Grade 8 Mathematics - Texas Education Agency

1 Copyright September 2014, Texas Education Agency . All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from the Texas Education Agency . _____ TEKS Curriculum Framework for staar Alternate 2 Grade 8 Mathematics Mathematics TEKS Curriculum Framework for staar Alternate 2 | Grade 8 September 2014 1 staar Alternate 2 Mathematics Instructional Terms The curriculum that will be assessed each year for staar Alternate 2 is determined by the essence statements that are selected for each administration. Teachers should refer to the Curriculum Framework documents for each selected essence statement to locate the prerequisite skills that are linked to that essence statement. Instruction should focus on the listed prerequisite skills. The teacher should determine what skills have been mastered and which need to be taught according to the developmental level of the student.

2 The goal should be to assist the student in attaining the highest academic level the student is capable of within a given year. In addition to the prerequisite skills, there are instructional terms that students will need exposure to during instruction. The following list includes the terms for all the essence statements and not just the ones selected for a given administration. Students need to become familiar with these terms as the student is developmentally able to comprehend the content. Students in higher grades need to also know the terms presented in earlier grades. Grade 3 Mathematics set /dividing equally alike/same as/different length/longer/longest three-dimensional geometric figures: sphere, cube, cone, rectangular prism, cylinder, pyramid addition/subtraction models pattern/extend order: least to greatest, longest to shortest equal/total number pair plus/minus graph: category, label, row, column measurement: weight, mass, capacity, area, height needs/wants as related to budgets number sentence chart/picture graph/bar graph earn money/save/spend fact family representation/represents attributes: vertices, faces, edges names and values of coins numeral/odd/even record/results/data two-dimensional shape: circle, triangle, rectangle, square, polygon next to/after/before/between fraction: whole, half, separate Grade 4 Mathematics less than/more than fractions.

3 Shaded parts of a whole, halves, fourths symmetry rounding most/least volume spending plan Grade 5 Mathematics equation triangles: right, acute, obtuse parallel/intersecting/ perpendicular lines coordinate grid equivalent fractions congruent decimal numerator/denominator square inch number line/point on a number line estimation attributes of geometric figures: sides Grade 6 Mathematics divide table of related or paired numbers area and formula of a rectangle or square: (length, width) income/saving/spending number line: whole numbers, halves pictograph/line graph/point ratio Grade 7 Mathematics multiply congruence linear relationships mean/median/mode/range attributes of geometric figures: bases formula for perimeter conversions proportional percent radius/diameter/circumference budget/deposit/withdrawal Grade 8 Mathematics line of symmetry horizontal/vertical increase/decrease/expenses probability Algebra I grid/unit square feet rate/rate of change expressions recycled Mathematics TEKS Curriculum Framework for staar Alternate 2 | Grade 8 September 2014 2 staar Reporting Category 1 Numerical Representations and Relationships: The student will demonstrate an understanding of how to represent and manipulate numbers and expressions.

4 TEKS Knowledge and Skills Statement/ staar -Tested Student Expectations Essence of TEKS Knowledge and Skills Statement/ staar -Tested Student Expectations ( ) N umber and operations. Th e stu d en t ap p lies m ath em atical p rocess stan d ard s to rep resen t an d u se real n u m bers in a variety of form s. Th e stu d en t is exp ected to (A) exten d p reviou s kn ow led ge of sets an d su bsets u sin g a visu al rep resen tation to d escribe relation ship s betw een sets of real n u m bers; Su p p ortin g Stan d ard (B) ap p roxim ate th e valu e of an irration al n u m ber, in clu d in g an d squ are roots of n u m bers less th an 225, an d locate th at ration al n u m ber ap p roxim ation on a n u m ber lin e; Su p p ortin g Stan d ard (C) con vert betw een stand ard d ecim al n otation and scien tific n otation ; Su p p ortin g Stan d ard (D) ord er a set of real n u m bers arisin g from m athem atical an d real-w orld contexts.

