ROCHESTER COMMUNITY SCHOOL MATHEMATICS SCOPE AND SEQUENCE, K-5 STRAND: NUMERATION

Size: px

Start display at page:

Download "ROCHESTER COMMUNITY SCHOOL MATHEMATICS SCOPE AND SEQUENCE, K-5 STRAND: NUMERATION"

Wilfrid Pearson
5 years ago
Views:

1 STRAND: NUMERATION Shows one-to-one correspondence for numbers 1-30 using objects and pictures Uses objects and pictures to show numbers 1 to 30 Counts by 1s to 100 Counts by 10s to 100 Counts backwards from 10 Recognizes numerals 0 to 30 in random order Writes numbers 0 to 30 in a variety of media Estimates using 1 to 30 real objects Explores fractional parts as part of a whole and/or part of a group using real objects Demonstrates understanding of addition and subtraction using concrete materials Uses ordinals to identify position in a sequence (1 st, 4 th ) Uses objects and pictures to show numbers 1 to110 Counts from 1 to 110 by 1s, 2s, 5s and 10s; counts to 500 by 10s and 100s Counts backward from 100 starting from any number Reads and write numerals from 1 to 110 Orders and compare numerals from 1 to 110 to determine less than, greater than, and equal Identifies one more, one less, 10 more, and 10 less than any number up to 100 Knows that a number to the right is larger, to the left is smaller on a number line Demonstrates an understanding of fractions as part of a whole and/or part of a group (1/2, 1/4, 1/10) Use models to compare and order fractions (1/2, 1/4, 1/10) Concretely composes and decomposes 1s and 10s place value for numbers to 90 Uses objects and pictures to show any number Counts by 1s, 2s, 5s, and 10s forward and backward Compares two sets to determine less than, greater than, or equal to, and explains using one-to-one correspondence Estimates (mentally computes) using real and pictorial objects Constructs & describes place value (1s, 10s, 100s, 1000s) Demonstrates an understanding of fractions (1/2, 1/3, 2/3, 1/4, 2/4, 1/10, and 3/4) Uses models to compare and order fractions Recognizes & uses fraction word names (one-half, onefourth, one-tenth, three-fourths) Reads, writes, and compares numbers to 1,000 ( >, <, =, more/less than) PAGE 1

2 STRAND: NUMERATION Demonstrates concepts of place value (10,000s) with models, symbols, and expanded notation Classifies numbers as even or odd Recognizes the reasonableness of ball park estimates Interprets the part-whole meaning of any fraction with models using fraction symbols and word names Adds, compares, and orders fractions on a number line Recognizes equivalent names with denominators 2, 4, and 8 Represents and orders decimals with models Multiplies and divides multi-digit numbers Uses the relationship between multiplication and division to estimate and check the reasonableness of answers Adds and subtracts fractions to solve problems Finds common denominators 2-12, and 100 (or when one denominator is a multiple of the other) Multiplies fractions to solve problems Understands fractions as parts of sets of objects Multiplies fractions by whole numbers using repeated addition and area or array of models Reads, writes and compares numbers from.01 to 1,000,000 Composes and decomposes numbers using place value to 1,000,000 including standard form, expanded notation, and powers of 10 Compares and orders decimal equivalents with common fractions and locate on a number line Uses models to explain equivalent fractions (denominator 12 or less or = to 100) Understands relationship among 1/2s, 1/4s, 1/8ss, 1/3s, 1/6s, and 1/12s Uses the calculator to change fractions to decimals Knows and writes mixed numbers and improper fractions Solves problems with decimals: ( +, - ) AND ( x, ) Recognizes equivalent names for fractions, decimals, and percents Adds and subtracts fractions (including unlike denominators) and decimals up to thousandths Uses multi-digit numbers to solve multiplication and division problems Multiplies and divides fractions using area models Understands percentages as parts of a hundred or part of a whole; uses % notation Constructs multiplication of fractions using area models Demonstrates division including remainders Divides a fraction by a whole number and a whole number by a fraction using simple unit fractions Divides fluently up to a four-digit number by a two-digit number Reads, writes, compares value, and rounds numbers from hundredths to millions Uses a calculator to convert fractions, decimals, and percents Finds prime factorization of numbers from 1-50 PAGE 2

