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2.1
Number, Number Sense and Operations
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2.1.A
Use place value concepts to represent whole numbers using numerals, words and physical models.
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2
Number and Number Systems
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2.1.A.1
Use place value concepts to represent, compare and order whole numbers using physical models, numerals and words, with ones, tens and hundreds. For example:
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2.1.A.1.a
Recognize 10 can mean "10 ones" or a single entity (1 ten) through physical models and trading games.
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2.1.A.1.b
Read and write 3-digit numerals (e.g., 243 as two hundred forty three, 24 tens and 3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent each.
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2.1.B
Recognize, classify, compare and order whole numbers.
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2
Number and Number Systems
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2.1.B.1
Use place value concepts to represent, compare and order whole numbers using physical models, numerals and words, with ones, tens and hundreds. For example:
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2.1.B.1.a
Recognize 10 can mean "10 ones" or a single entity (1 ten) through physical models and trading games.
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2.1.B.1.b
Read and write 3-digit numerals (e.g., 243 as two hundred forty three, 24 tens and 3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent each.
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2.1.B.2
Recognize and classify numbers as even or odd.
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2.1.C
Represent commonly used fractions using words and physical models.
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2
Number and Number Systems
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2.1.C.5
Represent fractions (halves, thirds, fourths, sixths and eighths), using words, numerals and physical models. For example:
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2.1.C.5.a
Recognize that a fractional part can mean different amounts depending on the original quantity.
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2.1.C.5.b
Recognize that a fractional part of a rectangle does not have to be shaded with contiguous parts.
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2.1.C.5.c
Identify and illustrate parts of a whole and parts of sets of objects.
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2.1.C.5.d
Compare and order physical models of halves, thirds and fourths in relation to 0 and 1.
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2.1.D
Determine the value of a collection of coins and dollar bills.
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2
Number and Number Systems
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2.1.D.4
Represent and write the value of money using the ยข sign and in decimal form when using the $ sign.
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2.1.E
Make change using coins for values up to one dollar.
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2
Number and Number Systems
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2.1.E.3
Count money and make change using coins and a dollar bill.
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2.1.F
Count, using numerals and ordinal numbers.
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2.1.G
Model, represent and explain addition as combining sets and counting on.
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2.1.H
Model, represent and explain subtraction as comparison, take-away and part-to-whole.
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2
Meaning of Operations
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2.1.H.6
Model, represent and explain subtraction as comparison, take-away and part-to-whole; e.g., solve missing addend problems by counting up or subtracting, such as "I had six baseball cards, my sister gave me more, and I now have ten. How many did she give me?" can be represented as 6 + ? = 10 or 10 - 6 = ?.
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2.1.I
Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting.
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2
Meaning of Operations
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2.1.I.7
Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting.
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2.1.J
Model, represent and explain division as sharing equally, repeated subtraction and rectangular arrays.
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2
Meaning of Operations
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2.1.J.8
Model, represent and explain division as sharing equally and repeated subtraction.
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2.1.K
Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions.
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2
Computation and Estimation
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2.1.K.10
Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions; e.g., 9 + 9 = 18, 18 - 9 = 9.
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2.1.L
Demonstrate fluency in adding and subtracting multiples of 10, and recognize combinations that make 10.
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2
Computation and Estimation
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2.1.L.11
Add and subtract multiples of 10.
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2.1.M
Add and subtract two-digit numbers with and without regrouping.
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2
Meaning of Operations
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2.1.M.9
Model and use the commutative property for addition.
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2
Computation and Estimation
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2.1.M.12
Demonstrate multiple strategies for adding and subtracting 2- or 3-digit whole numbers, such as:
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2.1.M.12.a
compatible numbers;
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2.1.M.12.b
compensatory numbers;
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2.1.M.12.c
informal use of commutative and associative properties of addition.
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2.1.M.13
Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers.
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2.2
Measurement
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2.2.A
Explain the need for standard units of measure.
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2.2.B
Select appropriate units for length, weight, volume (capacity) and time, using:
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2
Measurement Units
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2.2.B.1
Identify and select appropriate units of measure for:
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2.2.B.1.a
length - centimeters, meters, inches, feet or yards;
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2.2.B.1.b
volume (capacity) - liters, cups, pints or quarts;
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2.2.B.1.c
weight - grams, ounces or pounds;
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2.2.B.1.d
time - hours, half-hours, quarter-hours or minutes and time designations, a.m. or p.m.
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2.2.C
Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates.
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2
Measurement Units
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2.2.C.2
Establish personal or common referents for units of measure to make estimates and comparisons; e.g., the width of a finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper clip weighs about one gram.
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2.2.C.4
Tell time to the nearest minute interval on digital and to the nearest 5 minute interval on analog (dial) timepieces.
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2.2.D
Apply measurement techniques to measure length, weight and volume (capacity).
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2
Use Measurement Techniques and Tools
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2.2.D.5
Estimate and measure the length and weight of common objects, using metric and U.S. customary units, accurate to the nearest unit.
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2.2.D.6
Select and use appropriate measurement tools; e.g., a ruler to draw a segment 3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale to weigh 50 grams of candy.
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2.2.E
Recognize that using different units of measurement will yield different numbers for the same measurement.
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2
Measurement Units
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2.2.E.3
Describe and compare the relationships among units of measure, such as centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces and pounds; and hours, half-hours, and quarter-hours; e.g., how many inches in a foot?
