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3.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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3.PS.1
Explore, examine, and make observations about a social problem or mathematical situation
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3.PS.2
Understand that some ways of representing a problem are more helpful than others
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3.PS.3
Interpret information correctly, identify the problem, and generate possible solutions
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Students will solve problems that arise in mathematics and in other contexts.
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3.PS.4
Act out or model with manipulatives activities involving mathematical content from literature
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3.PS.5
Formulate problems and solutions from everyday situations
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3.PS.6
Translate from a picture/diagram to a numeric expression
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3.PS.7
Represent problem situations in oral, written, concrete, pictorial, and graphical forms
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3.PS.8
Select an appropriate representation of a problem
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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3.PS.9
Use trial and error to solve problems
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3.PS.10
Use process of elimination to solve problems
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3.PS.11
Make pictures/diagrams of problems
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3.PS.12
Use physical objects to model problems
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3.PS.13
Work in collaboration with others to solve problems
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3.PS.14
Make organized lists to solve numerical problems
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3.PS.15
Make charts to solve numerical problems
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3.PS.16
Analyze problems by identifying relationships
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3.PS.17
Analyze problems by identifying relevant versus irrelevant information
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3.PS.18
Analyze problems by observing patterns
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3.PS.19
State a problem in their own words
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Students will monitor and reflect on the process of mathematical problem solving.
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3.PS.20
Determine what information is needed to solve a problem
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3.PS.21
Discuss with peers to understand a problem situation
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3.PS.22
Discuss the efficiency of different representations of a problem
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3.PS.23
Verify results of a problem
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3.PS.24
Recognize invalid approaches
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3.PS.25
Determine whether a solution is reasonable in the context of the original problem
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3.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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3.RP.1
Use representations to support mathematical ideas
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3.RP.2
Determine whether a mathematical statement is true or false and explain why
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Students will make and investigate mathematical conjectures.
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3.RP.3
Investigate the use of knowledgeable guessing by generalizing mathematical ideas
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3.RP.4
Make conjectures from a variety of representations
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Students will develop and evaluate mathematical arguments and proofs.
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3.RP.5
Justify general claims or conjectures, using manipulatives, models, and expressions
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3.RP.6
Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
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3.RP.7
Discuss, listen, and make comments that support or reject claims made by other students
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Students will select and use various types of reasoning and methods of proof.
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3.RP.8
Support an argument by trying many cases
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3.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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3.CM.1
Understand and explain how to organize their thought process
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3.CM.2
Verbally explain their rationale for strategy selection
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3.CM.3
Provide reasoning both in written and verbal form
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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3.CM.4
Organize and accurately label work
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3.CM.5
Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form
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3.CM.6
Answer clarifying questions from others
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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3.CM.7
Listen for understanding of mathematical solutions shared by other students
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3.CM.8
Consider strategies used and solutions found in relation to their own work
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Students will use the language of mathematics to express mathematical ideas precisely.
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3.CM.9
Increase their use of mathematical vocabulary and language when communicating with others
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Geometry: Perimeter (Second grade - T.7)
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Geometry: Perimeter - word problems (Second grade - T.8)
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Geometry: Area (Second grade - T.9)
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Probability and statistics: Median, mode, and range (Second grade - V.3)
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Probability and statistics: Interpret graphs to find median, mode, and range (Second grade - V.4)
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Numbers and comparing: Ordinal numbers to 100th (Third grade - A.2)
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Place value: Place value names (Third grade - B.2)
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Properties: Addition, subtraction, multiplication, and division terms (Third grade - H.1)
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Equations and variables: Identify equations (Third grade - I.1)
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Probability and statistics: Certain, probable, unlikely, and impossible (Third grade - S.1)
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Probability and statistics: Mean, median, mode, and range (Third grade - S.2)
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Probability and statistics: Interpret charts to find mean, median, mode, and range (Third grade - S.3)
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3.CM.10
Describe objects, relationships, solutions and rationale using appropriate vocabulary
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3.CM.11
Decode and comprehend mathematical visuals and symbols to construct meaning
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3.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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3.CN.1
Recognize, understand, and make connections in their everyday experiences to mathematical ideas
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3.CN.2
Compare and contrast mathematical ideas
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3.CN.3
Connect and apply mathematical information to solve problems
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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3.CN.4
Understand multiple representations and how they are related
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3.CN.5
Model situations with objects and representations and be able to make observations
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Students will recognize and apply mathematics in contexts outside of mathematics.
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3.CN.6
Recognize the presence of mathematics in their daily lives
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3.CN.7
Apply mathematics to solve problems that develop outside of mathematics
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3.CN.8
Recognize and apply mathematics to other disciplines
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3.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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3.R.1
Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations
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Counting and number patterns: Roman numerals I, V, X (First grade - A.17)
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Names of numbers: Distinguishing ordinal and cardinal numbers (Second grade - C.5)
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Names of numbers: Roman numerals I, V, X, L (Second grade - C.6)
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Measurement: Read a thermometer (Second grade - S.1)
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Numbers and comparing: Roman numerals I, V, X, L, C, D, M (Third grade - A.3)
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Measurement: Read a thermometer (Third grade - O.1)
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Measurement: Reasonable temperature (Third grade - O.2)
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Geometry: Perimeter (Third grade - P.6)
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Geometry: Area (Third grade - P.7)
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Geometry: Volume (Third grade - P.8)
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Decimals: What decimal number is illustrated? (Third grade - R.1)
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Decimals: Understanding decimals expressed in words (Third grade - R.3)
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3.R.2
Share mental images of mathematical ideas and understandings
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3.R.3
Recognize and use external mathematical representations
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3.R.4
Use standard and nonstandard representations with accuracy and detail
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Students will select, apply, and translate among mathematical representations to solve problems.
