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4.1
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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4.1.1
Number sense
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4.1.1.1
Decompose and recompose whole numbers up to 10,000 using a variety of one, two- and three-digit combinations
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4.1.1.2
Determine factor pairs that make up a given number
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4.1.1.3
Develop an understanding of fractions as parts of unit wholes and division of whole numbers
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4.1.1.4
Demonstrate equivalent forms of common fractions using physical models, pictures, and number lines
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4.1.1.5
Compare and order fractions using physical models, pictures, and number lines
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4.1.1.6
Use decimal notation to show the value of coins
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4.1.1.7
Explore negative numbers by extending the number line using familiar applications (elevator, temperature, sea level, debt)
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4.1.2
Operations
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4.1.2.1
Choose the appropriate operation to solve a word problem and explain why
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4.1.2.2
Add and subtract larger numbers (e.g., three digits + two digits) and explain how the operation works
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4.1.2.3
Demonstrate mastery of mental math strategies for multiplying numbers (e.g., 25 * 8)
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4.1.2.4
Show how multiplication and division facts up to 50 are related, using arrays, skip counting, and area models
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4.1.2.5
Master multiplication facts and the related division facts up to the 10s tables
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4.1.2.6
Explain the meaning of the remainder in a division problem based on the context of the problem
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4.1.2.7
Develop and use strategies to estimate the results of operations on whole numbers
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4.1.2.8
Use physical models and pictures to add and subtract benchmark fractions
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4.1.2.9
Find 1/3, 1/4, and 1/5 of a given set or area using models
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4.1.2.10
Add and subtract decimals using money models
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4.1.2.11
Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper and pencil) depending on the context and nature of the computation
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4.2
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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4.2.1
Patterns and change
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4.2.1.1
Classify observed patterns of growth according to whether the growth is constant or varied (e.g., plant lab, geometric patterns)
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4.2.1.2
Record patterns of growth in tables and graphs
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4.2.1.3
Interpret tables, graphs and real-world events based on how they change over time
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4.2.2
Representations
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4.2.2.1
Model situations that involve the addition, subtraction, multiplication and division of whole numbers using objects, pictures, geometric model, and symbols
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4.2.3
Symbols
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4.2.3.1
Represent the idea of a variable as an unknown quantity using a letter or symbol
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4.2.3.2
Develop an understanding of the Commutative and Associative Properties of whole number multiplication as a tool to solve problems (e.g., is 4 × 5 always the same as 5 × 4?)
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4.3
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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4.3.1
Classification
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4.3.1.1
Identify and classify two-dimensional and three-dimensional shapes according to their properties
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4.3.1.2
Identify and build a three-dimensional object from two-dimensional representation of that object
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4.3.2
Location and transformation
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4.3.2.1
Identify line and rotational symmetry in two-dimensional shapes
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4.3.2.2
Describe a motion or series of motions that will show that two shapes are congruent (e.g., flip, slide, turn)
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4.3.2.3
Demonstrate an understanding of turn rotation through an angle
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4.3.3
Measurement
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4
Estimate and then measure the length of objects to the nearest whole unit (e.g., find your height in inches or centimeters)
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4.3.3.1
Extend the precision of a standard measurement by using fraction strips to develop 1/2, 1/4 or 1/10 as a "unit of measure."
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4.3.3.2
Describe the size of a turn angle using clock faces or geo logo
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4.3.3.3
Use a ruler to draw lines or geometric figures with given measurements
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4.3.3.4
Find the distance around a geometric figure to the nearest whole number (perimeter)
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4.3.3.5
Find the number of square units it takes to cover a rectangle (area)
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4.3.3.6
Count the number of cubes it takes to fill a three-dimensional figure (volume)
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4.3.3.7
Use measuring cups and graduated cylinders to find volume
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4.3.3.8
Estimate and then measure the mass of an object to the nearest whole unit
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4.3.3.9
Tell time to the nearest five minutes
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4.4
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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4.4.1
Collect
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4.4.1.1
Pose questions that can be answered with data; systematically collect and organize both categorical and numerical data
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4.4.1.2
Collect categorical data where the data is described using numbers (e.g., how many have five letters in their first name?)
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4.4.2
Represent
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4.4.2.1
Construct and use data displays (e.g., tables, scaled pictographs, bar graphs, line plots) in order to answer a question
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Data, charts, and graphs: Read a table (Fourth grade - J.1)
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Data, charts, and graphs: Line graphs (Fourth grade - J.2)
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Data, charts, and graphs: Bar graphs (Fourth grade - J.3)
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Data, charts, and graphs: Frequency charts (Fourth grade - J.4)
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Data, charts, and graphs: Stem-and-leaf plots (Fourth grade - J.5)
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Data, charts, and graphs: Circle graphs (Fourth grade - J.6)
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Data, charts, and graphs: Choose the best type of graph (Fourth grade - J.7)
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4.4.3
Analyze
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4.4.3.1
Describe a set of data as a whole, noting important features such as concentration of values, spread of the values, and extreme values
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4.4.3.2
Find and use measures of center (mode and median) to summarize and interpret data
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4.4.4
Probability
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4.4.4.1
Describe the outcomes of an experiment or event (e.g., possible/impossible, certain/uncertain, less likely/equally likely/more likely)
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