read, write, compare, & order numbers to 1000 apply place value concepts to thousands place

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1 Page 1 of 14 CALCULATIONS & ESTIMATIONS WHOLE NUMBERS rote count to 20 count to 1000 know one-to-one correspondence to 10 show understanding of 0 write, compare and order numbers to 10 recognize numerals out of sequence (0-10) recognize place value of ones and tens using physical models read, write, compare, (>, <)& order numbers to 1000 understand place value of ones, tens, hundreds Use physical models to show understanding of addition and subtraction know additon and subtraction facts to 10 read, write, compare, & order numbers to 1000 apply place value concepts to thousands place use physical models to show understanding of addition & subtraction understand place value of ones, tens hundreds, thousands, ten-thousands, hundred-thousands, millions understanding place value understand place value concept involved in addition & concept involved in additon and subtraction (without regrouping) subtraction (without regrouping) know addition and subtraction know addition and subtraction facts to 18 facts understand relationships among numbers and fact families. (3+2=5, 2+3=5, 5-3=2, 5-2=3) understand relationships among numbers and fact families. (3+2=5, 2+3=5, 5-3=2, 5-2=3) add and subtract to tens place add and subtract hundreds add 3-digit plus 3-digit whole numbers with regrouping subtract 3-digit minus 3-digit without regrouping place with & without regrouping whole numbers with regrouping know property of 0 (8+0=8), property of 1 (8+1=9), 9-1=8) for addtion and subtraction explore use of calculator know property of 0 (8+0=8), property of 1 (8+1=9), 9-1=8) for addtion and subtraction use calculator to check addition and subtraction solve simple story problems solve simple story problems involving addition & subtraction involving addition & subtraction round one-, two-, or three- digit numbers to the nearst 10, 100, or 1000 for addition & subtraction problems read, write, comapre, and order numbers to 1,000,000 use place values through billions show expanded form (8,675,657 = 8,000, , , , know addtion and subtraction facts add and subtract 5-digit numbers with and without regrouping read and order numbers to the billions place add and subtract up to five-digit numbers with regrouping round one, two or three digit numbers to the nearst 10,100, round to nearest 10, 100, 1000, 1000 for addition and to estimate answer to subtraction problems calculations estimate which place will be most helpful in estimating an answer

2 Page 2 of 14 CALCULATIONS & ESTIMATIONS WHOLE NUMBERS identify odd & even numbers identify odd & even numbers use ordinal numbers for calendar identify ordinal position (1st, 2nd, 3rd, etc.) know multiples of 10's and 5's to 100 read, write and order ordinal numbers (1st to 10th) know multiples of 5's, 10's and 2's to 100 apply concept of odd and even numbers order first through tenth, in numeric (1st) or word (first) form know multiplications facts understand concept of multiples know division facts use physical models to show understanding of multiplication know multiplication facts understand multiplication is repeated additon (3X4 = 4+4+4) demonstrate properties of 0 recognize properties of 0 (8X0=0) and of 1 (8X1=8) (8X0=0) and of 1 (8X1=8) understand concept of multiples solve 2-digit by 2-digit multiplication problems multiply two-digit numbers multiply multiples of 10, 100, 1000 (80X10, 90X100, multiply by powers of 10 up to 700X1000) 1000 to simplify calculations use physical models to show round to estimate answer to understanding of division calculations know division facts understand fact families (7X6, 6X7, 42 7, 42 6) understand division is repeated subtraction (12 4 = 4-4-4) demonstrate properties of 0 (8 0=0) and 1 (8 1=8) recognize properties of 0 (8 0=0) and 1 (8 1=8) use front-end estimation to predict ranges for quotients

3 Page 3 of 14 WHOLE NUMBERS DECIMALS CALCULATIONS & ESTIMATIONS read, write and recognize money amounts under $1.00 in decimal form read, write and recognize money amounts under $10.00 in decimal form apply place values to hundredths place using money solve division problems with a one digit divisor, with & without reminders. identfy the order of operations for multiple-step calculations (42-8 X 10) solve multiplication & division word problems divide up to 3-digits by onedigit numbers with remainders Identify the order of operations for multiple-step caluclations (include addition, subtraction, multiplication, division) identify correct operations for solving word problems pose equivalent questions for word problems add & subtract money amounts under $1.00 (written in decimal form) without regrouping add & subtract money amounts under $10.00 (written in decimal form) with regrouping add & subtract money to $ (written in decimal form) with regrouping estimate to the nearest dollar for amounts under $ add & subtract money to $ (written in decimal form) with regrouping read decimals to the hundredth place add & subtract decimals to the hundreths place round to the nearest hundreth to estimate answers read decimals to the thousandths place add, subtract, multiply & divide decmals to the hundredth place, division terminating at thousandths round to the nearest hundreth to estimate answers

