 23 Minus large, 272-274 distributive law and, 87, 182-85 using. 277-278 Percentage, 372 meanings of, 44 Luca~. 59 Percent, equations \Vith. 307 upstairs method and, 44-45 natural, 192, 503 Percent, decrease, 309-311 Minus area, 45 odd, 192-193 Percent increase. 306-308 prime, 274 upstairs blocks in, 48-49 Petfect square(s) rational, 231. 503 Minus sign, distributing, 87 differences of, 383 real, 503 sums of, 280 Mirror image diagram, 68 reciprocals of, 100 Mixture, 330, 372 rectangular, 34 Perfect square trinomial, 252, 276 Model, 15 small, in scientific notation, 320 Perimeter, 4-5,21-23 for division, I 01 square, 35 constant, 458-460 mathematical, 301-302 square roots of, 279-280 longest, 7 in science, 435-437 theory. 295 of pentomino, 23 of motion, 439-441 triangular, 33-34 ofpolyomino, 6-8.23, 34-35, 72, for multiplication, 100 whole, 9 360-361 scale, 277-278 x. absolute value of, 329 problems in, 24-26, 38 Money, 217 Numerator, rationalizing, 352 of stretched tetromino, 354 Perimeter function. 69-70 Monocube, 31 0 Phi, 504 Monomial(s), 172, 315-316 Observed probability, 413~414 ratios of, 316 Pi,407 Obtuse angle, 331 Motion, modeling, 439-441 Pick's formula, 158 Obtuse triangle, 331 Moves, 197-199 Plaintext, 92 algebra of, 198 Odd number, 192-193 Point(s) triangle, 198 One dimension, 5, !5 equations and, 128 Multiplication, 27-28.50-51 Open circle, 154 fixed,289,446,460 by-1.86 Operation(s). 55 lattice. 404,416 area and, 27-28, 88 function diagrams and, 67-68 on lines, 146, 384 lines through, 389-39! associative law for, 50 order of. 28~29 of binomials, 173 exponentiation and, ! 29 patterns from, 127 and Cartesian coordinate system, 85-86 radical, 337-338 in representations, 448 through graphs. 131-132 commutative law for, 50 Opposite(s), 44, 318-319 division and, 97-99 adding, 88 Polycube. 31-32 exponents and, 276 reciprocals and. 105 Polynomial(s)_, 18 function diagram and, 67-68 removing, 45, 48 cube of. 248 model for. I 00 Opposite function, 105 degree of, 18-19 order of operations and, 28 factoring, 174-175,259 Order of operations, 28-29 of polynomials, 99 multiplication of, 99 exponentiation and, 129 of radicals, 337 third~Jegree, factoring, 175 Origin, 7, 84 shortcut I 00-101 Polynomial function, 129-130 graphs through, 132 solving linear equations with. degree of, 129-130 227-229 lines through, 134-136 parabola through, 459-460 Polyomino, 4~5 of square roots, 335 area of, 23. 34-35 Outcome, 409-4 J0 symbols for, 9 eyes of. 72 table, for triangle moves, 198 Outside product, I 89 perimeter of, 6-8, 23, 34-35,72 of three factors, 50 p ratio of similarity and. 360-361 Multiply-subtract-solve technique, 399.402 stretched, 353 Paper, international standards for, 485 area of, 354~355 N Parabola, 177, 342 perimeter of, 354 , 192, 503 axis of symmetry of, 464 Polyomino function, 72-73 Negative, 44 frO\vn, 178 Polyomino spiraL 72-73 double, 84-86 graphing, 177-! 79 Polytan, 362 Negative base, 317-319 intercepts of, 465 smile, 178 Population(s) Negative exponent 317-319 through origin, 459-460 comparing. 303-305 Nested squares. 408 translating, 473 estimating, 349 Notation vertex of, 177,465,473-475 growth of, 301-302 exponential, 56 c.s .. 426-428

