Glossary Elementary School Level Mathematics Glossary English / Bengali Translation of Mathematics Terms Based on the Coursework for Mathematics Grades 3 to 5. Word-for-word glossaries are used for testing accommodations for ELL/LEP students Last Updated: 08/10/09 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234 Education - P-16 Office of Elementary, Middle, Secondary, and Continuing Education and Office of Higher Education Office of Bilingual Education and Foreign Language Studies http://www.emsc.nysed.gov/biling/ THE UNIVERSITY OF THE STATE OF NEW YORK Regents of the University MERRYL H. TISCH, Chancellor, B.A., M.A., Ed.D. ....................................................................... MILTON L. COFIELD, Vice Chancellor, B.S., M.B.A., Ph.D. ......................................................... ROBERT M. BENNETT, Chancellor Emeritus, B.A., M.S. ............................................................... SAUL B. COHEN, B.A., M.A., Ph.D................................................................................................ JAMES C. DAWSON, A.A., B.A., M.S., Ph.D. ................................................................................ ANTHONY S. BOTTAR, B.A., J.D. ................................................................................................... GERALDINE D. CHAPEY, B.A., M.A., Ed.D. ................................................................................. HARRY PHILLIPS, 3rd, B.A., M.S.F.S. ........................................................................................... JOSEPH E. BOWMAN, JR., B.A., M.L.S., M.A., M.Ed., Ed.D......................................................... JAMES R. TALLON, JR., B.A., M.A. ............................................................................................... ROGER TILLES, B.A., J.D. ................................................................................................................ KAREN BROOKS HOPKINS, B.A., M.F.A........................................................................................ CHARLES R. BENDIT, B.A. ............................................................................................................. BETTY A. ROSA, B.A., M.S. in Ed., M.S. in Ed., M.Ed., Ed.D..................................................... LESTER W. YOUNG, JR., B.S., M.S., Ed. D. ..................................................................................... CHRISTINE D. CEA, B.A., M.A., Ph.D. .......................................................................................... WADE S. NORWOOD, B.A. ............................................................................................................. New York Rochester Tonawanda New Rochelle Plattsburgh Syracuse Belle Harbor Hartsdale Albany Binghamton Great Neck Brooklyn Manhattan Bronx Oakland Gardens Staten Island Rochester Interim President of the University and Commissioner of Education CAROLE F. HUXLEY Senior Deputy Commissioner of Education, P–16 JOHANNA DUNCAN-POITIER Associate Commissioner