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4.1
Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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4.1.1
Students will represent and show relationships among positive rational numbers within the base-ten number system.
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4.1.1.a
Read and write numbers through the millions (e.g., 2,347,589 is the same as 2 million three hundred forty seven thousand five hundred eighty nine)
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4.1.1.b
Demonstrate multiple equivalent representations for decimal numbers through the hundredths place (e.g., 2 and 5 hundredths is 2.05; 6.23 is 6 +.2 +.03)
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4.1.1.c
Compare and order whole numbers and decimals through the hundredths place (e.g., money)
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4.1.1.d
Classify a number as even or odd
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4.1.1.e
Represent a fraction as parts of a whole and/or parts of a set
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4.1.1.f
Use visual models to find equivalent fractions (e.g., 2/4 = 1/2, 2/8 = 1/4, 1 = 2/2 = 5/5, 3/3)
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4.1.1.g
Determine the size of a fraction relative to one half using equivalent forms (e.g., Is 3/8 more or less than one half?)
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4.1.1.h
Locate fractions on a number line
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4.1.1.i
Round a whole number to millions
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4.1.2
Students will demonstrate the meaning of division with whole numbers.
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4.1.2.a
Use drawings, words, and symbols to explain the meaning of division [(e.g., as repeated subtraction: Sarah has 24 candies. She put them into bags of 6 candies each. How many bags did Sarah use?) (e.g., as equal sharing: Paul has 24 candies. He wants to share them equally among his 6 friends. How many candies will each friend receive?)]
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4.1.3
Students will compute fluently and accurately using appropriate strategies and tools.
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4.1.3.a
Compute whole number division facts 0 - 10 fluently
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4.1.3.b
Add and subtract decimals to the hundredths place (e.g., money)
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4.1.3.c
Multiply two-digit whole numbers
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4.1.3.d
Divide a three-digit number with one digit divisor with and without a remainder
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4.1.3.e
Mentally compute multiplication and division involving powers of 10
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4.1.3.f
Select and apply the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil)
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4.1.4
Students will estimate and check reasonableness of answers using appropriate strategies and tools.
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4.1.4.a
Estimate the three-digit product and the two-digit quotient of whole number multiplication and division and check the reasonableness
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4.2
Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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4.2.1
Students will classify two-dimensional shapes and three-dimensional objects.
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4.2.1.a
Identify two- and three-dimensional shapes according to their sides and angle properties
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4.2.1.b
Classify an angle as acute, obtuse, and right
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4.2.1.c
Identify parallel, perpendicular, and intersecting lines
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4.2.1.d
Identify the property of congruency when dealing with plane geometric shapes
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4.2.2
Students will describe locations using coordinate geometry.
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4.2.2.a
Identify the ordered pair of a plotted point in first quadrant by its location (e.g., (2, 3) is a point two right and three up from the origin)
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4.2.3
Students will identify simple transformations.
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4.2.3.a
Given two congruent geometric shapes, identify the transformation (e.g., translation, rotation, reflection) applied to an original shape to create a transformed shape
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4.2.4
Student will use geometric models to solve problems.
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4.2.4.a
Given a geometric model, use it to solve a problem (e.g., what shapes make a cylinder; streets run parallel and perpendicular)
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4.2.5
Students will apply appropriate procedures and tools to estimate and determine measurement using customary and metric units.
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4.2.5.a
Select and use appropriate tools to measure perimeter of polygons
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4.2.5.b
Identify time to the minute on an analog clock
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4.2.5.c
Solve problems involving elapsed time
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4.2.5.d
Identify the appropriate metric unit for measuring length, weight, and capacity/volume (e.g., cm, m, Km; g, Kg; mL, L)
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4.2.5.e
Estimate and measure length using customary (nearest ½ inch) and metric (nearest centimeter) units
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4.2.5.f
Measure weight and temperature using customary units
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4.2.5.g
Compute simple unit conversions for length within a system of measurement
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4.3
Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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4.3.1
Students will represent and analyze relationships.
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4.3.1.a
Describe, extend, and apply rules about numeric patterns
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4.3.1.b
Represent and analyze a variety of patterns using words, tables, and graphs
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4.3.1.c
Use "greater than or equal to", "less than or equal to" symbols to compare quantities
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4.3.1.d
Select appropriate operational and relational symbols to make a number sentence true
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4.3.2
Students will create and use models to represent mathematical situations.
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4.3.2.a
Model situations that involve the multiplication of whole numbers using number lines and symbols
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4.3.2.b
Describe and model quantitative change involving multiplication (e.g., money doubling)
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4.3.3
Students will identify and apply properties of whole numbers to solve equations involving multiplication and division.
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4.3.3.a
Represent the idea of a variable as an unknown quantity using a letter or a symbol (e.g., n + 3, b - 2)
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4.3.3.b
Use symbolic representation of the identity property of multiplication (e.g., 5 * 1 = 5)
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4.3.3.c
Use symbolic representations of the commutative property of multiplication (e.g., 2 * 3 = "Delta" * 2)
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4.3.3.d
Solve simple one-step whole number equations (e.g., x + 2 = 3, 3 * y = 6)
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4.3.3.e
Explain the procedure(s) used in solving simple one-step whole number equations
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4.4
Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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4.4.1
Students will organize, display, compare, and interpret data.
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4.4.1.a
Represent data using dot/line plots
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4.4.1.b
Compare different representations of the same data
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4.4.1.c
Interpret data and draw conclusions using dot/line plots
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4.4.1.d
Find the mode and range for a set of whole numbers
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4.4.1.e
Find the whole number mean for a set of whole numbers
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4.4.2
Students will construct predictions based on data.
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4.4.2.a
Make predictions based on data to answer questions from tables and bar graphs
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4.4.3
Students will find, describe, and compare experimental probabilities.
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4.4.3.a
Perform simple experiments and compare the degree of likelihood (e.g., more likely, equally likely, or less likely)
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