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2.1
Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.
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2.1.1
Number sense
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2.1.1.1
Develop efficient strategies for counting (e.g., skip counting by 1s, 2s, 5s and 10s)
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2.1.1.2
Demonstrate an understanding that our number system is based on combinations of ones and tens-place value
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2.1.1.3
Use combinations of one- and two-digit numbers to build larger (two-digit) numbers
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2.1.1.4
Use multiple strategies to compare size of two numbers (counting up, counting back)
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2.1.1.5
Connect number words for fractions with pictures and numerals (1/2, 1/3, 1/4)
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2.1.2
Operations
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2.1.2.1
Use number sentences to represent number combinations up to 20
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2.1.2.2
Use number sentences with missing addends to represent number combinations up to 20
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2.1.2.3
Use a variety of strategies to solve combination and separation problems up to 100
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2.1.2.4
Show number sentences that demonstrate that addition and subtraction are inverse operations (e.g., join, separate, part-part-whole, compare)
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2.1.2.5
Represent repeated addition using pictures and models
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2.1.2.6
Understand that addition of whole numbers result in a larger number and subtraction of whole numbers result in a smaller number
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2.2
Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.
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2.2.1
Patterns and change
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2.2.1.1
Sort objects by more than one attribute (e.g., boys with glasses, blue squares)
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2.2.1.2
Develop a system for sorting a given set of objects
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2.2.1.3
Create and extend patterns and then translate them into a rule or drawing
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2.2.1.4
Describe the rule for a pattern
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2.2.2
Representations
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2.2.2.1
Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, geometric models and symbols (e.g., multiplicative thinking may be represented by repeated addition and fair shares by repeated subtraction)
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2.2.3
Symbols
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2.2.3.1
Record mathematical thinking using conventional notation
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2.2.3.2
Use the = sign to connect equivalent parts in a number sentence
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2.3
Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.
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2.3.1
Classification
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2.3.1.1
Name and sort solid and plane figures by common attributes
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2.3.2
Location and transformation
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2.3.2.1
Recognize shapes that have symmetry
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2.3.3
Measurement
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2.3.3.1
Find objects that are the same in length
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2.3.3.2
Compare the length of two objects by counting the number of nonstandard units used to measure them (e.g., linking cubes)
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2.3.3.3
Balance an object using nonstandard units (e.g., it takes 5 paper clips to balance my pencil)
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2.3.3.4
Measure an object by counting repetitions of the same unit of measure (e.g., the length of the desk measured by an index card)
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2.3.3.5
Measure a large object more than once using a different tool as the unit of measure each time- decide which one is the "best" for the task
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2.3.3.6
Cover up or "fill in" a design using manipulatives (e.g., pattern blocks, color tiles)
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2.3.3.7
Fill up containers and estimate which container hold more
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2.3.3.8
Talk about the time that events happen (e.g., get up, go to lunch, go home, go to bed)
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2.3.3.9
Tell time to the hour
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2.3.3.10
Identify combinations of coin to make one dollar
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2.4
Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.
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2.4.1
Collect
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2.4.1.1
Collect (e.g., observe, count, or survey) categorical data to answer a question posed by the teacher or students
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2.4.2
Represent
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2.4.2.1
Demonstrate a variety of informal techniques for organizing and representing categorical data (e.g., tallies, pictures, or physical objects, bar graph with scale provided, line plot)
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2.4.3
Analyze
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2.4.3.1
Interpret data by noting characteristics of the graph (e.g., most, least, the same)
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2.4.4
Probability
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2.4.4.1
Explore events as more likely or less likely based on informal observation
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