for Curriculum and Instructional Support JEAN STEVENS Coordinator, Office of Bilingual Education and Foreign language Studies PEDRO J. RUIZ Acknowledgements: The New York State Education Department Glossaries for English Language Learners were reviewed and updated during the 2008-2009 school year. We would like to thank in these efforts the New York State Education Department Language BETACs (Spanish, Asian and Haitian Bilingual Education Technical Assistance Centers), the NYS Office of Curriculum, Instruction and Instructional Technology; the New York City Department of Education Office of English Language Learners, and the NYC Department of Education Translation and Interpretation Unit. The State Education Department does not discriminate on the basis of age, color, religion, creed, disability, marital status, veteran status, national origin, race, gender, genetic predisposition or carrier status, or sexual orientation in its educational programs, services and activities. Portions of this publication can be made available in a variety of formats, including brailed, large print or audio tape, upon request. Inquiries concerning this policy of nondiscrimination should be directed to the Department’s Office for Diversity, Ethics, and Access, Room 530, Education Building, Albany, NY 12234. Grades 3-5 English about above absolute value accurate accurately label work act it out acute angle acute triangle add addend addition addition fact addition sentence addition sign additive inverses after afternoon algebra algebraic expression algebraic patterns algebraic relationship algebraic relationships algebraically algorithm alike all all together almost amount analog clock analyze angle (∠) angles, adjacent answer ante meridian (a.m.) apex application apply approach appropriate mathematical language appropriate mathematical language organize work arc area argument argument conjecture counterexample arithmetic (numeric) expression arithmetic expression arithmetic fact arrange array Bengali cÖvq Dc‡i Pig gvb wbf©yj wbf©yjfv‡e wPwýZ KvR mgvavb Ki, K‡i †`LvI m~² †KvY m~² w·KvY †hvM Kiv Awf‡hvR¨, †h msL¨v¸‡jv‡K †hvM Kiv nq †hvM Kiv NUbv ev Z‡_¨i ms‡hvRb ev‡K¨i ms‡hvRb †hvMwPý †hŠwMK e¨¯Í AbycvZ, †h msL¨v¸‡jvi †hvMdj k~b¨ nq †mB msL¨v c‡i Acivý exRMwYZ exRMvwYwZK ivwk exRMvwYwZK c¨vUvb© ev web¨vm exRMvwYwZK m¤úK© exRMvwYwZK m¤úK©mg~n exRMwY‡Zi wbq‡g AvjMwi`&&g&, wewfbœ av‡c mgm¨v mgvavb cÖwµqv Abyiƒc, m`„k me me©‡gvU cÖvq cwigvY, msL¨v A¨vbvjM Nwo, cyi‡bv KvUvIqvjv Nwo we‡kølY †KvY †KvY, mwbœwnZ DËi c~e©vnè kxl© we›`y cÖ‡qvM cÖ‡qvM c×wZ h_v_© MvwYwZK cwifvlv h_v_© MvwYwZK cwifvlv msMwVZ KvR e„ËPvc †ÿÎdj, AvqZb hyw³ hyw³ AbywgZ cvëv `„óvšÍ MvwYwZK (mvswL¨K) ivwk MwYZ ivwk MvwYwZK web¨vm web¨vm as long as associative property attribute autumn (fall) average axis (axes) bar graph base base of a 3-dimensional figure base of a parallelogram base of a polygon base of a polyhedron base of a rectangle base of a triangle base ten number system before below beside between on big/bigger/biggest bisect calculate calendar capacity