Academic Vocabulary Mathematics Carolann DeMoss Teacher on Special Assignment - Mathematics These grade level lists of mathematical vocabulary words are the result of the compilation of a number of math word lists. An effort was made to include words that have a high frequency, are relevant to California mathematics standards and CST, and are found in the District s adopted math textbook, Scott Foresman. There are 7 graded lists, Kindergarten through Sixth Grade Each list is arranged in alphabetical order A key for each grade level is provided to identify the vocabulary word s origin and frequency of occurrence The following published lists were used: Nieroroda B. and Browning C. (1989). EDL core vocabularies in reading, mathematics, science, and social studies. Steck-Vaughn: Orlando. Marzano R. and Pickering D. (2005). Building academic vocabulary: Teacher s manual. Association for Supervision and Curriculum Development: Alexandria. California mathematics. (2001). Scott Foresman: Glenview. Other publications used: California Department of Education (2005). California CST released test questions. Retrieved at http://cde.ca.gov/ta/tg/sr on July 12, 2006. Mathematics framework for California public schools. (2006). California Department of Education: Sacramento. Use of the word lists: Vocabulary development, preview and review, English language development, word games, and a discussion regarding standard math language are a few of the potential uses for these word lists. Efforts towards the formulation of a school- or district-wide math vocabulary program could begin with these word lists.
CA Standards Vocabulary 2-dimensional shape 2-dimensional shape combination 2-dimensional shape decomposition 2-dimensional shape slide 2-dimensional shape turn 2-dimensional space 3-dimensional shape 3-dimensional shape combination actual acute angle acute angle acute angles addend addition addition algorithm analyze angle angle angle angle(s) angle measurement tool angle unit angle z apply approximate approximate, -d, -ly approximate measure approximate solutions arc arc area area area area area of a parallelogram area of a triangle - Page 1
CA Standards Vocabulary area of triangle associative property associative property of addition associative property of multiplication average average axes axis bar graph bar graph bar graph base base of a figure base five basic number combinations best describes best represents between billion break (down) a problem calculated results calculations capacity capacity centimeter central angle certainty (probability) charts chord circle graph circle graph(s) circumference circumference circumference classes of triangles classify - Page 2
CA Standards Vocabulary closed (no other form) closed sentence closest to the measure cluster clustering code, -d, -ing common (in common) common denominator common factor common fraction(s) common fractions common multiple commutative (order) property of addition commutative property commutative property of multiplication compact numeral compare, -ed compass compass compatible numbers compensation complex problems composite computation compute cone cone (geometric shape) congruent congruent conservation of area constant construct construct, -ion coordinate plane coordinates corresponding angles - Page 3
CA Standards Vocabulary corresponding sides cross, -ed, -ing cube cube cubed cubic (cube) unit cubic centimeter cubic foot (feet) cubic inch cubic inch cubic meter cubic yard cubic yard cylinder cylinder data data data data cluster data collection method data sets decimal decimal decimal(s) decimal addition decimal division decimal equivalents decimal estimation decimal form decimal multiplication decimal numeral decimal places decimal point decimal subtraction decimeter degree measure - Page 4
CA Standards Vocabulary degree of accuracy degrees denominator denominator depict, -ed describe determine diagram diagram diameter difference different size units dimension discount, -ed, -ing display distribute (-d) over distributive law (property) for (of) multiplication (over addition) distributive property distributive property distributive property dividend dividend divisibility divisible division division divisor divisor(s) double bar graph drawing software elapsed time English system of measurement equal equal decimals equally likely - Page 5
CA Standards Vocabulary equation equation equation(s) equilateral triangle equivalent forms equivalent fractional numerals equivalent fractions equivalent fractions equivalent fractions equivalent ratios equivalent representation estimate estimated data estimation estimation estimation of fractions estimation of height estimation of length estimation of width evaluate even numbers event event likelihood exact data exact solutions exact, -ly expanded form expanded notation experiment explain exponent exponent exponent(s) exponential form express, -ed, -ing, -ion expression - Page 6
