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6.A
Mathematical Process
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6.A.a
Reasoning
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6.A.a.1
Use reasoning and logic to:
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6.A.a.1.a
Perceive patterns
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6.A.a.1.b
Identify relationships
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6.A.a.1.c
Formulate questions
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6.A.a.1.d
Pose problems
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6.A.a.1.e
Make conjectures
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6.A.a.1.f
Justify strategies
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6.A.a.1.g
Test reasonableness of results
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6.A.b
Communication
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6.A.b.1
Communicate mathematical ideas and logical reasoning using the vocabulary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.
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6.A.c
Connections
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6.A.c.1
Connect mathematics to the real world, as well as within mathematics.
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6.A.d
Representation
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6.A.d.1
Create and use representations to organize, record, and communicate mathematical ideas.
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6.A.e
Problem Solving
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6.A.e.1
Solve and analyze routine and non-routine problems.
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6.B
Number Operations and Relationships
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6.B.a
Concepts
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6.B.a.1
Recognize and apply place-value concepts to whole numbers less than 10,000,000.
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6.B.a.2
Read, write and represent numbers using words, numerals, pictures (base-ten blocks), number lines, , arrays, expanded forms (12,436=10,000+2,000+400+30+6) and symbolic renaming e.g., 12,436=12,450-14.
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6.B.a.3
Compare and order numbers less than 100,000 represented in numbers, arrays, symbols (<, >, =) and words.
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6.B.a.4
Identify and use number theory concepts:
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6.B.a.4.a
prime and composite numbers
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6.B.a.4.b
divisibility potential of numbers (divisors of 1-10, 25).
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6.B.a.4.c
least common multiples through 24
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6.B.a.4.d
greatest common factors through 50
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6.B.a.5
Read, write and identify monetary amounts represented with visual models.
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6.B.a.6
Compare and order monetary amounts.
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6.B.a.7
Equate a monetary value with its benchmark fraction and percent. (Eg. $.25=1/4=25%)
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6.B.a.8
Demonstrate basic understanding of proportionality in proportional contexts.
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6.B.a.9
Read, write, identify, order, compare and mixed fractions.
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6.B.a.10
Represent fractions using numbers, pictures, and number lines.
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6.B.a.11
Rename improper fractions to mixed numbers in lowest terms.
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6.B.a.12
Identify and represent equivalence between fractions, percents, and decimals.
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6.B.b
Computation
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6.B.b.1
Use all operations in everyday situations to solve single or multi-step word problems.
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6.B.b.2
Solve three and four-digit addition and subtraction with regrouping, multiplication of three-digit by two-digit numbers, division with single-digit divisors and four-digit dividends with two-step or mixed operation problems.
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6.B.b.3
Compute with decimals in the context of money and make change.
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6.B.b.4
Solve problems using basic multiplication and division facts.
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6.B.b.5
Rename improper fractions.
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6.B.b.6
Add and subtract fractions with unlike denominators (halves, thirds, fourths, fifths, and tenths) with sums or differences between 0 and 1.
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6.B.b.7
Estimate using basic whole number operations, benchmark fractions and benchmark decimals.
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6.B.b.8
Determine reasonableness of answers.
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6.C
Geometry
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6.C.a
Describing Figures
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6.C.a.1
Recognize and name polygons with 3, 4, 5, 6 or 8 sides.
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6.C.a.2
Identify lines and line segments in a plane figure.
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6.C.a.3
Classify plane figures by characteristics of angles (acute, obtuse and right) and describe rays found in open-angle situations.
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6.C.b
Spatial Relationships and Transformations
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6.C.b.1
Use tangrams to describe, model, and construct plane figures.
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6.C.b.2
Identify figures that are congruent and/or similar.
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6.C.b.3
Describe and compare cubes, rectangular and triangular prisms and rectangular and triangular pyramids from nets (flat patterns).
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6.C.b.4
Use slides, flips and turns on figures. Identify congruent shapes using figures that have been manipulated by one or two motions (slides, flips and turns).
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6.C.b.5
Identify lines of symmetry and the number of lines of symmetry in figures and design shapes that have at least one line of symmetry.
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6.C.b.6
Identify and describe 3-dimensional figures from multiple perspectives.
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6.C.c
Coordinate Systems
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6.C.c.1
Identify and plot the coordinates of locations or objects on simple one quadrant grids using numbers only for coordinates, (e.g., (3, 2)).
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6.C.c.2
Locate the fourth coordinate pair when given three vertices of a rectangle or parallelogram on a coordinate grid.