cardinal numbers (1-10) cent centimeter (cm) chance charts circle circle graph circumference clarify classify triangles closed figure coin collaborate collection common common denominator common factor common multiple commutative property of 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convert coordinate coordinate grid coordinate plane corner corresponding angles corresponding sides count back count backwards count on counterexample counting numbers counting numbers cube cubic centimeter (cm3) cubic unit cup (c) currency symbols customary measurement system customary units of measure cylinder data data frequency table day daylight decagon decimal fraction decimal number decimal point decimeter decompose a number decompose shapes decrease decreasing sequences degree degree measure of an angle denominator density design diameter difference differences digit †gvPvK…wZ e¯‘, †Kvb me©mg me©mg wÎf~R AbywgwZ, Abygvb Kiv ms‡hvM. ms‡hvM ¯’vcb Ae¨ewnZ mvaviY evûwewkó ci¯úi mwbœwnZ `ywU †KvY aªe æ MVb Kiv, A¼b Kiv cÖwZZzjbv iƒcvšÍ‡ii e¨vL¨v iƒcvšÍi ¯’vbv¼ ¯’vbv¼ QK mwbœ‡ek mgZj †KvY m`„k †KvY m`„k evû Avevi MYbv Kiv D‡ëv MYbv Kiv ¸‡b hvIqv wecixZ D`vniY msL¨v MYbv msL¨v MYbv Nb/Nbdj Nb †mw›UwgUvi MY GKK kxl© (wm) g~`ªv wPý cÖ_vbyM cwigvc c×wZ cÖ_vbyM cwigvc GKK wmwjÛvi DcvË DcvË cwimsL¨v mviwY w`b w`ev‡jvK `kevû `kwgK fMœvsk `kwgK msL¨v `kwgK we›`y †WwmwgUvi msL¨v wefvRb AvK„wZ n«vm n«vmµg wWwMÖ/cwigvc †Kv‡Yi wWwMÖ cwigvc ni NbZ¡ bKkv, wWRvBb e¨vm e¨eavb msL¨v, ivwk digital clock digits dime dimension discuss distributive property divide dividend divisibility test divisible divisible by division divisor dodecahedron dollar ($) doubles minus one doubles plus one doubling draw a graph draw a graph draw a picture draw a picture drawings edge eight elapsed time ellipse endpoint eqivalent equations equal (=) equal to (=) equation equidistant marks equilateral polygon equilateral triangle equivalent equivalent equivalent decimals equivalent fractions equivalent numerical expressions equivalent ratios estimate estimation estimation strategies evaluate even number evening event examine example expanded form experimental results explain explain mathematical relationships mvswL¨K, wWwRUvj msL¨vmg~n, ivwkmg~n WvBg gvÎv Av‡jvPbv Ki wefvRb cÖK…wZ fvM Ki fvR¨, jf¨vsk wefvRbÿgZv cixÿv wefvR¨ †Kvb wKQzi Øviv wefvR¨ fvM/wefvRb wefvRK Øv`kf~R Wjvi `y¸Y †_‡K GK we‡qvM `y¸‡Yi mv‡_ GK †hvM wظY Kiv †iLwPÎ A¼b †iLwPÎ A¼b wPÎ A¼b wPÎ A¼b A¼b avi, wKbvi AvU AwZµvšÍ mgq wW¤^vK…wZ, Dce„Ë †kl we›`y mgv¼ mgxKiY mgvb (=) Gi mgvb (=) mgxKiY mg`~ieZx© mgevny enyf~R mgevny wÎf~R Z~j¨ Z~j¨ Z~j¨ `kwgK Zzj¨ fMœvsk Z~j¨ MvwYwZK ivwk Z~j¨ AbycvZ cÖvÿjb cÖvÿwjZ wnmve cÖvÿjb †KŠkj g~j¨vqb Kiv †Rvo msL¨v mܨv NUbv/cwiYvg cixÿv `„óvšÍ m¤úªmvwiZ i~c cixÿvg~jK dj e¨vL¨v Kiv MvwYwZK m¤úK© e¨vL¨v †`qv explore explore mathematical relationships exponential notations extend a pattern extend models extended fact face fact fact family (related facts) factor (noun) factor (verb) factorial fair share fewer fewer than fifths first five flip (reflection) foot (ft) formula formulate conclusions from graphs formulate predictions from graphs four four-digit number fourths fraction frequency table front-end estimation gallon (gal) generate solutions geometric figure geometric pattern geometric solid geometry gram (g) graphical representations graphs greater greater than (>) greatest greatest common divisor (GCD) greatest common factor (GCF) grid group how many guess half hour halves halving heavier height height of a 3-dimensional figure height of a parallelogram height of a rectangle cy•Lvbycy•Lfv‡e AbymÜvb Kiv cy•Lvbycy•Lfv‡e MvwYwZK m¤úK© AbymÜvb Kiv gvbm~PK A¼cvZb, GKwU ¸Ybxq‡Ki †cŠbtcywbK ¸Y‡bi m©wÿß cÖKvk c¨vUv‡b© we¯Ívi Ki g‡Wj we¯Ívi Kiv m¤úªmvwiZ NUbv Zj, cvk¦©, evû NUbv m¤^Ühy³ NUbv ¸YbxqK/Drcv`K ¸YbxqK †ei Ki †MŠwYK b¨vh¨ wnm¨v ¯^íZi n‡Z Kg cÂgvsk cÖ_g cuvP Dëv‡bv (cÖwZwe¤^) dzU (ft) m~Î wP·jL †_‡K wm×všÍ AvniY wP·jL †_‡K fwel¨ØvYx Pvi Pvi ivwki msL¨v PZy_©vsk fMœvsk cwimsL¨v mviwY g~‡j¨i cÖvwšÍK ch©vq M¨vjb mgvavb †ei Ki R¨vwgwZK AvK…wZ R¨vwgwZK c¨vUvb© R¨vwgwZK AvK…wZwewkó R¨vwgwZ MÖvg mwPÎ Dc¯’vcbv, ˆiwLK Dc¯’vcbv †iLwPÎ e„nËi n‡Z e„nËi e„nËg Mwiô mvaviY wefvRK Mwiô mvaviY ¸YbxqK wMÖW, QK KZ msL¨v K‡i MÖæc Abygvb Ki Aa© N›Uv A‡a©K wØav wef³ Kiv A‡cÿvK…Z fvix D”PZv wÎgvwÎK e¯‘i D”PZv mvgšÍwiK †ÿ‡Îi D”PZv AvqZ‡ÿ‡Îi D”PZv height of a triangle heptagon hexagon higher horizontal hour hour hand hundred chart hundred thousands hundred thousands millions hundreds hundreds place hundredths hundreths hypotenuse icosahedron identify identify the problem identity element for addition identity element for multiplication impossible outcomes improper fraction inch (in) increase increasing sequences inequality input values inscribed polygon inside integer interior angles interpret interpret models intersect intersecting lines invalid approach inverse operations inverse property investigate irrational numbers irregular polygon irregular shape irrelevant information isosceles triangle justify key sequence key to a graph kilogram (kg) kilometer (Km) kite label work language of logic(and, or, not) large/larger/largest wÎf~‡Ri D”PZv mßf~R lU‡KvY D”PZi Avbyf~wgK N›Uv N›Uvi KuvUv kZ mviwY jÿ nvRvi †KvwU kZ kZ kZ‡Ki Ni kZZg, kZvsk kZZg, kZvsk AwZf~R 20 cvk¦©-wewkó eûZjK †ÿÎ ev cwj‡nWªb hv mgevû wÎf‚R Øviv MwVZ nq kbv³ Kiv mgm¨v kbv³ Ki ms‡hvRb Kivi Rb¨ A‡f` †gŠwjK c`v_© ¸Y Kivi Rb¨ A‡f` †gŠwjK c`v_© Am¤¢e cwiYwZ AcÖK…Z fMœvsk Bw e„w× Ki ewa©Z µg AmgZv gvb emv‡bv AšÍe©ûf©~R Af¨šÍi c~Y©msL¨v AšÍt‡KvY e¨vL¨v Ki g‡Wj e¨vL¨v Ki ci¯úi †Q` Kiv ci¯úi †Q`bKvix †iLv Awm× cÖwµqv weeZ© wµqv weeZ© cÖK…wZ AbymÜvb Ki Ag~j` msL¨v welg eûf~R welg AvKvi AcÖvmw½K Z_¨ mgwØevû wÎf~R mg_©b Ki cÖavb µg ¯Í¤¢‡iLwP‡Îi m~Î wK‡jvMÖvg (‡KwR) wK‡jvwgUvi (wKwg) Nywo wPwýZ KvR hyw³i fvlv e„nr, e„nËi, e„nËg last least common denominator (LCD) least common multiple (LCM) leg of a right triangle length less less than (<) lighter like (common) denominators likely line line graph line of symmetry line plot line segment line symmetry listen liter (L) logical reasoning long/longer/longest longer longer