CA Standards Vocabulary expression expression(s) expression represents extend, -ed, -ing extreme value face faces of a shape factor tree factorization factors factors farther, -est figure flip (reflection) flip transformation formed by formula formula formula four quadrants fraction fraction fraction fraction(s) fraction addition fraction division fraction multiplication fraction subtraction fractional form fractional number fractional numeral fractions of different size frequency table front-end digits front-end estimation front-end estimation - Page 7
CA Standards Vocabulary function function rule function table geometric figure geometric pattern geometric pattern extension given given percent gram gram graph graph(s) graph ordered pairs greatest common factor greatest common factor greatest common factor (GCF) grid growing pattern height height histogram histogram histogram horizontal axis how many hundred thousand hundreds hundredth hundredths identify identify ordered pairs identify relationships identity property identity property identity property of addition improbability - Page 8
CA Standards Vocabulary improper fraction improper fraction inches increase inequality inequality solutions information integer integers integer values interior interpret interpret results intersecting lines intersection of shapes invalid argument inverse operations investigation irrelevant information irrelevant information in a problem isosceles triangle kilometer layer least least common denominator least common denominator (LCD) least common multiple least common multiple (LCM) left (was left?) length like denominator(s) line line line graph line graph line graph - Page 9
CA Standards Vocabulary line m line of symmetry line plot line segment linear equation linear functions linear pattern locate, -d, -cating located on location (on a grid) location (on a number line) long division lowest terms lowest terms fraction manipulate map mass mathematical notation mathematical reasoning mean mean mean measure measure of angle measurement measures of central tendency measures of height measures of length measures of width median median median median median meter meter - Page 10
CA Standards Vocabulary meters long metric system metric system metric system midpoint miles farther miles fewer miles per hour millimeter millions mixed number mixed number(s) mixed numbers mixed numeral mode mode mode mode model(s) month multidigit multidigit divisor(s) multiple multiple multiples of a factor multiplication multiplication natural number nearest ten nearest thousand nearest thousand square miles negative negative integers negative number nonnegative integers number line - Page 11
CA Standards Vocabulary number line number of faces number pairs number plane number sentence number triplet number(s) number(s) numeration system numerator numerator object(s) observe, -ing patterns obtuse angle obtuse angle obtuse angles odd numbers one-quarter hour ones' place (column) one-sixth hour one-third hour open sentence open sentence order of operations order of operations ordered (number) pairs ordered pair ordered pair ordered pairs organize outcome outcome outlier output number pair(s) parallel lines - Page 12
CA Standards Vocabulary parallel lines parallel lines parallel lines parallelogram parallelogram parallelogram parallelogram formula part of a hundred part to whole partial quotient path pattern pattern addition pattern subtraction per per per minute percent percent percent percent(s) percent, -age percentages percent equivalents perimeter perimeter perimeter period perpendicular perpendicular lines perpendicular lines perpendicular lines perpindicular lines pi pictograph picture graph - Page 13
CA Standards Vocabulary pie chart place value chart place-value chart plane plane figures plot plot results point point point (on a grid) point on a number line polygon positive decimal(s) positive fraction(s) positive integer powers positive integer(s) positive integers positive number pound(s) power power power of ten power(s) of ten precise calculations prime prime prime prime prime factor prime factors prime factorization prime factorization prime factorization prime factorization prime number prioritize, -ing - Page 14
CA Standards Vocabulary prism prism probability probability probability problem situation procedures process of elimination product product product of n (and a number) proof properties proportion protractor protractor pyramid pyramid quadrants quotient quotient quotient range range (of scores) rate rate rate ratio ratio rational number ray reasonableness reciprocal reciprocal record (a graph) rectangle - Page 15