,4516 In de: Power(s), 56~57, 272-274 Radical sign, 335, 451 Fibonacci, 59, 505 equal. 313-314 Raising to a power. 56 as functions, 200 products of, 315 Random walk, 415-417 geometric, 200 sums of, 398-400 of products, 315-316 Range, 342, 392 ratios of, 31 8 graphs of, 192 Rate of change, 286, 291, 296 of ratios, 316 Lucas, 59 square roots of, 349 Rational expression(s), 231-233 Sextillion. 273 comparing, 231 sums of, 280 Sh01test path, 328 equivalent, 231-232 Power notation, 198 Similar figures, 116.360-361 Rationalizing. 352 Power of a power law, 314 Similarity. 360 Rational number, 231.503 Power of a product law, 316 Similar rectangles, 116 Ratio(s), 134-135 Power of a ratio law, 316 ofatob, 134 Simple interest, 312, 346 Powers of 2. 56 bounce, 398-399 Simple radical form. 336, 338 Prediction, patterns and, 6 common, 200. 398 Simplification, 48 Prime factor, 406 equal, 121 of expressions, 209-2\0 Prime factorization, 406 golden, 504-505 of fractions, 172-J 73. 488-489 Prime number. 274 of monomials, 3 16 from inside out. 209-210 pov.rers of, 316 or quadratic equations, 488-489 Probability, 412-414 rectangle. 484-486 subjective, 414 Simultaneous equations, 374, 3?\7~388, 449 solving equations involving, 232 theoretical vs. observed, 413~414 system of, 376-379 Ratio of powers 1a\V, 318 Product(s) Slope. 293-295 constant, graphing. 169-170, I76 Ratio of similarity, 360 of a line, 296-297 inside, 189 Reaction distance, J4R from coordinates, 294 outside, 189 Real number, 503 on gcoboard, 293~294 y-intcrcept and, 297-29?\ of powers, 315 Reciprocal(s), 100-102,317,320 powers of, 315-316 opposites and, 105 Slope-intercept form, 297-298. 299. 386, Product of powers law, 315 solving equations with, 228 389-390 Proportional, inversely, 432 units and, 320-321 Slumber theory, 295 Proton. weight of, 325 Reciprocal function, 105 Small numbers, in scientific notation, 320 Pyramid, 202 Rectangle(s) Smile parabola, 178 Pythagoras, 332 area of, graphing, 14 Solid(s) dynamic, 485-486 surface area of. 30-31 Pythagorean theorem, 331-333 finding dimensions of, 479 volume of. 30 Q golden, 504 Solving the equation. 106-107 Quadrant. 84 ratios, 484~4?\6 Speed, 64-65, 135-136 similar, 116 Quadratic equation(s), 476-478 average, 151-152,439 square roots and, 334-335 fractions and, 490-491 distance vs., 126 uncovered, 52, RR, 183 real number solutions for, 502 hy graphs and formulas, 126 vertices of, 36 simplifying, 488-489 time vs., 124-125 solving, 261-263,477,497 Rectangular number, 34 Speedometer, calibrating, 421 with zero product property, 463-464 Rectangular pen, 458-460 Square(s), 246, 334 standard form of, 496 area of, 461-462 area of. 358 sum of solutions of. 503 constant, 466-467 of binomials, 251-252 x-intercepts for, 476-477 finding dimensions of, 479 completing, 471-472, 500 Quadratic formula, 497-498.500-501 partitioning of, 461 differences of. 254-256 Quadratic function(s), 177-179 Recurrence equation, 445 factoring, 255 intercept form of, 492-493 Relative frequency, 412-413 equal, 265,471,499-500 standard form of, 474, 493 Removing opposites, 45. 48 Square(s) (continued) vertex of, 492-494 Repeating decimal, 401 equations with, 264-266 x-intercepts of. 496-497 Right angle, 331 function diagrams for. 340-342 on geoboard, 238-240 Quadratic inequality(ies), 270-271 Right triangle. 293-294, 331-332 Quadrilateral, midpoint of, 363 graphs for, 342-343 Rise. 296 making cubes from, 248 Quadrillion, 273 Rotation, 197, 198 nested. 408 Quintillion, 273 Rounding, 150 perfect R Run. 296 differences of, 383 sums of, 280 Radical(s), 334-336 sides of, 383 addition of, 338 s Scale, 361 sums of, 260 disappearing, 351-352 of sums, 251 ·-253 division of, 337-33?\ Scale model. 277-278 of trinomials, 260 fractions and, 352 Science, mathematical models in, 435-437 of x, lO multiplication of, 337 Scientific notation, 273-274, 356 subtraction of, 338 small numbers in, 320 Square centimeter, 8, 28 I Radical expression(s), 335,351-352 using. 275-276 Square inch, 8 Radical gear, 351 Secret code, 92, 96 Square kilometer, 281 Radical operation, 337-338 Sequence(s), 59, 192-194 . 35 Radical rules, 349 arithmetic. 193 Square root(s), 279-280.334.451