5 Read in ess Stan d ard Recogn izes or m od els relation sh ip s betw een d ifferen t form s or sets of n u m bers. Prerequisite Skills/Links to TEKS Vertical Alignment Determining and Simplifying N umeric and A lgebraic Expressions extend previou s knowledge of sets an d subsets using a visual representation to describe relationships between sets of rational numbers gen erate equ ivalen t exp ression s u sin g th e p rop erties of op eration s: inverse, id en tity, com m u tative, associative, an d d istributive p rop erties d eterm in e if tw o exp ression s are equ ivalent u sin g con crete m od els, p ictorial m od els, an d algebraic rep resen tation s distinguish between expressions and equations verbally, numerically, and algebraically gen erate equ ivalen t n u m erical exp ression s u sin g ord er of op eration s, inclu d in g w h ole n u m ber exp on en ts an d p rim e factorization sim p lify n u m erical exp ression s th at d o n ot in volve exp on en ts, in clu d in g u p to tw o levels of grou p in g d escribe th e m ean in g of p aren th eses an d brackets in a n u m eric exp ression represent the value of the digit in decimals through the thousan dths using expanded notation and numerals rep resen t th e valu e of th e d igit in w h ole n u m bers th rou gh 1,000,000.

6 000 an d d ecim als to th e h u n d red th s u sin g exp an d ed n otation an d n u m erals in terp ret th e valu e of each p lace-valu e p osition as 10 tim es th e p osition to th e righ t an d as on e-ten th of th e valu e of th e p lace to its left Continued Mathematics TEKS Curriculum Framework for staar Alternate 2 | Grade 8 September 2014 3 Prerequisite Skills/Links to TEKS Vertical Alignment describe th e math ematical relationship s found in th e base-10 place valu e system through th e hundred thousan d s place compose an d d ecompose numbers u p to 100,000 as a sum of so many ten thousands, so man y thousands, so many hundreds, so many tens, and so many on es using objects, p ictorial models, an d numbers, includin g expanded notation as appropriate use standard, word, and expanded form s to rep resent numbers u p to 1,200 use concrete an d p ictorial models to compose an d d ecompose numbers u p to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones ap p ly p rop erties of op eration s to ad d an d su btract tw o or th ree n u m bers use objects, pictu res, and expanded and standard form s to rep resent numbers u p to 120 use concrete an d p ictorial models to compose an d d ecompose numbers u p to 120 in more than on e way as so man y hundreds, so many tens, an d so many ones compose an d d ecompose numbers u p to 10 with objects and p ictu res Comparing, Ordering, and Rounding Numbers Using Place Value order a set of rational numbers arising from mathematical and real-world contexts round decimals to tenth s or hundredths compare and order tw o decimals to thousandths an d represent comparisons using the symbols >, <.

7 Or = compare and order decimals using concrete and visual models to th e hundredths round whole numbers to a given place value through the hundred thousands place compare and order whole numbers to 1,000,000,000 and represent comparisons using the sym bols >, <, or = compare and ord er w hole numbers up to 100,000 an d rep resent comparisons using th e sym bols >, <, or = use an und erstanding of p lace valu e to d etermine th e number that is 10 or 100 more or less than a given number u p to 1,200 u se p lace valu e to com p are an d ord er w h ole n u m bers u p to 1,200 u sin g com p arative lan gu age, n u m bers, an d sym bols (>, <, or =) u se relationship s to d eterm in e th e n u m ber th at is 10 m ore an d 10 less th an a given n u m ber u p to 120 rep resen t the com p arison of two n u m bers to 100 u sin g th e sym bols >,<, or = ord er w h ole n u m bers u p to 120 u sin g p lace valu e an d op en n u m ber lin es u se p lace valu e to com p are w h ole n u m bers u p to 120 u sin g com p arative lan gu age u se com p arative lan gu age to d escribe tw o n u m bers u p to 20 p resen ted as w ritten n u m erals com p are sets of objects u p to at least 20 in each set u sin g com p arative lan gu age Recognizing N umbers and Counting classify w h ole n u m bers, integers.