CA Standards Vocabulary rectangle formula rectangular box rectangular prism rectangular prism rectangular prism reduced form regular regular polygon relationship relationships relative distance relative magnitude relative magnitude(s) relative magnitude of fractions relative size relevant information relevant information in a problem remainder remainder repeated multiplication repeating pattern represent represents represents values restate a problem results reversing order of operations rhombus right angle right angle right triangle right triangle rod rotation round round (-ed, -ing) off - Page 16
CA Standards Vocabulary rounded rounding ruler ruler same size units sample sample save per pound saved scale scale (of a drawing, map, etc.) sequence, -ing several shape similarity shape symmetry shape transformation short word form shortcut (short cut) shrinking pattern side similar simple simple closed curve simple closed figure simple closed surface simple expressions simpler parts simpler problems simplest form simplest form simplest form simplest numeral simplify single-variable data situation situation - Page 17
CA Standards Vocabulary slide (translation) solid figures solid geometric figures solution solution set solve problems specific values sphere sphere square foot (feet) square inch square inches square mile square miles square region square yard squared standard form standard unit standard vs. nonstandard units stem-and-leaf plot store coupon straight angle straightedge strategies studies subset substitution subtraction subtraction algorithm sum surface area surface area surface area surface area surface area - Page 18
CA Standards Vocabulary survey survey symbolic representation symbols symmetry system table table(s) tallies ten thousands tens' place (column) tenths tenths terms (of a numeral, etc.) thick, -ness thousands thousandth thousandths three-dimensional three-dimensional objects through time time zone total total land area trace, -d, tracing transformation tree diagram trend trial and error triangle triangle triangle formula true truncation turn (rotation) - Page 19
CA Standards Vocabulary twice two-dimensional two-dimensional pattern two-dimensional views union of sets unit conversion unit differences unit price unit(s) unknown number unlike denominator(s) unlike denominators valid argument validity value value value(s) value for z value of value of the expression values of the variable variability variable variable(s) Venn diagram verbal representation of a problem verification verify verify the reasonableness vertex vertical axis volume volume volume volume measurement volume of irregular shapes - Page 20
CA Standards Vocabulary volume of rectangular solids weigh whole number width word form write written as a fraction written as a percent year zero property of multiplication - Page 21
Appendix An explanation of the word lists used in the creation of this document: California Standards Vocabulary and Released Test Item Vocabulary The author attempted to identify key grade level terms and phrases that were critical to student understanding of mathematics and the development of mathematical academic language. EDL Math Core Vocabulary Educational Developmental Laboratories (EDL s) purpose for the development and publication of the core vocabulary list is to improve the readability of instructional materials. Two doctoral dissertations are the basis of the two grade level mathematics core vocabulary lists, grade levels 1 3 and grade levels 4-6. These lists provide information as to the frequency and importance of mathematical terms. Each word or phrase is ranked according to its frequency and placed in a category. EDL lists 473 math words in seven categories for grades K 3 and 743 math words in nine categories for grades 4 6. EDL Core Vocabularies in Reading, Mathematics, Science, and Social Studies is referenced by ETS, Educational Testing Network Service - the company that creates the CST and CAHSEE, and individuals under contract for writing test items. For the purposes of this LBUSD Mathematics Academic Vocabulary List, the following EDL math categories were used: Grades K 3: Words listed in Primary Categories I III; 169 math terms Grades 4 6: Words listed in Intermediate Categories I VI; 140 math terms Marzano Marzano and Pickering created the lists by taking words from national standards documents and organizing the words into grade level sections. The authors caution the user(s) to make determination as to which words are critically important, useful but not critical, and interesting but not very useful to the understanding of mathematics. Academic Vocabulary Word Lists: Level 1: grades K 2; 80 math terms on list Level 2: grades 3 5; 190 math terms on list Level 3: grades 6 8; 201 math terms on list Scott Foresman Vocabulary Grade level math words were obtained from each grade level s teacher editions. The words are listed as Building Vocabulary at the beginning of each chapter.