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3.R.5
Understand similarities and differences in representations
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3.R.6
Connect mathematical representations with problem solving
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3.R.7
Construct effective representations to solve problems
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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3.R.8
Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
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3.R.9
Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip)
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3.R.10
Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)
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3.N
Number Sense and Operations
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Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
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Number Systems
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3.N.1
Skip count by 25's, 50's, 100's to 1,000
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3.N.2
Read and write whole numbers to 1,000
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3.N.3
Compare and order numbers to 1,000
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3.N.4
Understand the place value structure of the base ten number system:
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3.N.4.a
10 ones = 1 ten
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3.N.4.b
10 tens = 1 hundred
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3.N.4.c
10 hundreds = 1 thousand
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3.N.5
Use a variety of strategies to compose and decompose three-digit numbers
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3.N.6
Use and explain the commutative property of addition and multiplication
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3.N.7
Use 1 as the identity element for multiplication
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3.N.8
Use the zero property of multiplication
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3.N.9
Understand and use the associative property of addition
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3.N.10
Develop an understanding of fractions as part of a whole unit and as parts of a collection
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3.N.11
Use manipulatives, visual models, and illustrations to name and represent unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10) as part of a whole or a set of objects
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3.N.12
Understand and recognize the meaning of numerator and denominator in the symbolic form of a fraction
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3.N.13
Recognize fractional numbers as equal parts of a whole
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3.N.14
Explore equivalent fractions (1/2, 1/3, 1/4)
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3.N.15
Compare and order unit fractions (1/2, 1/3, 1/4) and find their approximate locations on a number line
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Number Theory
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3.N.16
Identify odd and even numbers
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3.N.17
Develop an understanding of the properties of odd/even numbers as a result of addition or subtraction
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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3.N.18
Use a variety of strategies to add and subtract 3-digit numbers (with and without regrouping)
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3.N.19
Develop fluency with single-digit multiplication facts
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3.N.20
Use a variety of strategies to solve multiplication problems with factors up to 12 x 12
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3.N.21
Use the area model, tables, patterns, arrays, and doubling to provide meaning for multiplication
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3.N.22
Demonstrate fluency and apply single-digit division facts
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3.N.23
Use tables, patterns, halving, and manipulatives to provide meaning for division
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3.N.24
Develop strategies for selecting the appropriate computational and operational method in problem solving situations
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Students will compute accurately and make reasonable estimates.
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Estimation
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3.N.25
Estimate numbers up to 500
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3.N.26
Recognize real world situations in which an estimate (rounding) is more appropriate
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3.N.27
Check reasonableness of an answer by using estimation
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3.A
Algebra
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Students will perform algebraic procedures accurately.
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Equations and Inequalities
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3.A.1
Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers and unit fractions, (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10)
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Students will recognize, use, and represent algebraically patterns, relations, and functions.
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Patterns, Relations, and Functions
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3.A.2
Describe and extend numeric (+, -) and geometric patterns
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3.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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3.G.1
Define and use correct terminology when referring to shapes (circle, triangle, square, rectangle, rhombus, trapezoid, and hexagon)
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Geometry: Identify planar and solid shapes (Third grade - P.1)
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Geometry: Count and compare sides, edges, faces, and vertices (Third grade - P.2)
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Geometry: Angles: greater than, less than, or equal to a right angle (Third grade - P.9)
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Geometry: Lines, line segments, and rays (Third grade - P.10)
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Geometry: Is it a polygon? (Third grade - P.11)
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Geometry: Triangles: equilateral, isosceles, and scalene (Third grade - P.12)
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Geometry: Triangles: acute, right, and obtuse (Third grade - P.13)
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3.G.2
Identify congruent and similar figures
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3.G.3
Name, describe, compare, and sort three-dimensional shapes: cube, cylinder, sphere, prism, and cone
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3.G.4
Identify the faces on a three-dimensional shape as two-dimensional shapes
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Students will apply transformations and symmetry to analyze problem solving situations.
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Transformational Geometry
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3.G.5
Identify and construct lines of symmetry
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3.M.
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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3.M.1
Select tools and units (customary) appropriate for the length measured
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3.M.2
Use a ruler/yardstick to measure to the nearest standard unit (whole and ½ inches, whole feet, and whole yards)
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3.M.3
Measure objects, using ounces and pounds
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3.M.4
Recognize capacity as an attribute that can be measured
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3.M.5
Compare capacities (e.g., Which contains more? Which contains less?)
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3.M.6
Measure capacity, using cups, pints, quarts, and gallons
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Students will use units to give meaning to measurements.
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Units
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3.M.7
Count and represent combined coins and dollars, using currency symbols ($0.00)
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3.M.8
Relate unit fractions to the face of the clock:
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3.M.8.a
Whole = 60 minutes
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3.M.8.b
½ = 30 minutes
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3.M.8.c
¼ = 15 minutes
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Students will develop strategies for estimating measurements.
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Estimation
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3.M.9
Tell time to the minute, using digital and analog clocks
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3.M.10
Select and use standard (customary) and non-standard units to estimate measurements
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3.S
Statistics and Probability
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Students will collect, organize, display, and analyze data.
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Collection of Data
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3.S.1
Formulate questions about themselves and their surroundings
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3.S.2
Collect data using observation and surveys, and record appropriately
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Organization and Display of Data
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3.S.3
Construct a frequency table to represent a collection of data
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3.S.4
Identify the parts of pictographs and bar graphs
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3.S.5
Display data in pictographs and bar graphs
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3.S.6
State the relationships between pictographs and bar graphs
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Analysis of Data
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3.S.7
Read and interpret data in bar graphs and pictographs
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Students will make predictions that are based upon data analysis.
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Predictions from Data
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3.S.8
Formulate conclusions and make predictions from graphs
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