3 STRAND: MEASUREMENT Explores all concepts of time (including calendar, clock, and sequencing personal events) Tells time to the hour Compares length, weight, and capacity Identifies pennies, nickels, and dimes States value of pennies, nickels, and dimes Estimates and compare length using non-standard and standard units Estimates, compares, and records time to the hour and half-hour Names and sequences the days of the week and months of the year using the calendar; identifies dates on the calendar Identifies coins and bills and distinguishes their value Tells the amount of money in cents up to $1, in dollars up to $100 Adds and subtracts coins to $1, in dollars to $100 Matches one coin or bill of one denomination to an equivalent set of coins/bills of other denominations Solves one-step word problems using addition and subtraction of length, money, and time Tells, records, interprets time to 5-minute intervals and as minutes before and after the hour Measures lengths to the nearest whole unit (cm, m, in, ft, yd) Interprets the meaning of a temperature on a thermometer Sorts, classifies, and identifies pennies, nickels, dimes, quarters, half-dollars, and dollars and distinguishes the difference in value Uses pennies, nickels, dimes, quarters, and halfdollars to solve problems to $1.00 using decimal notation PAGE 3

4 STRAND: MEASUREMENT Chooses appropriate units for measuring distance, time, weight, and temperature Records time to the minute Measures in mixed units (feet & inches, centimeters & meters, grams & kilograms, ounces & pounds, milliliters & liters, minutes & hours, and months & years) Determines the area of an object using square units (inches, centimeters) Describes the perimeter and measures line segments to determine the perimeter of simple polygons Solves story problems involving the addition and subtraction of money Converts one unit to another (Metric and U.S. Customary) Measures and compares integer temperature in degress both Celsius and Fahrenheit Calculates perimeter and area of a given shape Finds one dimension of a rectangle given the other dimension and its perimeter or area Measures using common tools and selects appropriate unit of measurement Estimates and measures length, area, and weight (determine if reasonable estimate) Measures area of rectangular prisms by covering and counting area of the faces Finds the volume of geometric solids using multiplication and division and using the appropriate units Uses formulas to find areas of rectangles, parallelograms, triangles, and circles Compares the relative size of one cubic centimeter, inch foot, and meter Converts measurements of length, weight, area, volume, and time within a given system Recognizes the equivalence between liter, milliliter, and cubic centimeter PAGE 4

5 STRAND: GEOMETRY Identifies circles, squares, rectangles, and triangles Identifies positional concepts (in front of, first, next, last, high, low, behind, between, middle, inside, top, bottom, over, under, above, below) Creates common 2- and 3-dimensional shapes and describes their physical and geometric attributes Recognizes symmetry using concrete and manipulative materials Describes relative position of objects on a plane and in space Classifies and explains simple attributes of two- and three-dimensional geometric figures Plans & constructs designs & structures using geometric shapes (with paper & pencil) Recognizes and repeats symmetry, rotation, flipping, or sliding using concrete materials, pictures, and shapes Identifies and compares properties of 2- and 3- Identifies and constructs basic geometric figures and Classifies angles by names and degrees dimensional shapes uses their properties to solve problems Identifies properties of lines, line segments, rays, planes, and perpendicular and parallel lines within the environment Explains symmetry, similarity, and congruence with simple plane shapes and creates and art piece showing use of geometry Identifies and constructs faces, edges and vertices of basic 3-D geometric solids Uses geometric tools to measure angles and construct geometric figures Explains symmetry, similarity, and congruence with simple plane shapes Recognizes rigid motion transformations (flips, slides, turns of a 2-D object) Associates quarter turn angles around a fixed point Recognizes the sum of the interior angles of a triangle and quadrilateral and applies them to solving problems Knows that angles on a straight line add up to 180 and angles surrounding a point add up to 360; justifies informally by surrounding a point with angles Measures and constructs angles using geometric tools PAGE 5

6 STRAND: NUMERICAL AND ALGEBRAIC OPERATIONS AND ANALYTICAL THINKING Explores and develops an understanding of addition and subtraction combinations 1 to 10 using objects and pictures Shows what a simple problem entails using objects or pictures Compares two or more sets in terms of the difference in number of elements Knows all addition facts up to and solves the related subtraction problems fluently Adds three one-digit numbers Applies knowledge of fact families to solve simple open sentences for addition and subtraction Lists number facts (partners inside of numbers) for 2 through 10 Understands the inverse relationship between addition and subtraction Calculates mentally sums and differences involving a two-digit number and a one-digit number without regrouping Computes sums and differences up to two-digit numbers using number facts and strategies Models addition and subtraction for numbers less than 20 for a given contextual situation using objects or pictures Demonstrates that addition and subtraction facts 1 to 20 are memorized (10+10, 20-10) Understands multiplication as the result of counting the total number of objects in a set of equal groups (3 groups of 5 objects or 3 x 5) Uses multiple strategies to add and subtract numbers up to 20 (Doubles + 1, counting on ) Demonstrates multiplication & division concepts using objects; limit divisor to 1 5 Demonstrates a strategy for addition and subtraction of two- and three-digit numbers Finds missing values in open sentences (42 + = 57) Recognizes and extends an arithmetical problem involving objects (growing by a constant amount) Uses a variety of strategies to solve word problems and records using numbers and symbols Decides if an estimate is reasonable and rounds to the nearest ten Identifies and use problem solving strategies to defend decisions PAGE 6

