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2.4.1
Number and Numerical Operations
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2.4.1.2 A
Number Sense
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2.4.1.2 A.1
Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well).
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2.4.1.2 A.1.a
Whole numbers through hundreds
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2.4.1.2 A.1.b
Ordinals
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2.4.1.2 A.1.c
Proper fractions (denominators of 2, 3, 4, 8, 10)
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2.4.1.2 A.2
Demonstrate an understanding of whole number place value concepts.
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2.4.1.2 A.3
Understand that numbers have a variety of uses.
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2.4.1.2 A.4
Count and perform simple computations with coins.
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2.4.1.2 A.4.a
Amounts up to $1.00 (using cents notation)
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2.4.1.2 A.5
Compare and order whole numbers.
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Numbers and counting up to 10: Number lines (Kindergarten - C.7)
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Numbers and counting up to 10: Before, after, and between (Kindergarten - C.8)
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Sorting, ordering, and classifying: Put numbers up to 10 in order (Kindergarten - N.6)
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Sorting, ordering, and classifying: Put numbers up to 30 in order (Kindergarten - N.7)
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Comparing: Comparing - review (First grade - G.1)
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Comparing: Comparing numbers up to 10 (First grade - G.2)
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Comparing: Comparing numbers up to 100 (First grade - G.3)
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Comparing: Comparison word problems (First grade - G.4)
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Sorting, ordering, and classifying: Put numbers in order (First grade - Q.2)
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Comparing and ordering: Comparing numbers up to 100 (Second grade - B.1)
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Comparing and ordering: Inequalities with addition and subtraction - up to 100 (Second grade - B.2)
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Comparing and ordering: Comparing numbers up to 1,000 (Second grade - B.3)
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Comparing and ordering: Put numbers up to 100 in order (Second grade - B.4)
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Comparing and ordering: Put numbers up to 1,000 in order (Second grade - B.5)
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2.4.1.2 B
Numerical Operations
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2.4.1.2 B.1
Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems.
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2.4.1.2 B.1.a
Joining, separating, and comparing
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2.4.1.2 B.2
Explore the meanings of multiplication and division by modeling and discussing problems.
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2.4.1.2 B.3
Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as "counting on" and "near doubles") and then commit them to memory.
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2.4.1.2 B.4
Construct, use, and explain procedures for performing addition and subtraction calculations with:
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2.4.1.2 B.4.a
Pencil-and-paper
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2.4.1.2 B.4.b
Mental math
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2.4.1.2 B.4.c
Calculator
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2.4.1.2 B.5
Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.
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2.4.1.2 B.5.a
Addition of 2-digit numbers
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2.4.1.2 B.5.b
Subtraction of 2-digit numbers
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2.4.1.2 B.6
Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
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2.4.1.2 B.7
Check the reasonableness of results of computations.
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2.4.1.2 B.8
Understand and use the inverse relationship between addition and subtraction.
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2.4.1.2 C
Estimation
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2.4.1.2 C.1
Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.
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2.4.1.2 C.2
Determine the reasonableness of an answer by estimating the result of computations (e.g., 15 + 16 is not 211).
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2.4.1.2 C.3
Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation.
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2.4.2
Geometry and Measurement
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2.4.2.2 A
Geometric Properties
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2.4.2.2 A.1
Identify and describe spatial relationships among objects in space and their relative shapes and sizes.
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2.4.2.2 A.1.a
Inside/outside, left/right, above/below, between
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Positions: Inside and outside (Kindergarten - K.1)
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Positions: Left, middle, and right (Kindergarten - K.2)
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Positions: Top, middle, and bottom (Kindergarten - K.3)
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Positions: Above and below (Kindergarten - K.4)
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Positions: Location in a three-by-three grid (Kindergarten - K.5)
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Spatial sense: Left, middle, and right (First grade - K.1)
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Spatial sense: Above, below, top, middle, and bottom (First grade - K.2)
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Spatial sense: Location in a three-by-three grid (First grade - K.3)
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2.4.2.2 A.1.b
Smaller/larger/same size, wider/narrower, longer/shorter
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2.4.2.2 A.1.c
Congruence (i.e., same size and shape)
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2.4.2.2 A.2
Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes.
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2.4.2.2 A.2.a
Vertex, edge, face, side
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Geometry: Count sides and corners (Kindergarten - S.5)
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Geometry: Compare sides and corners (Kindergarten - S.6)
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Geometry: Identify 2-dimensional shapes (First grade - J.1)
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Geometry: Count sides and vertices (First grade - J.5)
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Geometry: Count edges, vertices, and faces (First grade - J.6)
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Geometry: Compare sides and vertices (First grade - J.7)
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Geometry: Compare edges, vertices, and faces (First grade - J.8)
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Geometry: Compare sides, vertices, edges, and faces (Second grade - T.2)
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Geometry: Count sides, vertices, edges, and faces (Second grade - T.3)
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2.4.2.2 A.2.b
3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid
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2.4.2.2 A.2.c
2D figures - square, rectangle, circle, triangle
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2.4.2.2 A.2.d
Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape)
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2.4.2.2 A.3
Describe, identify and create instances of line symmetry.
