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4.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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4.PS.1
Explore, examine, and make observations about a social problem or mathematical situation
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4.PS.2
Understand that some ways of representing a problem are more helpful than others
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4.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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4.PS.4
Act out or model with manipulatives activities involving mathematical content from literature
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4.PS.5
Formulate problems and solutions from everyday situations
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4.PS.6
Translate from a picture/diagram to a numeric expression
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4.PS.7
Represent problem situations in oral, written, concrete, pictorial, and graphical forms
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4.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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4.PS.9
Use trial and error to solve problems
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4.PS.10
Use process of elimination to solve problems
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4.PS.11
Make pictures/diagrams of problems
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4.PS.12
Use physical objects to model problems
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4.PS.13
Work in collaboration with others to solve problems
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4.PS.14
Make organized lists to solve numerical problems
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4.PS.15
Make charts to solve numerical problems
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4.PS.16
Analyze problems by identifying relationships
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4.PS.17
Analyze problems by identifying relevant versus irrelevant information
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4.PS.18
Analyze problems by observing patterns
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4.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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4.PS.20
Determine what information is needed to solve a problem
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4.PS.21
Discuss with peers to understand a problem situation
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4.PS.22
Discuss the efficiency of different representations of a problem
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4.PS.23
Verify results of a problem
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4.PS.24
Recognize invalid approaches
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4.PS.25
Determine whether a solution is reasonable in the context of the original problem
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4.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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4.RP.1
Use representations to support mathematical ideas
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4.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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4.RP.3
Investigate the use of knowledgeable guessing by generalizing mathematical ideas
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4.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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4.RP.5
Justify general claims or conjectures, using manipulatives, models, and expressions
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4.RP.6
Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
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4.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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4.RP.8
Support an argument by trying many cases
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4.RP.9
Disprove an argument by finding counterexamples
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4.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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4.CM.1
Understand and explain how to organize their thought process
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4.CM.2
Verbally explain their rationale for strategy selection
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4.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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4.CM.4
Organize and accurately label work
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4.CM.5
Share organized mathematical ideas through the manipulation of objects, drawing, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form
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4.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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4.CM.7
Restate mathematical solutions shared by other students
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4.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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4.CM.9
Increase their use of mathematical vocabulary and language when communicating with others
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4.CM.10
Describe objects, relationships, solutions, and rationale using appropriate vocabulary
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4.CM.11
Decode and comprehend mathematical visuals and symbols to construct meaning
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4.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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4.CN.1
Recognize, understand, and make connections in their everyday experiences to mathematical ideas
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4.CN.2
Compare and contrast mathematical ideas
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4.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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4.CN.4
Understand multiple representations and how they are related
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4.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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4.CN.6
Recognize the presence of mathematics in their daily lives
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4.CN.7
Apply mathematics to solve problems that develop outside of mathematics
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4.CN.8
Recognize and apply mathematics to other disciplines
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4.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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4.R.1
Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations
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4.R.2
Share mental images of mathematical ideas and understandings
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4.R.3
Recognize and use external mathematical representations
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4.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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4.R.5
Understand similarities and differences in representations
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4.R.6
Connect mathematical representations with problem solving
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4.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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4.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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4.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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4.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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4.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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4.N.1
Skip count by 1,000's
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4.N.2
Read and write whole numbers to 10,000
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4.N.3
Compare and order numbers to 10,000
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4.N.4
Understand the place value structure of the base ten number system:
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4.N.4.a
10 ones = 1 ten
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4.N.4.b
10 tens = 1 hundred
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4.N.4.c
10 hundreds = 1 thousand
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4.N.4.d
10 thousands = 1 ten thousand
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4.N.5
Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers
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4.N.6
Understand, use, and explain the associative property of multiplication
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4.N.7
Develop an understanding of fractions as locations on number lines and as divisions of whole numbers
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4.N.8
Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations
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4.N.9
Use concrete materials and visual models to compare and order unit fractions or fractions with the same denominator (with and without the use of a number line)
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4.N.10
Develop an understanding of decimals as part of a whole
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4.N.11
Read and write decimals to hundredths, using money as a context
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4.N.12
Use concrete materials and visual models to compare and order decimals (less than 1) to the hundredths place in the context of money
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Number Theory
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4.N.13
Develop an understanding of the properties of odd/even numbers as a result of multiplication
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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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4.N.14
Use a variety of strategies to add and subtract numbers up to 10,000
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4.N.15
Select appropriate computational and operational methods to solve problems
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4.N.16
Understand various meanings of multiplication and division
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4.N.17
Use multiplication and division as inverse operations to solve problems
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4.N.18
Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping)
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4.N.19
Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping)
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4.N.20
Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000
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4.N.21
Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders)
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4.N.22
Interpret the meaning of remainders
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4.N.23
Add and subtract proper fractions with common denominators
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4.N.24
Express decimals as an equivalent form of fractions to tenths and hundredths
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4.N.25
Add and subtract decimals to tenths and hundredths using a hundreds chart
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Students will compute accurately and make reasonable estimates.