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2
Use Measurement Techniques and Tools
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2.2.E.7
Make and test predictions about measurements, using different units to measure the same length or volume.
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2.3
Geometry and Spatial Sense
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2.3.A
Describe and create plane figures: circle, rectangle, square, triangle, hexagon, trapezoid, parallelogram and rhombus, and identify them in the environment.
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2
Characteristics and Properties
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2.3.A.1
Identify, describe, compare and sort three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the faces or the numbers of faces, edges or vertices.
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2.3.A.2
Predict what new shapes will be formed by combining or cutting apart existing shapes.
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2.3.B
Describe solid objects: cube, rectangular prism, sphere, cylinder, cone and pyramid, and identify them in the environment.
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2
Characteristics and Properties
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2.3.B.1
Identify, describe, compare and sort three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the faces or the numbers of faces, edges or vertices.
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2.3.C
Sort and compare two-dimensional figures and three-dimensional objects according to their characteristics and properties.
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2
Characteristics and Properties
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2.3.C.1
Identify, describe, compare and sort three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the faces or the numbers of faces, edges or vertices.
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2.3.D
Identify, explain and model (superposition, copying) the concept of shapes being congruent and similar.
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2
Spatial Relationships
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2.3.D.4
Identify and determine whether two-dimensional shapes are congruent (same shape and size) or similar (same shape different size) by copying or using superposition (lay one thing on top of another).
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2.3.E
Recognize two- and three-dimensional objects from different positions.
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2
Characteristics and Properties
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2.3.E.3
Recognize two-dimensional shapes and three-dimensional objects from different positions.
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2.3.F
Describe location, using comparative (before, after), directional (above, below), and positional (first, last) words.
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2.3.G
Identify and draw figures with line symmetry.
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2
Transformations and Symmetry
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2.3.G.5
Create and identify two-dimensional figures with line symmetry; e.g., what letter shapes, logos, polygons are symmetrical?
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2.4
Patterns, Functions and Algebra
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2.4.A
Sort, classify and order objects by size, number and other properties, and describe the attributes used.
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2.4.B
Extend sequences of sounds and shapes or simple number patterns, and create and record similar patterns.
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2
Use Patterns, Relations and Functions
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2.4.B.1
Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns.
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2.4.C
Create and extend patterns, and describe the rule in words.
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2
Use Patterns, Relations and Functions
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2.4.C.2
Use patterns to make generalizations and predictions; e.g., determine a missing element in a pattern.
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2.4.C.3
Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns.
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2.4.D
Model problem situations, using objects, pictures, numbers and other symbols.
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2
Use Algebraic Representations
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2.4.D.4
Use objects, pictures, numbers and other symbols to represent a problem situation.
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2.4.E
Solve open sentences and explain strategies.
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2
Use Algebraic Representations
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2.4.E.5
Understand equivalence and extend the concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5, and 4 + 5 = 3 + 6 = "triangle" + "square"...
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2.4.F
Represent an unknown quantity as a variable using a symbol, such as "square", "triangle", "circle".
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2
Use Algebraic Representations
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2.4.F.6
Use symbols to represent unknown quantities and identify values for symbols in an expression or equation using addition and subtraction; e.g., "square" + "circle" = 10, "triangle" - 2 = 4.
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2.4.G
Describe and compare qualitative and quantitative change.
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2
Analyze change
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2.4.G.7
Describe qualitative and quantitative changes, especially those involving addition and subtraction; e.g., a student growing taller versus a student growing two inches in one year.
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2.5
Data Analysis and Probability
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2.5.A
Pose questions and gather data about everyday situations and familiar objects.
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2
Data Collection
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2.5.A.1
Pose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs.
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2
Statistical Methods
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2.5.A.6
Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents.
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2.5.B
Sort and classify objects by attributes, and organize data into categories in a simple table or chart.
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2
Data Collection
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2.5.B.1
Pose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs.
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2
Statistical Methods
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2.5.B.4
Write a few sentences to describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole.
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2.5.C
Represent data using objects, picture graphs and bar graphs.
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2
Data Collection
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2.5.C.2
Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs.
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2.5.C.3
Read and construct simple timelines to sequence events.
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2
Statistical Methods
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2.5.C.5
Identify untrue or inappropriate statements about a given set of data.
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2.5.D
Describe the probability of chance events as more, less or equally likely to occur.
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2
Probability
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2.5.D.7
List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur.
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2.5.D.8
Use physical models and pictures to represent possible arrangements of 2 or 3 objects.
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2.6
Mathematical Processes
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2.6.A
Use a variety of strategies to understand problem situations; e.g., discussing with peers, stating problems in own words, modeling problems with diagrams or physical materials, identifying a pattern.
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2.6.B
Identify and restate in own words the question or problem and the information needed to solve the problem.
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2.6.C
Generate alternative strategies to solve problems.
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2.6.D
Evaluate the reasonableness of predictions, estimations and solutions.
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2.6.E
Explain to others how a problem was solved.
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2.6.F
Draw pictures and use physical models to represent problem situations and solutions.
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2.6.G
Use invented and conventional symbols and common language to describe a problem situation and solution.
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2.6.H
Recognize the mathematical meaning of common words and phrases, and relate everyday language to mathematical language and symbols.
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2.6.I
Communicate mathematical thinking by using everyday language and appropriate mathematical language.
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