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2.4.2.2 A.4
Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.
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2.4.2.2 B
Transforming Shapes
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2.4.2.2 B.1
Use simple shapes to make designs, patterns, and pictures.
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2.4.2.2 B.2
Combine and subdivide simple shapes to make other shapes.
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2.4.2.2 C
Coordinate Geometry
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2.4.2.2 C.1
Give and follow directions for getting from one point to another on a map or grid.
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2.4.2.2 D
Units of Measurement
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2.4.2.2 D.1
Directly compare and order objects according to measurable attributes.
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2.4.2.2 D.1.a
Attributes - length, weight, capacity, time, temperature
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2.4.2.2 D.2
Recognize the need for a uniform unit of measure.
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2.4.2.2 D.3
Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems.
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2.4.2.2 D.3.a
Length - inch, foot, yard, centimeter, meter
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2.4.2.2 D.3.b
Weight - pound, gram, kilogram
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2.4.2.2 D.3.c
Capacity - pint, quart, liter
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2.4.2.2 D.3.d
Time - second, minute, hour, day, week, month, year
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2.4.2.2 D.3.e
Temperature - degrees Celsius, degrees Fahrenheit
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2.4.2.2 D.4
Estimate measures.
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2.4.2.2 E
Measuring Geometric Objects
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2.4.2.2 E.1
Directly measure the perimeter of simple two-dimensional shapes.
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2.4.2.2 E.2
Directly measure the area of simple two-dimensional shapes by covering them with squares.
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2.4.3
Patterns and Algebra
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2.4.3.2 A
Patterns
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2.4.3.2 A.1
Recognize, describe, extend, and create patterns.
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2.4.3.2 A.1.a
Using concrete materials (manipulatives), pictures, rhythms, & whole numbers
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2.4.3.2 A.1.b
Descriptions using words and symbols (e.g., "add two" or "+ 2")
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2.4.3.2 A.1.c
Repeating patterns
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2.4.3.2 A.1.d
Whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward)
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2.4.3.2 B
Functions and Relationships
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2.4.3.2 B.1
Use concrete and pictorial models of function machines to explore the basic concept of a function.
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2.4.3.2 C
Modeling
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2.4.3.2 C.1
Recognize and describe changes over time (e.g., temperature, height).
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2.4.3.2 C.2
Construct and solve simple open sentences involving addition or subtraction.
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2.4.3.2 C.2.a
Result unknown (e.g., 6 - 2 = __ or n = 3 + 5)
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2.4.3.2 C.2.b
Part unknown (e.g., 3 + [] = 8)
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2.4.3.2 D
Procedures
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2.4.3.2 D.1
Understand and apply (but don't name) the following properties of addition:
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2.4.3.2 D.1.a
Commutative (e.g., 5 + 3 = 3 + 5)
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2.4.3.2 D.1.b
Zero as the identity element (e.g., 7 + 0 = 7)
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2.4.3.2 D.1.c
Associative (e.g., 7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)
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2.4.4
Data Analysis, Probability, and Discrete Mathematics
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2.4.4.2 A
Data Analysis
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2.4.4.2 A.1
Collect, generate, record, and organize data in response to questions, claims, or curiosity.
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2.4.4.2 A.1.a
Data collected from students' everyday experiences
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2.4.4.2 A.1.b
Data generated from chance devices, such as spinners and dice
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2.4.4.2 A.2
Read, interpret, construct, and analyze displays of data.
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2.4.4.2 A.2.a
Pictures, tally chart, pictograph, bar graph, Venn diagram
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2.4.4.2 A.2.b
Smallest to largest, most frequent (mode)
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Probability and statistics: Mode and range (First grade - P.3)
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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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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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2.4.4.2 B
Probability
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2.4.4.2 B.1
Use chance devices like spinners and dice to explore concepts of probability.
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2.4.4.2 B.1.a
Certain, impossible
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2.4.4.2 B.1.b
More likely, less likely, equally likely
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2.4.4.2 B.2
Provide probability of specific outcomes.
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2.4.4.2 B.2.a
Probability of getting specific outcome when coin is tossed, when die is rolled, when spinner is spun (e.g., if spinner has five equal sectors, then probability of getting a particular sector is one out of five)
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2.4.4.2 B.2.b
When picking a marble from a bag with three red marbles and four blue marbles, the probability of getting a red marble is three out of seven
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2.4.4.2 C
Discrete Mathematics-Systematic Listing and Counting
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2.4.4.2 C.1
Sort and classify objects according to attributes.