4 Page 4 of 14 FRACTIONS CALCULATIONS & ESTIMATIONS demonstrate knowledge of whole & half (of a group and parts of a whole) using physical models read and write fractions (1/4, 1/2, 3/4) read and write fractions (1/4, 1/2, 3/4) read & write proper fractions name simple fractions with name fractions from pictoral numerators and single-digit representation (parts of a common denominators from whole or parts of a group pictoral representations name simple fractions with numerators and single-digit common denominators from pictoral representations read, write, and order proper fractions add and subtract like fractions order fractions with single-digit numerators & unlike denominators add, subtract, multiply & divide fractions with common denominators (no improper fractions) use factors and multiples to reduce fractions to lowest terms and identify fraction equivalents recognize primes less than 100 recognize multiplicative identify fractions equal to 0 or 1 inverses (3/4 X 4/3 =1) OTHER interpret pictoral representations of percents recognize common percentages (25%, 50%, 75%) recognize negative numbers (using temperature or number lines)

5 Page 5 of 14 MONEY TIME MEASUREMENT identify coins (penny, nickel, dime, quarter) name 7 days of the week understand "yesterday", "today", and "tomorrow identify coins (penny, nickel, dime, quarter) state value of coins. combine coins to make given amounts up to 25 cents show a variety of coin combinations to make the same amount. (up to 25 cents) name 7 days of the week name 12 months of the year tell and write time to the hour identify coins (penny, nickel, dime, quarter) state value of coins. identify all coins identify all coins identify all coins combine coins to make given amounts up to $1.00 make change from $1.00 make change from $10.00 make change from $ show a variety of coin combinations to make the same amount (up to $1.00) use money to create & solve word problems (to $1.00) name 7 days of the week name 12 months of the year tell number of days in a month and a year tell numbers of weeks in year use money to create & solve word problems (to $1.00) tools to measure time - seconds, minutes, hours, days, weeks, months, years solve word problems with monetary amounts (to $10.00) tools to measure time - seconds, minutes, hours, days, weeks, months, years and half hour tell & write time to 1 minute tell & write time to 1 minute understand "past", "present", "future", "the day after tomorrow", "a week ago", "last year understand "yesterday", "today", and "tomorrow" write date in words and numbers (March 19, 1998 and ) write date in words and numbers (march 19, 1998 and ) solve a variety of word problems with monetary amounts, finding totals and change due for amounts under $ tools to measure time - seconds, minutes, hours, days, weeks, months, years tell time from illustrations of digital and analog clocks understand "past", "present", "future", "the day after tomorrow", "a week ago", "last year tell and write elapsed time tell and write elapsed time

6 Page 6 of 14 LENGTH PERIMETER WEIGHT MEASUREMENT Identify: shorter/longer, larger/smaller, thicker/thinner, wider/narrower, taller/shorter identify: more/less identify: heavier/lighter (use balance to compare weights) identify: shorter than, longer than, bigger than, etc (>,<) measure length in nonstandard units and inches explore concepts of weight using non standard units of measurements & balance tools to measure length, inch, foot yard measure length in inches, feet, yards know relationships and equivalents of inches to feet and yards understand perimeter is the distance around an area choose appropriate units and tools to measure weight - ounce, pound using balance or scale to measure weight of objects in ounces, pounds chose appropriate units & tools to measure length - inch, foot, yard, mile; centimeter, meter, kilometer measure lengths in inches, feet, yards, centimeters know relationships and equivalents of inches to feet and yards measure perimeter in inches, feet, yards; centimeters tools to measure weight - ounce, pound; gram, kilogram measure weight of objects in pounds and kilograms chose appropriate units & tools to measure length - inch, foot, yard, mile; centimeter, meter, kilometer measure lengths in inches, feet, yards, centimeters know relationships and equivalents of inches to feet and yards estimate length in inches, feet, yards; centimeters, meters, kilometers calculate perimeter from measurements given of sides of polygons tools to measure weight - ounce, pound; gram, kilogram measure weight of objects in pounds and kilograms estimate weight in ounces, pounds, tons; grams, kilograms chose appropriate units & tools to measure length - inch, foot, yard, mile; centimeter, meter, kilometer read lengths from illustrations of rulers know equivalents: 12in =1ft, 3ft=1yd estimate length in inches, feet, yards; centimeters, meters, kilometers calculate perimeter from measurements given of sides of polygons tools to measure weight - ounce, pound, tons; grams, kilograms read measurements from illustrations of scales estimate weight in ounces, pounds, tons; grams, kilograms

