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Number Sense

  • Whole Numbers:
    Count, read, and write whole numbers to 1,000 and identify the place value for each digit.
  • Representing Numbers:
    Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).
  • Use of Symbols:
    Order and compare whole numbers to 1,000 by using the symbols < =, >.
  • Addition and Subtraction:
    Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions.
  • Multiplication of Numbers:
    Use repeated addition, arrays, and counting by multiples to do multiplication.
  • Division of Numbers
    Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.
  • Multiplication Tables:
    Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory.
  • Fractions
  • Money Problems:
    Solve problems using combinations of coins and bills.
  • Decimals:
    Know and use the decimal notation and the dollar and cent symbols for money.
  • Rounding and Estimation:
    Recognize when an estimate is reasonable in measurements (e.g., closest inch).
Algebra and Functions
  • Laws of Algebra:
    Use the commutative and associative rules to simplify mental calculations and to check results.
  • Word Problems:
    Relate problem situations to number sentences involving addition and subtraction.
Measurement and Geometry
  • Measurement:
    Measure the length of objects by iterating (repeating) a nonstandard or standard unit.
  • Units of measurement:
    Use of different units to measure the same object and predicting whether the measure will be greater or smaller when a different unit is used.
  • Time Determination and Conversion:
    Determination of time to the nearest quarter hour and relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).
  • Classification of Shapes:
    Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.
  • Properties of shapes:
    Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle).
Statistics, Data Analysis, and Probability
  • Data Collection:
    Record numerical data in systematic ways, keeping track of what has been counted.
  • Representing Data:
    Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).
  • Interpreting Data:
    Identify features of data sets (range and mode).
  • Understanding Patterns:
    Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12...; the number of ears on one horse, two horses, three horses, four horses).
  • Problems Involving Patterns:
    Solve problems involving simple number patterns.
Mathematical Reasoning
  • Use of Tools and Strategies:
    Determine the approach, materials, and strategies to be used. Use tools, such as manipulatives or sketches, to model problems.
  • Reasoning:
    Defend the reasoning used and justify the procedures selected.
  • Calculations and Result Verification:
    Make precise calculations and check the validity of the results in the context of the problem.

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