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The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students NUMBER SENSE UNDERSTAND THE BASE 10 NUMBER SYSTEM Whole numbers Understand relationships among numbers, including one to one correspondence Identify, write and order numbers 0-10,000 (<,>,=) Identify and use place values from hundredths to ten thousands Identify and write odd/even numbers Use strategies for skip counting by 2s, 5s, 10s and 100s Represent numbers, and equivalent forms of the same number, with many different models including concrete objects Decimals Compare decimals values using tenths/hundredths as they relate to cents Write money values using decimals Fractions - focus on student understanding of what a fraction represents Write and use manipulatives to show fractions (halves, thirds, fourths) Identify and explain the numerator and denominator as it relates to parts of a whole or parts of a set Order fractions (<,>,=) Use fractions to represent quantities Use drawings, models and diagrams to show the concept of fraction as part of a whole Show real world examples of fractional divisions (pizza, bookshelves, floor tiles, etc.) Key: UNDERSTAND THE RELATION SHIP BETWEEN ADDITION AND SUBTRACTION Understand the process Understand various meanings of addition and subtraction Understand addition and subtraction as inverses of each other Understand addition as: combining sets increasing an amount comparing two sets equalizing groups (missing addends) Understand subtraction as: separating sets taking away from a set comparing sets and finding the difference Problem solving Use estimation/rounding to verify answer Use properties to solve problems (commutative, associative) Use mental math strategies Use different strategies to solve addition/subtraction problems Analyze the problem to identify the correct operation Bold = Mastery Italics = Introduce Regular font – Teach and practice rd 3 Grade The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students Apply and explain multi-digit addition and subtraction algorithms Fluency REVIEW: Addition/Subtraction facts to 20 Add numbers up to 4 digits Subtract whole numbers with 3 digits or less with and without regrouping Add and subtract money/make change Add/subtract fractions with like denominators Add/subtract decimals related to money UNDERSTAND MULTIPLICATION AND DIVISION WITHIN 100 Understand the process Understand multiplication as: repeated addition combining equal groups using arrays area models linear models Cartesian models Understand division as: repeated subtraction finding equal shares Understand the relationship between multiplication and division Understand Problem Solving Represent multiplication and division problems using different models Use different strategies to solve multiplication and division facts and problems including multi-step problems and determine reasonableness of answers Analyze the problem to identify the correct operation Solve single digit multiplication problems using a variety of strategies Fluency MASTER: Multiplication facts 10x10 Division facts 10 x 10 Use multiplication facts to solve division facts division as repeated subtraction, finding equal shares Solve single digit multiplication problems using a variety of strategies VOCABULARY: Relative, magnitude, equivalence, whole numbers, expanded form, fraction, place value, estimate, subtraction, skip count, odd, even division, multiplication, decimal, product, factor, numerator, denominator, quotient, addend, commutative, associative, identify property, multiples, base 10 system, zero property, digit, tens, thousands, greater than, less than, addition, fact family, problem, sum, all together, total, difference, equal Key: Bold = Mastery Italics = Introduce 3rd Grade Regular font – Teach and practice The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students GEOMETRY GEOMETRIC ELEMENTS Represent and use terms and concepts of: angles vertex, face, edge and sides, bases, vertices ANALYZE CHARACTERISTICS AND PROPERTIES OF 2 DIMENSIONAL SHAPES Name, describe attributes and provide examples: circles, triangles, squares, rectangles, trapezoids, rhombuses, pentagons, hexagons Identify 2D shapes when turned, flipped or slide ANALYZE CHARACTERISTICS AND PROPERTIES OF 3 DIMENSIONAL SHAPES Name, describe attributes and provide examples of 3D shapes: spheres, cones, cylinders, pyramids, cubes COORDINATE GRAPHING Locate points on a grid representing a positive coordinate system IDENTIFY AND DESCRIBE SYMMETRY Describe and provide examples of lines of symmetry Vocabulary: edges, sides, corners, faces, vertices, angles, hexagon, cones, cylinders, pyramids, cubes, sides, corner, trapezoid, symmetry, points, grid, coordinate system, ordered pairs, bases, circle, triangle, square, rectangle, rhombus, two-dimensional, three dimensional, geometric elements, flips, sides, turns, sort, classify, edges, vertex, attribute, reflections (flips), translations (slides), rotations (turns) MEASUREMENT UNDERSTAND MEASURABLE ATTRIBUTES Apply understanding of measurement Measurement is used to describe attributes of objects. Different measurement systems are used to measure different attributes (length, weight, etc.) Measurement systems are predictable once you understand how it is organized. Apply understanding of length Measure objects to nearest ½ inch or nearest centimeter Use a ruler to measure length Choose and use appropriate tool Describe and compare and order objects on the basis of length (longer/shorter) Estimate length Convert units for length (inch, foot). Apply understanding of weight Weigh objects to the nearest pound (oz, pound) Use a scale or balance Describe and compare attributes of an object using weight. Estimate weight Convert units for weight (ounce, pound) Apply understanding of time Key: Bold = Mastery Italics = Introduce Regular font – Teach and practice rd 3 Grade The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students Identify parts of a clock Measure time (hours, half-hours, quarter hours, five and one minute intervals Use a clock Estimate time Convert units for time (minutes, hours, days, weeks, months) Determine elapsed time by half hours Apply understanding of money Identify coins and bills by value Use coins and bill to count to $5.00 Identify, compare and order amounts of money using coins and bills Use correct symbols for money Combine coins and bills to make a given amount Estimate cost Convert units within the same measurement system including money (dollars, cents) Apply understanding of temperature Measure temperature using Fahrenheit and Celsius to the nearest degree Use a thermometer Describe attributes of an object using temperature Estimate temperature Vocabulary: standard, nonstandard, inch, foot, centimeter, length, weight, unit, Fahrenheit, Celsius, thermometer, weight, measure, length, coin, bill, hour, half hour, quarter hour, ruler, o’clock, hour, half hour, meter, yard, ounce, gram, perimeter, elapsed time, dollar, penny, nickel, dime, quarter At 3rd Grade teach time and money during math time, teach measurement of length, weight and temperature in Science. ALGEBRA UNDERSTAND PATTERNS, RELATIONS, AND FUNCTIONS Extend patterns (numbers, pictures, words) Describe functions (input-output) through pictures and words Describe and explain a pattern Demonstrate simple function rules EXPLORE UNKNOWNS AND OPEN SENTENCES TO EXPRESS RELATIONSHIP Solve simple addition and subtraction equations with missing values Model real world and mathematical problems with simple number sentences Determine the value of an output given as a function rule and an input value Vocabulary: patterns, functions, input, output, function rules, open sentences, unknowns, equations, missing values Key: Bold = Mastery Italics = Introduce Regular font – Teach and practice rd 3 Grade The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students DATA AND PROBABILITY Graphs should be used across the curriculum USE, ORGANIZE AND DISPLAY DATA Read and interpret drawings, tables/charts, tally tables, pictographs, bar graphs circle graphs with 2 or 3 sectors, line plots, 2 circle Venn diagram Analyze and make inferences from the data Make predictions Describe data using mode and range of a set of data Identify cause/effect relationships Draw simple conclusions Form and justify an opinion on whether a given statement is reasonable based on the analyzed data Identify the specific purpose of various graphs Bar graph: compare data Pictograph: compare data using pictures Tables/charts: organize data Circle graph: shows parts of a whole Choose the appropriate graph to use based on the data: bar graph, circle graph and pictograph Use data to answer questions: Ask a question with a quantifiable answer Collect data Organize and display data using bar graphs, pictographs, venn diagrams, tables/charts Use parts of a graph: labels, appropriate scale, title, x & y axis APPLY BASIC CONCEPTS OF PROBABILITY Describe and give examples of the probability of an unlikely event and a likely event Use simple experiments to explore probability Determine if events are probable or improbable Vocabulary: graph, tally tables, pictograph, bar graph, circle graph, venn diagram, line plot, likely, unlikely, probability, chance, inferences, drawings, tables, charts, data display, sector, mode, range, display, conclusion Key: Bold = Mastery Italics = Introduce 3rd Grade Regular font – Teach and practice The mathematical processes – problem solving, communication, representations, reasoning and proof and connections are the mathematical competencies that embody the “doing” of mathematics. These processes should form the core of activities that students do and should provide focus and purpose for the entire mathematics experience for students Key: Bold = Mastery Italics = Introduce 3rd Grade Regular font – Teach and practice