7 Page 7 of 14 TEMPERATURE VOLUME CAPACITY AREA VOLUME ANGLES MEASUREMENT understand concept of cold, hot, cool, warm know thermometer rises & falls as temperature increases & decreases explore cup, pint, gallon read thermometer for room or outdoor temperature in Fahrenheit know teaspoon,tablespoon, cup, pint, quart, gallon tools to measure temperature - degrees Fahrenheit, degrees Celsius measure temperatures of degrees Fahrenheit and degrees Celsius using thermometers tools to measure capacity - teaspoon, tablespoon, cup, pint, quart, gallon; milliliter, liter choose appropriate units and tools to measure area - square units measure area by counting square units choose appropriate units and tools to measure angles - degrees tools to measure temperature - degrees Fahrenheit, degrees Celsius read measurements from illustrations of thermometers know freezing & boiling points - ºF, ºC tools to measure capacity - teaspoon, tablespoon, cup, pint, quart, gallon; milliliter, liter know equivalents - 2 cups = 1 pint, 2 pints = 1quart, 4 quarts = 1 gallon estimate capacity choose appropriate units and tools to measure area - square units measure area by dividing rectangular shape into square units choose appropriate units and tools to measure angles - degrees know acute, righ (90º), obtuse angles tools to measure temperature - degrees Fahrenheit, degrees Celsius read measurements from illustrations of thermometers know freezing & boiling points - ºF, ºC tools to measure capacity - teaspoon, tablespoon, cup, pint, quart, gallon; milliliter, liter know equivalents - 2 cups = 1 pint, 2 pints = 1quart, 4 quarts = 1 gallon estimate capacity choose appropriate units and tools to measure area - square units measure area by dividing rectangular shape into square units calculate area from measurements given of sides polygons (l X w) measure volume by dividing rectangular solids into cube units calculate volume from measurements given of edges of rectangular solids ( l X w X h) choose appropriate units and tools to measure angles - degrees measure acute, right, obtuse angles using protractor

8 Page 8 of 14 PROBABILITY DATA CHARTS GRAPHS STATISTICS & PROBABILITY collect data for bar graphs, pictograps, & calendars. Recognize organization of number line (counting days in school so far) Use terms "likely" and "unlikely" predict, collect, record data collect data and read bar graphs, pictographs, calendar. Read number line make predictions using terms "likely" and "unlikely" make prediction using coins, dice, evenly divided spinners predict, collect, record data, compare results to prediction collect data and read horizontal & vertical bar graphs, pictographs, charts, calendar use "likely", "unlikely", and use "likely", "unlikely", and "certain" to describe probability "certain" to describe probability determine probability using coins, dice, spinners, (evenly and unevenly divided), up to 100 objects hidden containers, daily happening such as chance of rain predict, collect, record data, compare results to prediction interpret data from charts or tables with five or fewer entries, horizontal & vertical bar graphs with five or few bars, & pictographs with 10 or fewer data pieces (data limited to whole numbers up to 200, whole dollar amounts up to $100) determine probability using coins, dice, spinners (evenly & unevenly divided), drawing objects from a container, charting observed natural occurrences, interpreting data from games or sports events. Express probability as chance probable to total chances possible. read information form number lines, bar graphs, line graphs, charts and compare two quantities on the same display determine mean and median of 10 or fewer numbers determine probability using coins, dice, spinners (evenly & unevenly divided), drawing objects from a container, charting observed natural occurrences, interpreting data from games or sport events. Express probability as a fraction, decimal, ratio. read information form number lines, bar graphs, circle graphs, stem and leaf plots, charts, histograms and compare two uantities on the same display (data may include time, money, height, weight, length, distance, age, quantity, speed) determine mean, median, mode of 10 or fewer numbers that are no larger than 100 Find one missing piece when the mean is missing.

