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4.A
Mathematical Process
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4.A.a
Reasoning
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4.A.a.1
Use reasoning and logic to:
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4.A.a.1.a
Perceive patterns
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4.A.a.1.b
Identify relationships
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4.A.a.1.c
Formulate questions
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4.A.a.1.d
Pose problems
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4.A.a.1.e
Make conjectures
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4.A.a.1.f
Justify strategies
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4.A.a.1.g
Test reasonableness of results
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4.A.b
Communication
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4.A.b.1
Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.
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4.A.c
Connections
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4.A.c.1
Connect mathematics to the real world, as well as within mathematics.
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4.A.d
Representation
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4.A.d.1
Create and use representations to organize, record, and communicate mathematical ideas.
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4.A.e
Problem Solving
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4.A.e.1
Solve and analyze routine and non-routine problems.
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4.B
Number Operations and Relationships
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4.B.a
Concepts
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4.B.a.1
Recognize and apply place-value concepts to whole numbers less than 10,000.
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4.B.a.2
Read, write, and represent numbers using words, numerals, pictures (e.g. base ten blocks), number lines, , arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7.
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4.B.a.3
Compare and order whole numbers less than 10,000
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4.B.a.4
Count by 2s, 3s, 5s, 10s, 25s and 100s starting with any multiple and 100s starting with any number.
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4.B.a.4.a
Identify and name counting patterns
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4.B.a.5
Count, compare and make change up to $10.00 using a collection of coins and one-dollar bills..
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4.B.a.6
Identify a fractional part of a collection/set or parts of a whole.
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4.B.a.7
Read, write, order and represent unit fractions (e.g.,1/2, 1/3, 1/4) and part(s) of a set.
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4.B.b
Computation
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4.B.b.1
Use addition and subtraction in everyday situations and solve one-and two-step word problems
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4.B.b.2
Solve double-and triple-digit addition and subtraction problems with regrouping in horizontal and vertical format in problems with and without context.
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4.B.b.3
Demonstrate understanding of multiplication as grouping or repeated addition or arrays in problems with and without context (without context up to 5 x 9; in context products up to 100).
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4.B.b.4
Demonstrate understanding of the concept of division as repeated subtraction, partitioning/sharing or measuring (dividend up to 45 and divisors up to 5).
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4.B.b.5
Use fractions to represent quantities when solving problems involving equal sharing or partitioning including fractions less than one as well as mixed numbers.
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4.B.b.6
Represent with shaded circles, rods, squares or pictorial representations of objects (for a set).
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4.B.b.7
Estimate sums to tens, hundreds and thousands and differences of ten and hundreds.
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4.B.b.8
Determine reasonableness of answers.
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4.C
Geometry
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4.C.a
Describing Figures
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4.C.a.1
Identify, describe, and compare properties of 2 and 3 dimensional figures such as squares, triangles, rectangles, pentagon, hexagon, octagon, pattern block shapes, circles, cubes, pyramids, rectangular prisms, tetrahedrons, cylinders, and spheres (e.g., comparing sides, faces, corners, and edges).
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4.C.b
Spatial Relationships and Transformations
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4.C.b.1
Create and identify 2-dimensional geometric shapes by combining or decomposing other shapes.
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4.C.b.2
Identify cubes and square pyramid shapes from their nets (flat patterns).
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4.C.b.3
Apply concepts of single-motion geometry (e.g., slides, flips and turns) to match two identical shapes.
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4.C.c
Coordinate Systems
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4.C.c.1
Use simple 2-dimensional coordinate systems to find locations on maps and to represent points and simple figures with coordinates using letters and numbers, (e.g., (E, 3)).
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4.C.c.2
Identify and use relationships among figures (e.g., location, position and intersection).
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4.D
Measurement
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4.D.a
Measurable Attributes
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4.D.a.1
Describe attributes of length, time, temperature, liquid capacity, weight/mass, volume and identify appropriate units to measure them. Units include: inches, feet, yards, miles, meters, centimeters, millimeters, cups quarts, gallons, liters, seconds, minutes, hours, days, months, years, ounces, pounds, grams and degrees Fahrenheit/Celsius.
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4.D.a.2
Compare attributes of length, volume and weight by observation or when given actual measurements.
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4.D.a.3
Make measurement conversions within a system (e.g., yards to feet; feet to inches; hours to minutes; days to hours; years to months; gallons to quarts).
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4.D.b
Direct Measurement
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4.D.b.1
Read and interpret and use measuring instruments to determine the measurement of objects with nonstandard and standard units to the nearest centimeter, 1/4-inch.
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4.D.b.2
Read thermometers to the nearest 5 degrees F/C.
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4.D.b.3
Tell time to the nearest minute and translate time from analog to digital clocks and vice versa.
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4.D.b.4
Determine and compare elapsed time in multiples of 15 minutes in problem-solving situations.
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4.D.b.5
Investigate measurements of area and perimeter.
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4.D.c
Indirect Measurement
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4.D.c.1
Apply estimation techniques using non-standard units.
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4.E
Statistics and Probability
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4.E.a
Data Analysis and Statistics
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4.E.a.1
Answer and pose questions about collecting, organizing and displaying data. Work with data in the context of real-world situations by formulating questions that lead to data collection and analysis and determining what data to collect and when and how to collect the data.
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4.E.a.2
Collect, organize and display data in simple bar graphs and charts, including translating data from one form to the other.
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4.E.a.3
Draw reasonable conclusions based on simple interpretations of data.
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4.E.a.4
Read, use information and draw reasonable conclusions from data in graphs, tables, charts and Venn diagrams.
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4.E.b
Probability
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4.E.b.1
Determine if the occurrence of future events are more, less or equally likely to occur.
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4.E.b.2
Design a fair and an unfair spinner.
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4.E.b.3
Predict the outcomes of a simple event using words to describe probability. Ex: Flipping a coin has a 1 out of 2 chance of getting a head.
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4.E.b.4
Describe and determine the number of combinations for choosing 2 out of 3 items. Ex: Red hat, blue jacket and green jacket. What are the combinations of wearing a hat and a jacket?
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4.F
Algebraic Relationships
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4.F.a
Patterns, Relations and Functions
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4.F.a.1
Recognize, extend, describe, create and replicate a variety of patterns including attribute, number and geometric patterns. Such as:
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4.F.a.1.a
Picture patterns
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4.F.a.1.b
Patterns in tables and charts
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4.F.a.1.c
"What's-my-rule?" patterns
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4.F.a.1.d
Patterns using addition and subtraction rules.
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4.F.a.2
Focusing on relationships within patterns as well as extending patterns e.g., patterns and relationships represented with pictures, tables and charts; "what's-my-rule?" patterns using addition and subtraction rules.
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4.F.a.3
Determine odd or even.
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4.F.b
Expressions, Equations and Inequalities
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4.F.b.1
Demonstrate an understanding that the " =" sign means "the same as" by solving open or true/false number sentences.
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4.F.b.2
Use notation to represent mathematical thinking: letter or box (variable); operation symbols (+, - , =).
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4.F.b.3
Demonstrate a basic understanding of equality and inequality using symbols (<, >, =) with simple addition and subtraction.
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4.F.c
Properties
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4.F.c.1
Use properties and relationships of arithmetic to determine what number goes in a "box" to make a number sentence true,
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4.F.c.1.a
Identity property of zero Ex: 12 + 0 ="box"
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4.F.c.1.b
Identity property of one Ex: 5 x 1 = "box"
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4.F.c.1.c
Commutative property for addition of single-digits
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4.F.c.1.d
Associative property
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4.F.c.2
Use simple equations in a variety of ways to demonstrate the properties above.
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