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4.1
Patterns and Algebraic Reasoning
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4.1.1
Discover, describe, extend, and create a wide variety of patterns using tables, graphs, rules, and models (e.g., use 1-inch tiles to demonstrate that doubling the length of the side of a square more than doubles the area, explore the characteristics of odd and even numbers, extend patterns of geometric shapes).
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4.1.2
Elementary Function Concepts
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4.1.2.a
Use a variety of techniques to generalize number patterns (e.g., use function machines and "t-tables" to demonstrate "What is the rule?").
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4.1.2.b
Solve simple open sentences involving operations on whole numbers (with a variable, e.g., a + 17 = 23).
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4.2
Number Sense
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4.2.1
Place Value
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4.2.1.a
Apply the concept of place value through 6 digits (e.g., write numbers in expanded form, play a trading game involving place value).
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4.2.1.b
Read, write and rename whole numbers through 6 digits and decimal numbers to the hundredths (e.g., money, numerals to words).
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4.2.2
Compare and order whole numbers and decimals to the hundredths place (e.g., pictures of shaded regions of two-dimensional figures, use >, < , = symbols).
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4.2.3
Fractions
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4.2.3.a
Use 0, 1/2, and 1 or 0, 0.5, and 1, as benchmarks and place additional fractions and decimals on a number line (e.g., 1/3 , 3/4 , 0.7, 0.4).
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4.2.3.b
Create physical and pictorial models of equivalent and nonequivalent fractional parts to be compared, added or subtracted (e.g., egg cartons, fraction strips, circles, and squares).
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4.3
Number Operations and Computation
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4.3.1
Estimate and find the product of 2- and 3-digit numbers to solve application problems.
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4.3.2
Division Concepts
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4.3.2.a
Demonstrate fluency with basic division facts and fact families.
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4.3.2.b
Develop division algorithms (e.g., use physical materials to show 12 objects arranged in 3 groups, show division as repeated subtraction and as the inverse of multiplication).
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4.3.2.c
Estimate and find the quotient (with and without remainders) with a 1-digit divisor and a 2- or 3-digit dividend to solve application problems.
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4.3.3
Apply a variety of estimation and mental math techniques to simplify computations (e.g., use rounding to estimate 82 - 58 is about 80 - 60 or 20, use 30 x 5 to find the product of 300 x 5).
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4.3.4
Develop operation sense by applying the associative property of multiplication (e.g., 6 x (2 x 3) = (6 x 2) x 3).
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4.4
Geometry and Measurement
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4.4.1
Basic Characteristics of Lines and Angles
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4.4.1.a
Identify, draw, and construct models of intersecting, parallel, and perpendicular lines (e.g., use spaghetti, straws, toothpicks).
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4.4.1.b
Identify and compare angles equal to, less than, or greater than 90 degrees (e.g., use right angles to determine the approximate size of other angles; make a variety of angles using flexible straws and compare).
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4.4.2
Identify basic characteristics of the rectangular coordinate system and find the distance between horizontal and vertical lines of a rectangular coordinate system (e.g., the x-axis is the horizontal axis).
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4.4.3
Spatial Reasoning
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4.4.3.a
Describe the effects on two- and three-dimensional objects when they slide (translate), flip (reflect), and turn (rotate) (e.g. tessellations).
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4.4.3.b
Predict and verify the effects of combining, subdividing, and changing two- and three-dimensional figures (e.g., folding paper, tiling, and rearranging pieces of solids).
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4.4.4
Measurement
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4.4.4.a
Establish benchmarks for customary and metric units and estimate the measures of a variety of objects and compare units (e.g., mass: the mass of a raisin is about 1 gram, length: the width of a finger is about 1 centimeter).
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4.4.4.b
Select appropriate customary and metric units of measure to solve application problems involving length, weight, and volume.
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4.4.4.c
Solve application problems involving money, time and temperature (e.g., elapsed time).
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4.5
Data Analysis and Probability
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4.5.1
Data Analysis
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4.5.1.a
Examine data displays such as tallies, tables, charts and graphs and use the observations to pose and answer questions (e.g., choose a table in social studies of population data and write problems).
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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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4.5.1.b
Collect, organize and record data in tables and graphs (e.g., bar, pictograph, line plots).
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4.5.2
Investigate and record probabilities by experimenting with devices that generate random outcomes (e.g., coins, number cubes, spinners).
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