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2.4.4.2 C.1.a
Venn diagrams
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Sorting, ordering, and classifying: Same (Kindergarten - N.1)
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Sorting, ordering, and classifying: Different (Kindergarten - N.2)
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Sorting, ordering, and classifying: Same and different (Kindergarten - N.3)
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Sorting, ordering, and classifying: Classify by color (Kindergarten - N.4)
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Sorting, ordering, and classifying: Venn diagrams (Kindergarten - N.5)
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Sorting, ordering, and classifying: Venn diagrams (First grade - Q.1)
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2.4.4.2 C.2
Generate all possibilities in simple counting situations (e.g., all outfits involving two shirts and three pants).
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2.4.4.2 D
Discrete Mathematics-Vertex-Edge Graphs and Algorithms
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2.4.4.2 D.1
Follow simple sets of directions (e.g., from one location to another, or from a recipe).
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2.4.4.2 D.2
Color simple maps with a small number of colors.
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2.4.4.2 D.3
Play simple two-person games (e.g., tic-tac-toe) and informally explore the idea of what the outcome should be.
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2.4.4.2 D.4
Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges").
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2.4.4.2 D.4.a
Paths from one vertex to another
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2.4.5
Mathematical Processes
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2.4.5.2 A
Problem Solving
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2.4.5.2 A.1
Learn mathematics through problem solving, inquiry, and discovery.
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2.4.5.2 A.2
Solve problems that arise in mathematics and in other contexts.
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2.4.5.2 A.2.a
Open-ended problems
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2.4.5.2 A.2.b
Non-routine problems
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2.4.5.2 A.2.c
Problems with multiple solutions
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2.4.5.2 A.2.d
Problems that can be solved in several ways
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2.4.5.2 A.3
Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.
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2.4.5.2 A.4
Pose problems of various types and levels of difficulty.
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2.4.5.2 A.5
Monitor their progress and reflect on the process of their problem solving activity.
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2.4.5.2 A.6
Distinguish relevant from irrelevant information, and identify missing information.
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2.4.5.2 B
Communication
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2.4.5.2 B.1
Use communication to organize and clarify their mathematical thinking.
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2.4.5.2 B.1.a
Reading and writing
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2.4.5.2 B.1.b
Discussion, listening, and questioning
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2.4.5.2 B.2
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.
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2.4.5.2 B.3
Analyze and evaluate the mathematical thinking and strategies of others.
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2.4.5.2 B.4
Use the language of mathematics to express mathematical ideas precisely.
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2.4.5.2 C
Connections
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2.4.5.2 C.1
Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).
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2.4.5.2 C.2
Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).
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2.4.5.2 C.3
Recognize that mathematics is used in a variety of contexts outside of mathematics.
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2.4.5.2 C.4
Apply mathematics in practical situations and in other disciplines.
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2.4.5.2 C.5
Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).
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2.4.5.2 C.6
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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2.4.5.2 D
Reasoning
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2.4.5.2 D.1
Recognize that mathematical facts, procedures, and claims must be justified.
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2.4.5.2 D.2
Use reasoning to support their mathematical conclusions and problem solutions.
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2.4.5.2 D.3
Select and use various types of reasoning and methods of proof.
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2.4.5.2 D.4
Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.
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2.4.5.2 D.5
Make and investigate mathematical conjectures.
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2.4.5.2 D.5.a
Counterexamples as a means of disproving conjectures
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2.4.5.2 D.5.b
Verifying conjectures using informal reasoning or proofs.
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2.4.5.2 D.6
Evaluate examples of mathematical reasoning and determine whether they are valid.
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2.4.5.2 E
Representations
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2.4.5.2 E.1
Create and use representations to organize, record, and communicate mathematical ideas.
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2.4.5.2 E.1.a
Concrete representations (e.g., base-ten blocks or algebra tiles)
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2.4.5.2 E.1.b
Pictorial representations (e.g., diagrams, charts, or tables)
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2.4.5.2 E.1.c
Symbolic representations (e.g., a formula)
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2.4.5.2 E.1.d
Graphical representations (e.g., a line graph)
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2.4.5.2 E.2
Select, apply, and translate among mathematical representations to solve problems.
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2.4.5.2 E.3
Use representations to model and interpret physical, social, and mathematical phenomena.
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2.4.5.2 F
Technology
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2.4.5.2 F.1
Use technology to gather, analyze, and communicate mathematical information.
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2.4.5.2 F.2
Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.
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2.4.5.2 F.3
Use graphing calculators and computer software to investigate properties of functions and their graphs.
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2.4.5.2 F.4
Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).
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2.4.5.2 F.5
Use computer software to make and verify conjectures about geometric objects.
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2.4.5.2 F.6
Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).
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