7 STRAND: NUMERICAL AND ALGEBRAIC OPERATIONS AND ANALYTICAL THINKING Estimates and computes addition problems with up to 3-digit numbers Estimates and computes subtraction problems with up to 3-digit numbers Constructs models to show 1-digit multiplication problems Demonstrates that multiplication facts 0-10 are memorized Demonstrates that division facts 0-10 are memorized Describes multiplication and division using mathematical terminology (factor, product, divisor, dividend, quotient) Explains, solves, and writes number stories Reads, writes, adds, subtracts, and compares decimals up to hundredths Demonstrates problem solving skills using the four operations involving fractions, decimals, and whole numbers Uses different problem solving strategies such as guess and check, make and use a model, or make a list Uses geometric and numerical patterns to solve problems Writes and solves an equation and number story using a variable Multiplies fluently any whole numbers up to 3 digits using the distributive property Determines whether a number sentence containing parentheses is true or false Given an equation, writes a multiplication number story Determines factors of whole numbers through 50 Finds the prime factorization for numbers between 1 and 50 Expresses ratios in several ways and finds equivalent ratios Demonstrates and understands multiplying and dividing by powers of ten (including decimals) Demonstrates that all multiplication and division facts through twelve are memorized Recognizes and is able to explain common computational errors in a multi-digit multiplication problem Multiplies and divides numbers by powers of ten Divides numbers by 10s, 100s, 1,000s using mental strategies Relates division of whole numbers with remainders to the form a=d*q+r Uses different problem solving strategies such as eliminate possibilities, find a pattern, or draw a picture Checks a solution by evaluating the reasonableness of the answer Finds solutions to open sentences for +, -, x, problems (Ex. x 7 = 21) Identifies prime numbers Given an equation, writes a division number story; given a division number story, writes an equation Using different strategies, solves and explains problems Solves open sentences with symbols or letters using fractions, e.g. 2(b+3)=16 Solves for the unknown in such equations as ¼ + y=7/12 Writes a number sentence for a given situation involving addition and/or subtraction of fractions Solves applied problems involving fractions and decimals (including money); includes rounding of answers and checking reasonableness) PAGE 7

8 STRAND: PATTERNS, RELATIONSHIPS, AND FUNCTIONS Sorts and identifies sets of objects by their attributes Reads and copies simple patterns using concrete materials Extends simple patterns using concrete materials Identifies patterns in the environment Matches, copies, and extends simple patterns using concrete materials, pictures, and numerals Creates, describes, and distinguishes between growing and repeating patterns using number, shape, and size Matches, copies, and extends patterns Identifies, constructs, records, and searches for patterns in the environment Recognizes, describes, and extends patterns using models including square numbers Recognizes and determines the first ten multiples of whole numbers 0-9 Identifies, uses, constructs, and explains repeating, shrinking, and growing patterns Recognizes geometric and numerical patterns in the environment Formulates a rule for sorting objects using no more than two attributes PAGE 8

9 STRAND: STATISTICS, DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS Records data and reads concrete graphs and pictorial graphs Collects, records, and interprets data from concrete, pictorial, and simple bar graphs Creates, reads, and solves problems using pictographs with scale factors of 2 & 3 (= 2 apples) Predicts the likelihood of simple events occurring Organizes data to create a graph or table Draws conclusions supported by data in table or graph form (using the terms maximum, minimum, and range) Makes predictions based on outcomes of probability experiments Interprets and solves problems from given data in a table or graph Uses fractions to report the likelihood that an event will occur Uses mean, mode, median, range minimum, and maximum to explain patterns or trends Uses data to construct and interpret problems with line graphs PAGE 9

Third Grade Mathematics

Third Grade Mathematics By the end of grade three, students develop understandings of multiplication and division of whole numbers. They use properties to develop increasingly more sophisticated strategies