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5.1
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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5.1.1
Students will represent and show relationships among positive rational numbers.
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5.1.1.a
Demonstrate multiple equivalent representations for whole numbers and decimals through the thousandths place (e.g., 3.125 is 3 +.1 +.02 +.005)
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5.1.1.b
Compare and order whole numbers, fractions, and decimals through the thousandths place
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5.1.1.c
Identify and name fractions in their simplest form and find common denominators for fractions
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5.1.1.d
Recognize and generate equivalent forms of commonly used fractions, decimals, and percents (e.g., one third, one fourth, one half, two thirds, three fourths)
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5.1.1.e
Classify a number as prime or composite
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5.1.1.f
Identify factors and multiples of any whole number
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5.1.1.g
Round whole numbers and decimals to any given place
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5.1.2
Students will demonstrate the meaning of arithmetic operations with whole numbers.
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5.1.2.a
Use words and symbols to explain the meaning of the identity properties for addition and multiplication
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5.1.2.b
Use words and symbols to explain the meaning of the commutative and associative properties of addition and multiplication
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5.1.2.c
Use words and symbols to explain the distributive property of multiplication over addition (e.g., 5 (y + 2) = 5y + 5 x 2)
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5.1.3
Students will compute fluently and accurately using appropriate strategies and tools.
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5.1.3.a
Add and subtract positive rational numbers (e.g., proper and improper fractions, mixed numbers, fractions with common and uncommon denominators, decimals through the thousandths place)
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5.1.3.b
Select, apply and explain the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology)
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5.1.3.c
Multiply decimals
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5.1.3.d
Divide a decimal by a whole number
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5.1.4
Students will estimate and check reasonableness of answers using appropriate strategies and tools.
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5.1.4.a
Estimate the sums and differences of positive rational numbers to check the reasonableness of such results
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5.2
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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5.2.1
Students will describe relationships among two-dimensional shapes and three-dimensional objects.
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5.2.1.a
Identify the number of edges, faces, and vertices of triangular and rectangular prisms
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5.2.1.b
Justify congruence of two-dimensional shapes
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5.2.1.c
Justify the classification of two-dimensional shapes (e.g., triangles by angles and sides)
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5.2.1.d
Identify degrees on a circle (e.g., 45, 90, 180, 270, 360)
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5.2.2
Students will identify locations using coordinate geometry.
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5.2.2.a
Plot the location of an ordered pair in the first quadrant
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5.2.3
Students will identify and use simple transformations.
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5.2.3.a
Perform one-step transformations on two dimensional shapes (e.g., translation, rotation, reflection, of 90, 180, and 270)
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5.2.4
Students will create and use geometric models to solve problems.
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5.2.4.a
Build or sketch a geometric model to solve a problem
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5.2.4.b
Sketch congruent shapes
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5.2.4.c
Build rectangular prisms using cubes
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5.2.5
Students will apply appropriate procedures, tools, and formulas to determine measurements using customary and metric units.
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5.2.5.a
Select and use appropriate tools to measure perimeter and angles
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5.2.5.b
Identify correct unit (customary or metric) to the measurement situation (e.g., distance from home to school; measure length of a room)
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5.2.5.c
Estimate and measure length with customary units to the nearest ΒΌ inch
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5.2.5.d
Measure capacity/volume with customary units
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5.2.5.e
Measure weight (mass) and temperature using metric units
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5.2.5.f
Determine the area of rectangles and squares
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5.3
Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
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5.3.1
Students will represent, analyze, and generalize relationships.
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5.3.1.a
Describe, extend, apply rules, and make generalizations about numeric, and geometric patterns
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5.3.1.b
Create and analyze numeric patterns using words, tables, and graphs
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5.3.1.c
Communicate relationships using expressions and equations
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5.3.2
Students will create, use, and compare models representing mathematical situations.
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5.3.2.a
Model situations that involve the addition, subtraction, and multiplication of positive rational numbers using words, graphs, and tables
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5.3.2.b
Represent a variety of quantitative relationships using tables and graphs
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5.3.2.c
Compare different models to represent mathematical situations
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5.3.3
Students will apply properties of simple positive rational numbers to solve one-step equations.
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5.3.3.a
Explain the addition property of equality (e.g., if a = b, then a + c = b + c)
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5.3.3.b
Use symbolic representations of the associative property (e.g., (2 + 3) + 4 = 2 + (3 + n), (2 * 3) * 4 = 2 * (3 * n))
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5.3.3.c
Evaluate numerical expressions by using parentheses with respect to order of operations (e.g., 6 + (3 * 5))
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5.3.3.d
Evaluate simple algebraic expressions involving addition and subtraction
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5.3.3.e
Solve one-step addition and subtraction equations involving common positive rational numbers
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5.3.3.f
Identify and explain the properties of equality used in solving one-step equations involving common positive rational numbers
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5.4
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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5.4.1
Students will organize, display, compare, and interpret data.
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5.4.1.a
Represent data using line graphs
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5.4.1.b
Represent the same set of data in different formats (e.g., table, pictographs, bar graphs, line graphs)
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5.4.1.c
Draw conclusions based on a set of data
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5.4.1.d
Find the mean, median, mode, and range for a set of whole numbers
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5.4.1.e
Generate questions and answers from data sets and their graphical representations
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Data, charts, and graphs: Read a table (Fifth grade - R.1)
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Data, charts, and graphs: Bar graphs (Fifth grade - R.3)
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Data, charts, and graphs: Pictographs (Fifth grade - R.4)
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Data, charts, and graphs: Frequency charts (Fifth grade - R.5)
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Data, charts, and graphs: Stem-and-leaf plots (Fifth grade - R.6)
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Data, charts, and graphs: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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5.4.2
Students will construct predictions based on data.
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5.4.2.a
Make predictions based on data to answer questions from tables, bar graphs, and line graphs
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5.4.3
Students will determine theoretical probabilities.
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5.4.3.a
Perform and record results of probability experiments
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5.4.3.b
Generate a list of possible outcomes for a simple event
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5.4.3.c
Explain that the likelihood of an event that can be represented by a number from 0 (impossible) to 1 (certain)
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