than look for a pattern lower lowest terms (simplest form) make a chart make a diagram make an organized chart make an organized list make conjectures make observations map legend map scale mass match mathematical statements mathematics mean measure measurement median mental math meter (m) metric system of measurement metric units of measure mile milliliter (mL) millimeter (mm) millions minuend minus minus sign minute minute †kl jwNô mvaviY ni jwNô mvaviY MywYZK (jmv¸) mg‡KvYx wÎf~‡Ri evû, Z‡e AwZfzR bq ˆ`N©¨ Kg jNyZi Zzjbvg~jKfv‡e nvév m`„k nimg~n m¤¢e †iLv ˆiwLK ¯Í¤¢‡jLwPÎ cÖwZmvgm¨ †iLv †iLv wPÎ e„Ëvsk †iLv †iLv mgwgwZ †kvbv wjUvi (wj) †hŠw³K Kvh©KviY `xN©/`xN©Zi/`xN©Zg `xN©Zi Zzjbvg~jK `xN© c¨vUvb© †LuvRv Zzjbvg~jK wb‡P jwNô ivwk (mij iƒc) mviwY ˆZwi Kiv WvqvMÖvg ˆZwi Kiv myk„•Lj mviwY ˆZwi Kiv myk„•Lj ZvwjKv ˆZwi Kiv AbywgwZ wbg©vY Kiv ch©‡eÿY Kiv gvbwP‡Îi ms‡KZ gvbwP‡Îi †¯‹j fi wgj MvwYwZK wee„wZ MwYZ ga¨K, Mo cwigvc Ki cwigvc/gvb ga¨gv/ga¨‡iLv gvbmv¼ wgUvi (wg) †gwUªK c×wZi cwigvc †gwUªK c×wZ‡Z cwigv‡ci GKK gvBj wgwj wjUvi (wgwj) wgwj wgUvi (wgwg) `k jvk (wgwjqb) †h msL¨v‡K we‡qvM †`qv nq we‡qvM we‡qvM wPý wgwbU, weeiY wgwbU, weeiY minute hand mixed number mode money months of the year more more than (>) more/most morning multiple multiple representations multiplicand multiplication multiplicative inverses multiplier multiply negative number negative rational numbers next nickel night nine nonagon nonstandard measure nonstandard representations nonstandard units noon not equal to (¹) not equal to = number number in words number line number model number sentence number system numeral numeration numerator numeric expression numeric patterns numerical problems numerically objects objects created using technology obtuse angle obtuse triangle octagon octagon parallel lines odd number one one-digit number ones ones place open figure wgwb‡Ui KvUv †hŠwMK msL¨v msL¨vMwiô gvb A_© ev‡iv gvm AwaK Zzjbvg~jK †ewk †ewk/me‡P‡q †ewk mKvj eny eny‡Z¡i cªwZwbwaZ¡Kvix MyYbxqK MyY Kiv weeZ…/e¨¯Í MyYb ¸YbxqK, MyYK MyY Ki FYvZ¥K msL¨v FYvZ¥K †hŠw³K msL¨v cieZx© wb‡Kj, 5 †m›U gv‡bi g~`ªv ivZ bq bqf~R AcÖwgZ cwigvc AcÖwgZ cÖwZwbwaZ¡ AcÖwgZ GKK ga¨vnè mgvb bq mgvb bq msL¨v msL¨vi K_vq cÖKvk msL¨v †iLv b¤^i cÖwZgvb ev‡K¨i b¤^i msL¨v c×wZ msL¨vm~PK/msL¨vMZ msL¨vqb, msL¨v‡K K_vq cÖKvk je msL¨vm~PK ivwk msL¨vm~PK c¨vUvb© msL¨vm~PK mg¨mv msL¨vMZfv‡e welq, e¯‘ cÖhyw³ e¨envi K‡i cÖ¯‘Z e¯‘ ¯’‚†KvY ¯’‚j‡KvY wÎf~R Aóf~R mgvšÍivj evû Aóf~R †e‡Rvo msL¨v GK GKivwk msL¨v GKK gy³ AvK…wZ open sentence operation operational method/operation oral representations order order of operations ordered number pair ordinal numbers organize organize work organized chart organized list origin ounce (oz) over pan balance parabola parallel lines parallelogram part part-to-part ratio part-to-whole ratio pattern penny pentagon percent perimeter perpendicular lines personal references per-unit rate physical models pi pictograph pictorial representations pint (pt) place value plane plane figure plot plus point poll polygon polyhedron positive number positive