Index 517 function diagram~ for, 340-342 in-out, 61 reciprocals and, 320-321 graphs for, 342-343 multiplication, for triangle moves. 19H Unit conversion, 148,418-420 multiplying, 335 Tan, 362 two-step, 419-420 of numbers less than ! , 340 Tangent, 262 C.S. population (1890-1990), 426~428 of powers, 349 Taxicab circle, 328 Unlike terms, 54 rectangles and, 334-335 Taxicab distance, 328~329 of two, 406-407 Upstairs block, in minus area, 48-49 Temperature Square root function, 340-343 Upstairs method, 44-45 estimating, 140-14 J Square root symbol, 335 volume of gases and, 435 v Staircase sums, 190-191 Temperature scale, 103-104 Variable(s). 9,11-13 Stairs, on lines. 403-404 Celsius, I 03~ 104 dependent, 436~437 Standard forrn, 381-383,474 Fahrenheit, 103·-104 independent, 436-437 of quadratic equation, 496 Kelvin, 120 in simultaneous equations, .373-375. of quadratic function, 493 Terminating decimaL 401 387-388 subscripted, 192 Step function, 154 Tenns, 18, 192 subtraction with, 44 Straight line, 328 combining like, 19 Variation, direct, 138, 146-147 Stuart Little, 236 like, 39-40 Vertex, 36,473-475 Subjective probability. 414 unlike, 54 Tetracube, 31 of parabola, 177, 465 Subscript, 109 of quadratic function, 492-494 Tetratan, 362 Subscripted variable, 192 Vertex form, 474,499 Tetromino, 4, 5 Substitution. 11 Vertical axis, 6 for simultaneous equations, 376-377 perimeter of. 354 stretched, 353 Vertical line, 154-155 Substitution code, 89 The BFG, 327 Volume, 30 Substitution rule, 12 Theoretical probability. 413-414 of gases, 435 Subtraction, 44, 49 maximizing, 469 Third-degree polynomial, factoring of, 175 equivalent addition for. 88 units of, 8 function diagram and 68 Three dimem.ions, 5, 15, 30-32 length model of, 52 Three factors, multiplication of, 50 w linear, 52 Time Weight, 137-138 of radicals, 338 distance vs., 125-126, 156 as function of age, 287 .<;o]ving linear equations using, 221-223 vs. speed, 124-125 as function of height, 287-299 oft wo negatives, 84 Time-distance function diagram, 64~65 Weighted average, 220 with variables, 44 Topology, 76 White, E. B.. 236 Success, 412 2 Translation ofy = ax , 499-501 Whole number, 9 Sum(s) Trianglc(s) Word figures, 33-35 constant, graphing. 167-168, 176 acute, 331 Word ladder, 33-34 cubes of, 260 area of, 74-75 of geometric sequences, 398-400 Word squares. 35 on geoboard, 36-37,74-75 means and, 195-196 Word triangle, 33 home position for, 197 of perfect squares, 280 midpoint of, 363 X of powers, 280 obtuse, 331 of squares, 260 X Pascal's, 417 squares of. 251-253 absolute value of, 329 right, 293~294, 331~332 staircase, 190-191 cubed, lO symmetry group for, 198 two-dice, 409-410 finding, 12 uncovered, 253 squared, 10 Superscript, 56 vertices qf, 36 testing values of. 95-96 SuperTangram, 362 Triangle mOves, 197-199 x-axis, 84 Surface area, 30-31 multiplication table for, 198 x-block, 15 Surface area function, 70-71 operation on, 198 x-coordinate, 84, 297 Symbol(s) , 33-34 x-intercept, 131 division. 97 Tricube. 31 for quadratic equation. 476-477 greater than. 93. 155 , 273 for quadratic function, 496-497 greater than or equal to, I 55 TrinomiaL 172 grouping, 209 X}'-biock, 15 factoring. 174-175 less than, 93, 155 petfect square, 252, 276 y less than or equal to, 155 squaring 260 y-axis, 84 multiplication, 9 square root, 335 Tritan, 362 y-coordinate, 84 Symbolic notation, 398 Tromino, 4 y-intercept, 131_. 297 slope and, 297-29S Symmetry, axis of, 464 Turns, 197 Symmetry group, 198 Two-dice sums. 409-410 z System of simultaneous equations. 376-379 Two dimensions, 5. l 5 Zero adding, 46, 48 T u in denominator. 489 Uncovered rectangle, 52, 88, 183 Table(s) dividing by, 108 cubing with, 248 Uncovered triangle, 253 exponent, 267-268 division, 145 Unit(s) Zero product property, 463-465 for identities, 215 metric system, 321 Zones. 76~ 77

,4518 Index