9 Page 9 of 14 STATISTICS & PROBABILITY recognize, describe, extend, and create a variety of geometric patterns recognize, describe, extend, and create a variety of geometric patterns recognize, describe, extend & create a variety of numeric patterns supply the next element in a pattern supply an element that is missing from a pattern identify an element that does not belong in a pattern (patterns include additon and subtraction, monetary relationships under $1.00, arrangements of geometric figures) supply the next element in a give pattern supply an element that is missing from a pattern identify an element that does not belong in a pattern chose a written description that explains how to generate the pattern in a single step. reproduce a pattern in another format. (patterns may include addition & subtraction, multiples of the numbers 2 through 9, monetary relationships under $10.00, relationships between numerator and denominator of a fraction using common multiples, divisions or arrangements of twodimensional geometric figures, examples of real-world events - season, cycles, architecture) supply an element that is missing from a pattern identify an element that does not belong in a pattern chose a written description that explains how to generate the pattern in a single step. reproduce a pattern in another format. (patterns may include addition, subtractions, multiplication, division of whole numbers, relationships between numerator and denominator of a fraction using common multiples, monetary relationships, arrangement of two-dimensional geometric figures, relationships among component parts of geometric figures) supply an element that is missing from a pattern identify an element that does not belong in a pattern choose a written description that explains how to generate a pattern in another format reproduce a pattern in another format. create a pattern that models an everyday event. (patterns may include addition, subtractions, multiplication, division of whole numbers, addition of decimals to hundredths, relationships between the numerator and denominator of a fraction using common multiles or factors, monetary relationships, arrangements of two- or threedimensional geoetric figures, relationships among component parts of geometric figures)

10 Page 10 of 14 PATTERNS OPEN SENTENCES ALGEBRAIC RELATIONSHIPS Solve problems that demonstrate a relationship between two quantities such as number of people who cam be seated at a table & the number of tables needed, measurement equivalences. supply missing addends in addition equations (8 + = 10) recognize patterns & supply missing elements in a table supply missing addends in addition & subtraction equations (6 + = 10, 17 - = 9) recognize patterns & supply missing elements in a table recognize patterns and supply missing elements tn table fomat recognize mathematical relationship in a word problem extend and / or generalize patterns to solve word problems supply missing addends and factors in equations (10 + =21, x 5 = 15) recognize patterns and supple missing elements in twocolumn tables, bar graphs, Cartesian graphs (first quadrant), number sentences, written descriptions of the reationship (problems include adding and mutiplying whole numbers, open sentences and addition, subtraction, multiplication, division of whole numbers 8 x P = 72 P=?) interpret patterns in two-column tables, bar graphs, coordinate graphs, number sentences, written description of the reationship (emphasis on simple, single step relationships, problems include relationships with adding or multiplying whole numbers, open sentences model single operations - addition, subtraction, multiplication, division of whole numbers 8 x P =72)

11 Page 11 of 14 GEOMETRY GEOMETRY identify circle, square, triangle, rectangle, oval sort and classify geometric shapes by attributes compare geometric shapes using terms "same" and "different" identify circle, square, triangle, oval, rectangle sort and classify geometric shapes by attributes recognize sphere, cube compare geometric shapes using the terms "same" and "different" identify circle, square, triangle, oval, rectangle identify line segments and angles of square, triangle, rectangle recognize sphere, cube, cone, cylinder, pyramid recognize symmetry identify properties of geometric figures by determining which shape does not belong to a group of shapes identify properties of geometric figures by indicating shapes that are identical in all properties recognize, describe, & provide real-world counterparts for line segments, angles (acute, right, obtuse), triangles, quadrilaterals (tapezoid, paralellogram, rectangle, rhombus, square), pentagons, hexagons, octagons, spheres, cubes understand concept of inside & outside of a shape identify closed and not-closed figures visualize 3-dimensional shapes shown "unfolded" in 2- dimensional representations visualize folding individual shapes to show symmertry identify properties of geometric figures by determining which shape does not belong to a group of shapes identify properties of geometric figures by indicating shapes that are identical in all properties identify properties of geometric figures by recognizing similar shapes (those that maintain the same shape, but are different sizes) visualize shapes that may be reflected and rotated-line segments, angles, triangles, quadrilaterals, circles (including location of diameter & radius), spheres, and cubes identify, measure & visualize geometric figures and their component parts for points, line segments, rays, angles (acute, right, obtuse), circles (rasius, diameter) polygons (triangle, quadrilaterals, trapezoid, paralellogram, rectangle, rhombus, square, pentagon, hexagon, octagon), three dimensional solids ( sphere, cube), concepts of parallel and perpendicular identify similarity and symmetry of figures - polygons, cubes, spheres that have been transformed by translation - slide, rotation - turn, relfection - flip, dilation - shrinking or enlarging identify, measure & visualize goemetric figures and their component parts for points, line segments, rays, angles (acute, right, obtuse), circle (radius, chord, diameter) polygons (triangle, quadrilaterals, trapezoid, parallelogram, rectangle, rhombus, square, pentagon, hexagon, octagon), three-dimensional solids (sphere, cylinder, pyramid, rectangular solid, cube), concepts of parallel and perpendicular identify congruence, similarity, and symmetry of figurespolygons (of 8 sides or less), simple irregular shapes, rectangular solids, spheres, & cylinders that have been transformed by translationslide, rotation-turn, reflectionflip, dilation-shrinking or enlarging (formal or informal terminology used)