power of 10 positive rational numbers possible outcomes post meridian (p.m.) pound (lb) power power of 10 predict prediction gy³ evK¨ wµqv Kvh©cYÖ vwj kvwãK cÖwZwbwaZ¡ k„•Ljv, µg wµqvµg hyMj msL¨vµg web¨¯Í msL¨v web¨vm Kiv Kg©web¨vm web¨¯Í mviwY web¨¯Í ZvwjKv Drm AvDÝ Dc‡i, Avevi, †ewk c¨vb e¨vjvÝ Awae„Ë mgvšÍivj †iLv mvgšÍwiK †ÿÎ Ask wewfbœ As‡ki AbycvZ mg‡MÖi mv‡_ As‡ki AbycvZ c¨vUvb© †cwb (GKkZ fv‡Mi GK fvM) cÂf~R kZvsk cwimxgv j¤^ †iLvmg~n e¨w³MZ Z_¨ GKK g~j¨ †fŠZ Av`k© cvB wP·jL mwPÎ cÖwZwbwaZ¡ cvB›U ¯’vbxq gvb mgZj mgZj AvK…wZ A¼b Kiv, cwiKíbv Kiv †hvM we›`y †fvU Kiv eûf~R enZjK abvZ¥K msL¨v 10 Gi abvZ¥K NvZ abvZ¥K †hŠw³K msL¨v m¤¢ve¨ dj Acivnè cvDÛ (cv) NvZ 10 Gi NvZ c~e©vfvm Kiv c~e©vfvm prime factorization prime number prism probability problem solving strategies process of elimination product proper fraction property protractor pyramid Pythagorean Theorem quadrangle quadrant quadrilateral quart (qt) quarter questions quotient radious random number randomly range rate ratio rational number rationale ray real number real world math real world situation reasonable estimates reasonableness reasonableness of a solution recognize rectangle reference frame regroup (regrouping) regular polygon regular polyhedron related facts relation symbol relevant information remainder repeated addition repeated subtraction repeating decimal rhombus right angle rotation round a number rounding rule ruler †gŠwjK ¸YK wbY©q †gŠwjK msL¨v †Zwkiv KuvP/wcÖRg m¤¢vebv mgm¨v mgvavb †KŠkj Ac‡bv`b cÖwµqv ¸Ydj/Drcbœ e¯‘ cÖKZ … fMœvsk ag©/cÖKzwZ †KvY cÖwigvcK wcivwgW wc_v‡Mvixq Dccv`¨ PZzf~©R/PZz‡®‹vY cwiwai GK PZy_©vsk PZzf~©R/PZz‡®‹vY †KvqvU© wmwK (GK PZz_©vsk) cÖkœ fvMdj e¨vmva© G‡jv‡g‡jv msL¨v G‡jv‡g‡jvfv‡e we¯Í…wZ nvi AbycvZ †hŠw³K msL¨v †gŠj hyw³/†hŠw³K wfwË iwk¥ ev¯Íe msL¨v ˆ`bw›`b MwYZ ˆ`bw›`b NUbv †hŠw³K cÖvÿjb †hŠw³KZv mgvav‡bi †hŠw³KZv ¯^xK…wZ AvqZ‡ÿÎ cwiPvqK KvVv‡gv bZzb `jwefvRb Kiv mylg eûf~R mylg enZjK mswkøó Z_¨ m¤^Ü wPý cÖvmw½K Z_¨ Aewkó c~bive„Ë †hvM c~bive„Ë we‡qvM c~bive„Ë `kwgK welg‡KvY mvgšÍwiK †ÿÎ/i¤^vm mg‡KvY NyY©b c~Y© msL¨vq cwiYZ Kiv m¤úbœ Kiv m~Î/ixwZ/wbqg cwigvcK same sample space scale drawing scale on a graph scale to measure mass scalene triangle scientific notation seasons in relation to the months second sector semicircle set of data set of objects seven shape share shorter shorter than show side similar figures similar triangles similar triangles square similarities simplest form simplify an expression simplify fractions single event single-event experiment six sixths size skip count slide (translation) small/smaller/smallest solid figure solution solution(s) solve solve a simpler problem some sort special case speed sphere spring square square array square number square of a number square root of a number square unit standard measure standard notation mgiƒc bgybv cwimi †¯‹j A¼b †jLwP‡Îi †¯‹j fi cwigvcK welg wÎf~R ˆeÁvwbK cÖZxK FZzi mv‡_ m¤úwK©Z gvm wØZxq/gyn«Z© kvLv/wefvM Aa©e„Ë DcvË web¨vm e¯‘ivwk mvZ AvK…wZ eÈb AwaKZi Lv‡Uv †P‡q Lv‡Uv `„k¨ cvk¦© Abyiƒc AvK…wZ m`„k wÎf~R m`„k †KvY wewkó