| Knowledge of Algebra, Patterns, and Functions: Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships. |
| Patterns and Functions
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Identify and copy numeric patterns |
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Use manipulatives with numeric qualities to build patterns
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Identify, copy, describe, create, and extend non-numeric patterns |
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Represent patterns kinesthetically such as: clap/snap/clap
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Represent and analyze repeating patterns using no more than 3 objects in the core of the pattern
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Sort a collection of objects according to a rule
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Identify patterns in real life situations
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Recognize the difference between patterns and non-patterns
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Continue patterns
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| Expressions, Equations, and Inequalities
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Write and identify expressions |
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Represent numeric quantities using concrete and pictorial representations to model addition expressions with a value of no more than 10
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Identify equations and inequalities |
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Represent relationships by comparing groups of no more than 10 objects to determine more or less
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Model and name the value of the missing part in a part-part-whole situation using no more than 10 manipulatives
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Describe addition using terms such as: and, add, plus, join, equal
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| Numeric and Graphic Representations of Relationships
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Locate points on a number line |
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Identify and represent whole numbers up to 10 on a number line using manipulatives, symbols, and one-to-one correspondence
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| Knowledge of Geometry: Students will apply the properties of one-, two-, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects. |
| Plane Geometric Figures
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Recognize and describe the attributes of plane geometric figures |
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Sort and regroup everyday objects and geometric figures according to attributes such as: shape, color, size
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Describe plane figures and their attributes such as: shape, color, size
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Identify triangles, circles, squares, and rectangles
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Compare, trace, and reproduce triangles, circles, squares, and rectangles
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| Solid Geometric Figures
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Recognize, describe, and use the attributes of solid geometric figures |
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Match, sort, and regroup objects according to attributes
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Describe solid figures
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Identify solid geometric figures in the environment
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| Congruence
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Recognize congruent objects |
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Identify everyday objects which have the same size and shape
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| Transformations
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Begin to recognize a transformation |
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Use position words such as: over, under, above, on, next to, below, beside, behind
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Use spatial reasoning to solve simple puzzles
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Demonstrate slides using simple objects
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Analyze geometric figures and pictures |
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Recognize the concept of symmetry using pictures
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| Knowledge of Measurement: Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements. |
| Measurement Units
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Explore measurement units |
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Order, compare, and describe objects by attributes such as: length/height, weight, capacity
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Recognize time by identifying days of the week and by using terms such as: yesterday, today, tomorrow, morning, afternoon, night, before, after
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Compare and describe temperature such as: temperature in January as compared to temperature in July
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| Measurement Tools
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Measure in non-standard units |
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Measure length of objects and pictures of objects
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Explore and compare the capacity of containers
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Explore and compare weight of objects
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| Knowledge of Number Relationships and Computation/Arithmetic: Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. |
| Knowledge of Number and Place Value
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Apply knowledge of whole numbers and place value |
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Extend concept of number
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Construct relationships between and among quantities using language such as: more than, less than, fewer than, as many as, one more, one less
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Demonstrate cardinality by answer of how many
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Build meaningful relationships by using 5 and 10 frames
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Use concrete materials to build sets 0 to 10
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Use concrete materials to compose and decompose quantities up to 10
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Match a numeral to a set
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Count to 31
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Count backward from 10
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Use ordinal numbers to indicate position such as: first, second, third, fourth, fifth
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Show initial awareness of fractional parts (halves) using concrete materials
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Identify and name the value of pennies, nickels, and dimes
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Choose the coin named from a given set of mixed coins
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Use money in real-world situations such as a classroom store
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| Number Computation
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Analyze number relations and compute |
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Model addition by combining sets of concrete objects and describe the results using words and pictures
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Model subtraction by separating sets of concrete objects and describe the results using words and pictures
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Solve a given story problem cooperatively that is based on the combining and separating of models
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| Processes of Mathematics: Students demonstrate the processes of mathematics by making connections and applying reasoning to solve problems and to communicate their findings. |
| Problem Solving
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Apply a variety of concepts, processes, and skills to solve problems |
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Identify the question in the problem
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Decide if enough information is present to solve the problem
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Make a plan to solve a problem
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Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
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Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
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Identify alternative ways to solve a problem
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Show that a problem might have multiple solutions or no solution
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Extend the solution of a problem to a new problem situation
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| Reasoning
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Justify ideas or solutions with mathematical concepts or proofs |
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Use inductive or deductive reasoning
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Make or test generalizations
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Support or refute mathematical statements or solutions
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Use methods of proof, i.e., direct, indirect, paragraph, or contradiction
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| Communication
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Present mathematical ideas using words, symbols, visual displays, or technology |
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Use multiple representations to express concepts or solutions
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Express mathematical ideas orally
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Explain mathematically ideas in written form
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Express solutions using concrete materials
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Express solutions using pictorial, tabular, graphical, or algebraic methods
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Explain solutions in written form
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Ask questions about mathematical ideas or problems
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Give or use feedback to revise mathematical thinking
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| Connections
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Relate or apply mathematics within the discipline, to other disciplines, and to life |
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Identify mathematical concepts in relationship to other mathematical concepts
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Identify mathematical concepts in relationship to other disciplines
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Identify mathematical concepts in relationship to life
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Use the relationship among mathematical concepts to learn other mathematical concepts
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