8 Rational n u m bers u sing a visu al rep resentation su ch as a Venn d iagram to d escribe relationsh ip s betw een sets of n u m bers identify prime and composite numbers d eterm in e if a n u m ber is even or od d u sin g d ivisibility ru les determine whether a number up to 40 is even or odd using pairings of objects to represent the number Continued Mathematics TEKS Curriculum Framework for staar Alternate 2 | Grade 8 September 2014 4 Prerequisite Skills/Links to TEKS Vertical Alignment gen erate a n u m ber th at is greater th an or less than a given w h ole n u m ber u p to 1,200 skip count by twos, fives, an d tens to d etermin e th e total number of objects up to 120 in a set recite numbers forward and backward from any given number between 1 and 120 gen erate a n u m ber th at is greater th an or less than a given w h ole n u m ber u p to 120 recogn ize instantly th e qu an tity of stru ctu red arran gem en ts recite numbers up to at least 100 by on es and ten s beginning with an y given number gen erate a n u m ber th at is on e m ore th an or on e less th an an oth er n u m ber u p to at least 20 gen erate a set u sin g con crete an d p ictorial m od els th at rep resen ts a n u m ber th at is m ore th an , less th an.

9 An d equ al to a given n u m ber u p to 20 recogn ize instantly th e qu an tity of a sm all grou p of objects in organ ized an d ran d om arran gem en ts cou n t a set of objects u p to at least 20 an d d em on strate th at th e last n u m ber said tells th e n u m ber of objects in the set regard less of th eir arran gem en t or ord er read , w rite, an d rep resent w h ole n u m bers from 0 to at least 20 w ith an d w ith ou t objects or p ictu res cou n t forw ard an d backw ard to at least 20 w ith an d w ith ou t objects Counting skills recogn ize on e d igit n u m erals, 0 9 verbally id en tify, w ith ou t cou n tin g, th e n u m ber of objects from 1 to 5 u se th e verbal ord in al term s d em on strate u n d erstan d in g th at w h en cou n tin g, th e item s can be ch osen in an y ord er cou n t u p to 10 item s, and d em on strate th at th e last cou n t in d icates h ow m an y item s w ere cou n ted d em on strate th at th e ord er of th e cou n tin g sequ en ce is alw ays th e sam e, regard less of w h at is cou n ted cou n t 1-10 item s, w ith one cou n t p er item u se w ord s to rote cou n t from 1 to 30 kn ow th at objects, or p arts of an object, can be cou n ted N OTE: Un d er each head in g th e p rerequ isite skills are arran ged from th e h igh est grad e level to th e low est grad e level.

10 Mathematics TEKS Curriculum Framework for staar Alternate 2 | Grade 8 September 2014 5 staar Reporting Category 2 Computations and Algebraic Relationships: The student will demonstrate an understanding of how to perform operations and represent algebraic relationships. TEKS Knowledge and Skills Statement/ staar -Tested Student Expectations Essence of TEKS Knowledge and Skills Statement/ staar -Tested Student Expectations ( ) Proportionality. The stu d en t ap p lies m ath em atical p rocess stan d ard s to exp lain p rop ortion al an d n on-p rop ortion al relation sh ip s in volvin g slop e. Th e stu d en t is exp ected to (A) u se sim ilar righ t trian gles to d evelop an u n d erstan d in g th at slop e, m, given as th e rate com p aring th e ch an ge in y-valu es to th e ch an ge in x-valu es, (y2 y1)/(x2 x1), is th e sam e for an y tw o p oin ts (x1, y1) an d (x2, y2) on the sam e line; Su p p ortin g Stan d ard (B) grap h p rop ortion al relation ship s, in terp retin g th e u nit rate as th e slop e of th e lin e th at m od els th e relation sh ip ; Read in ess Stan d ard (C) u se d ata from a table or grap h to d eterm in e the rate of ch an ge or slop e an d y-in tercep t in m ath em atical an d real-w orld p roblem s.