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Estimation
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4.N.26
Round numbers less than 1,000 to the nearest tens and hundreds
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4.N.27
Check reasonableness of an answer by using estimation
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4.A
Algebra
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Students will represent and analyze algebraically a wide variety of problem solving situations.
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Variables and Expressions
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4.A.1
Evaluate and express relationships using open sentences with one operation
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Students will perform algebraic procedures accurately.
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Equations and Inequalities
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4.A.2
Use the symbols <, >, =, and "not equal to", (with and without the use of a number line) to compare whole numbers and unit fractions and decimals (up to hundredths)
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4.A.3
Find the value or values that will make an open sentence true, if it contains < or >
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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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4.A.4
Describe, extend, and make generalizations about numeric (+, -, x, ÷) and geometric patterns
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4.A.5
Analyze a pattern or a whole-number function and state the rule, given a table or an input/output box
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4.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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4.G.1
Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)
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4.G.2
Identify points and line segments when drawing a plane figure
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4.G.3
Find perimeter of polygons by adding sides
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4.G.4
Find the area of a rectangle by counting the number of squares needed to cover the rectangle
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4.G.5
Define and identify vertices, faces, and edges of three-dimensional shapes
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Students will identify and justify geometric relationships, formally and informally.
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Geometric Relationships
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4.G.6
Draw and identify intersecting, perpendicular, and parallel lines
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4.G.7
Identify points and rays when drawing angles
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4.G.8
Classify angles as acute, obtuse, right, and straight
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4.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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4.M.1
Select tools and units (customary and metric) appropriate for the length being measured
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4.M.2
Use a ruler to measure to the nearest standard unit (whole, ½ and ¼ inches, whole feet, whole yards, whole centimeters, and whole meters)
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4.M.3
Know and understand equivalent standard units of length:
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4.M.3.a
12 inches = 1 foot
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4.M.3.b
3 feet = 1 yard
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4.M.4
Select tools and units appropriate to the mass of the object being measured (grams and kilograms)
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4.M.5
Measure mass, using grams
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4.M.6
Select tools and units appropriate to the capacity being measured (milliliters and liters)
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4.M.7
Measure capacity, using milliliters and liters
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Students will use units to give meaning to measurements.
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Units
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4.M.8
Make change, using combined coins and dollar amounts
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4.M.9
Calculate elapsed time in hours and half hours, not crossing A.M./P.M.
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4.M.10
Calculate elapsed time in days and weeks, using a calendar
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4.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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4.S.1
Design investigations to address a question from given data
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4.S.2
Collect data using observations, surveys, and experiments and record appropriately
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Organization and Display of Data
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4.S.3
Represent data using tables, bar graphs, and pictographs
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Analysis of Data
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4.S.4
Read and interpret line graphs
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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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4.S.5
Develop and make predictions that are based on data
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4.S.6
Formulate conclusions and make predictions from graphs
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