eM©‡ÿÎ mv`„k¨ mijZg AvK…wZ †Kvb ivwk‡K mijxKiY Kiv fMœvs‡ki mijxKiY GKK `„óvšÍ GKK `„óvšÍwewkó cixÿv Qq lôZg AvKvi MYbv †_‡K weiZ _vKv Mov‡bv (Abyev`) ÿz`ª/ÿz`ªZi/ÿz`ªZg c~Y© Nbv¼ mgvavb mgvavbmg~n mgvavb Kiv mij mgm¨vi mgvavb Kiv wKQz web¨vm we‡kl D`vniY MwZ ejq emšÍ eM© eM© web¨vm eM© msL¨v msL¨vi eM© msL¨vi eM©g~j eM© GKK cÖwgZ cwigvc cÖwgZ A¼cvZb standard representation standard units stem-and-leaf plot step graph straight angle strategies substitute substitution subtract subtraction subtraction fact subtraction sentence subtraction sign subtrahend sum summer supplementary angles survey symbols symbols in verbal form symbols in written form table take away tall/taller/tallest tallies tally mark ten ten thousands tens tens place tenth term terminating decimal tessellation theorem third thirds thought process thousands thousandths three three-digit number three-dimensional figure tiling time to challenge thinking to clarify thinking to elicit thinking to extend thinking together ton translate trapezoid trial and error cÖwgZ cÖwZwbwaZ¡ cÖwgZ GKK KvÐ †_‡K cvZv ch©šÍ (ïiæ †_‡K †kl ch©šÍ) MÖvd‡K Aej¤^b K‡i mij †KvY †KŠkj cÖwZKí cÖwZ¯’vcb we‡qvM Kiv we‡qvM we‡qv‡Mi aviYv ev‡K¨i c„_KxKiY we‡qvM wPý we‡qvR¨ mgwó MÖx®§ m¤ú~iK †KvY Rwic cÖZxK cÖZx‡Ki †gŠwLK iƒc cÖZx‡Ki wjwLZ iƒc mviwY mwi‡q †bqv j¤^v/AwaKZi j¤v^/AwaKZg j¤^v Uvwj wgj wPý `k `k nvRvi `‡ki Pj `k‡Ki Ni GK `kgvsk c`, ivwk, kZ© mmxg `kwgK web¨¯Í Kiv Dccv`¨ Z…Zxq GK-Z„Zxqvsk wPšÍbwµqv nvRvi nvRvi GK-mnmªvsg wZb wZb ivwki msL¨v wÎgvwÎK AvK…wZ UvBwjs mgq wPšÍv‡K P¨v‡jÄ Kiv wPšÍv‡K e¨vL¨v Kiv wPšÍv‡K cÖKvk Kiv wPšÍv‡K cÖmvwiZ Kiv GKmv‡_ Ub Abyev` AmgvšÍivj evû PZzf©~R mwVK DËi bv cvIqv ch©šÍ cÖ‡Pó Ae¨vnZ ivLv triangle true/false turn (rotation) two two-digit number two-dimensional figure types of representations under understand unit unit fraction unit fractions unlike denominators unlikely use manipulatives valid approach value variable Venn diagram verbal expression verbal form of reasoning verbal language verbal process verbal symbols verify claims of others verify results vertex vertical vertical angles vertices volume week whole whole number whole numbers whole unit width winter work backwards write an equation written form of reasoning written language written representations written symbols yard (yd) year zero zero as the identy element in addition zero property of addition zero property of multiplication wÎf~R mZ¨/wg_¨v †gvo †bqv/µgvbyhvqx `yB `yB ivwki msL¨v wØgvwÎK AvK…wZ cÖwZwbwa‡Z¡i cÖKvi‡f` wb‡P, Kg Abyaveb Kiv GKK GKK fMœvsk GKK fMœvskmg~n Amv`„k nimg~n nqbv cwiPvjbvi †KŠkj e¨envi wm× c×wZ g~j¨/gvb cwieZ©bkxj ivwk e„Ë †jLwPÎ †gŠwLK Awf¨e¨w³ hyw³i K_¨ iƒc K_¨ fvlv †gŠwLK cÖwµqv †gŠwLK cÖZxK A‡b¨i `vwe cÖgvwYZ Kiv d‡ji wbf©yjZv cÖgvY kxl© j¤^ kxl© †KvY kxl© Nbdj, e¯‘i cwigvY, AvqZb mßvn c~Y© c~Y© msL¨v c~Y© msL¨vmg~n c~Y© GKK cÖ¯’ kxZ m~Pbvi w`‡K AMÖmi nIqv mgxKiY MVb Kiv hyw³i wjwLZ iƒc wjwLZ fvlv wjwLZ cÖwZwbwaZ¡ wjwLZ cÖZxK MR eQi k~b¨ †hv‡Mi k~b¨ cwiwPwZ †hv‡Mi k~b¨ ag© MY‡bi k~b¨ ag©
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