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6.D
Measurement
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6.D.a
Measurable Attributes
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6.D.a.1
Identify appropriate units to measure length, liquid capacity, volume, time, weight/mass, temperature, including mixed measures. Units include: inches, feet, yards,(i.e. 1 foot 3 inches) miles, centimeters, millimeters, meters, kilometers, ounces, cups quarts, gallons, liters, hours, minutes, seconds (i.e. 1 hour 15 minutes) , days, months, years, ounces, pounds, grams, kilograms and degrees Fahrenheit/Celsius.
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6.D.a.2
Compare attributes of length, volume and weight by observation or when given actual measurements.
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6.D.a.3
Make measurement conversions within a system between units (e.g., feet and yards; inches and yards; quarts and gallons; meters and centimeters; seconds and hours).
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6.D.b
Direct Measurement
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6.D.b.1
Measure down to the nearest -1/8-inch, centimeter or millimeter.
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6.D.b.2
Determine angle measurement to nearest five degrees using a protractor.
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6.D.b.3
Read and interpret measuring instruments to determine the measurement of objects with standard units (U.S. customary).
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6.D.b.4
Determine and compare elapsed time in problem-solving situations.
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6.D.c
Indirect Measurement
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6.D.c.1
Estimate measurements using U.S. customary and metric measurement.
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6.D.c.2
Determine the area of regular shapes including right triangles.
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6.D.c.3
Determine distance between points using a scale.
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6.E
Statistics and Probability
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6.E.a
Data Analysis and Statistics
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6.E.a.1
Formulate questions to collect, organize and display data.
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6.E.a.2
Collect, organize and display data in appropriate graphs or charts.
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6.E.a.3
Draw reasonable conclusions based on contextual data.
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6.E.a.4
Use data to predict outcomes or trends from graphs and tables.
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6.E.a.5
Extract, interpret and analyze data from single bar graphs, tables and charts, line plots, context, circle graphs and Venn diagrams.
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6.E.a.6
Describe a given set of data of ten or fewer items/numbers using the terms mean, median, mode and range to extract information from organized charts, tables, graphs and Venn diagrams in problems with and without context.
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6.E.b
Probability
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6.E.b.1
Determine the likelihood of future events, predict outcomes of future events and test predictions using data from a variety of sources.
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6.E.b.2
Choose or design an event that is fair or unfair.
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6.E.b.3
Determine the probability of events in context using words, percents or fractions.
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6.E.b.4
Describe and determine the number of combinations of selecting 3 items from 4 or more items.
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6.F
Algebraic Relationships
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6.F.a
Patterns, Relations and Functions
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6.F.a.1
Recognize, extend, describe, create and replicate a variety of patterns including attribute, numeric and geometric patterns.
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6.F.a.2
Represent patterns and relationships with pictures, table and charts.
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6.F.a.3
Describe a rule that explains a functional relationship or pattern using addition, subtraction or multiplication rules.
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6.F.a.4
Determine a future event in a pattern up to the tenth item when given the first five.
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6.F.a.5
Solve simple two-step, two operation patterns. Ex: 5, 8, 6, 9, 7, 10, 8..... (Pattern: +3-2...)Represent patterns and relationships with pictures, table and charts.
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6.F.b
Expressions, Equations and Inequalities
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6.F.b.1
Demonstrate basic understanding of equality and inequality using symbols (<, >, =) with multi-step, mixed operations.
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6.F.b.2
Solve one-step equations with "box" variable and whole number coefficients in problems with and without context using whole number coefficients.
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6.F.b.3
Solve two-step multi-operation equations with "box" or letter variable and whole number coefficients with and without context. Ex: 3 * "box" +1 = 7
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6.F.b.4
Represent problem situations with one or two-step equations or expressions. Solve simple two-step, two operation patterns.
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6.F.b.5
Solve two-step open sentences involving all operations.
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6.F.b.6
Solve equations involving any two operations. Ex: 3 * 4 -2=?; Ex: 12/3 +1="box"; Ex: 5 * 2 - 1 = a
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6.F.c
Properties
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6.F.c.1
Use the commutative property of multiplication with positive single digits.
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6.F.c.2
Use the inverse relationship of division and multiplication with single whole digits.
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6.F.c.3
Simplify (evaluate) two-step numerical expressions using correct order of operations.
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6.F.c.4
Demonstrate understanding of distributive property.
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6.F.c.5
Demonstrate understanding of order of operations by solving two-step open sentences involving all operations.
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