12 Page 12 of 14 PROBLEM SOLVING CONCEPTUAL UNDERSTANDI NG identify problems identify problems identify problems PROCESS AND STRATEGIES select pertinent information select pertinent information select pertinent information use pictures and models to show mathematical concepts discuss a solution process use symbols and models to show mathematical concepts select & use clues & guess & check or estimation for problem solving strategies COMMUNICATI ON discuss the problem discuss the problem VERIFICATION recognize math terminology explain, manipulate, draw & use symbols understand and use math terminology use symbols and models to show mathematical concepts select and use clues & guess & check, estimation, or look for a pattern for problem-solving strategies write problem's main idea clearly explain, manipulate, draw & use symbols clearly write solution process for one-step problems write math terminology reread written solution process use pictures, models, diagrams, and symbols to show main mathematical concepts in the problem select and use relevant information in the problem to solve it select and use mathematical strategies. Apply graphic and/or numeric models to solve the problem communicate the solution with clear reasoning applicable to the problem review the work (calculations & strategies) to verify the accuracy & reasonableness fo the results use pictures, models, diagrams, and symbols to show main mathematical concepts in the problem select and use relevant information in the problem to solve it select and use mathematical strategies. Apply graphic and/or numeric models to solve the problem communicate the solution with clear reasoning applicable to the problem review the work (calculations & strategies) to verify the accuracy & reasonableness fo the results use pictures, models, diagrams, and symbols to show main mathematical concepts in the problem select and use relevant information in the problem to solve it select and use mathematical strategies. Apply graphic and/or numeric models to solve the problem communicate the solution with clear reasoning applicable to the problem review the work (calculations & strategies) to verify the accuracy & reasonableness fo the results

13 Page 13 of 14 ESTIMATION MEASUREMENT RELATIONSHIPS GEOMETRY STATISTICS & PROBABILITY PROBLEM SOLVING Numbers: Length: equations Lines: mode solve ones inch value side mean process tens foot patterns parallel lines median figure out hundreds yard open sentence intersecting lines average chart thousands mile addend perpendicular random graphs millions millimeter factor line segment data diagrams billions centimeter curved line graphs models place value meter Angles: charts symbols rounding kilometer acute tables explain odd/even ruler right chance / chances example standard numeral yardstick obtuse equally likely strategy original number width\ Shapes: most likely guess and check missing number height 2-dimensional just as likely pattern expanded form perimeter polygon half as likely estimate decimals Weight: square triangle twice as likely solution Operations: ounce quadrilateral exactly twice as likely check compute pounds rectangle three times as likely solve tons parallelogram fewest add grams trapezoid most reasonable sum kilograms rhombus not likely subtract scale hexagon certain difference balance octagon unlikely multiply Volume / Capacity 3 - dimensional product cup sphere divide pint cube quotient quart cone regrouping gallon cylinder round (to nearest) milliliter pyramid front-end estimation Liter edge estimate (reasonable) Area: face count length, width rectangle double square units prism / solid half square inch Circle average square foot diameter number sentence square centimeter radius calculator Other: chord properties metric visualize Comparisons: measure congruent sequence measurement similar order Volume / Capacity symmetry least to greatest cubic transformations smallest to largest Money: rotation (turn) closest to decimal point translation (slide) less than spend reflection (flip) greater than buy / bought dilation (shrinking or enlarging) equal dollar sign decrease cents sign increase change which is most cheaper

14 Page 14 of 14 ESTIMATION MEASUREMENT RELATIONSHIPS GEOMETRY STATISTICS & PROBABILITY PROBLEM SOLVING word name Fractions: whole half 1/2 quarter 1/4 third 1/3 lowest terms numerator denominator equivalents multiples factors prime numbers combination of (coins) largest smallest greater than less than least fewest Time: seconds minutes hours day digital clock analog clock elapsed time Temperature: degrees Celsius Fahrenheit thermometer