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M6.A
Numbers and Operations
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M6.A.1
Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.
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M6.A.1.1
Express numbers in equivalent forms.
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M6.A.1.1.1
Represent common percents as fractions and/or decimals (e.g., 25% = ¼ =.25) - common percents are 1%, 10%, 25%, 50%, 75%, 100%.
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M6.A.1.1.2
Convert between fractions and decimals and/or differentiate between a terminating decimal and a repeating decimal.
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M6.A.1.1.3
Represent a number in exponential form (e.g., 10x10x10=10³).
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M6.A.1.1.4
Represent a mixed number as an improper fraction.
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M6.A.1.2
Compare quantities and/or magnitudes of numbers.
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M6.A.1.2.1
Compare and/or order whole numbers, mixed numbers, fractions and/or decimals (do not mix fractions and decimals - decimals through thousandths).
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M6.A.1.3
Apply number theory concepts (i.e., factors, multiples).
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M6.A.1.3.1
Find the Greatest Common Factor (GCF) of two numbers (through 50) and/or use the GCF to simplify fractions.
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M6.A.1.3.2
Find the Least Common Multiple (LCM) of two numbers (through 50) and/or use the LCM to find the common denominator of two fractions.
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M6.A.1.3.3
Use divisibility rules for 2, 3, 5 and/or 10 to draw conclusions and/or solve problems.
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M6.A.1.4
Use or develop models to represent percents.
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M6.A.1.4.1
Model percents (through 100%) using drawings, graphs and/or sets (e.g., circle graph, base ten blocks, etc)
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M6.A.2
Understand the meanings of operations, use operations and understand how they relate to each other.
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M6.A.2.1
Select and/or use operations to simplify or solve problems.
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M6.A.2.1.1
Complete equations by using the following properties: associative, commutative, distributive and identity.
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M6.A.3
Compute accurately and fluently and make reasonable estimates.
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M6.A.3.1
Apply estimation strategies to a variety of problems.
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M6.A.3.1.1
Use estimation to solve problems involving whole numbers and decimals (up to 2-digit divisors and 4 operations).
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M6.A.3.2
Solve problems with and without the use of a calculator.
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M6.A.3.2.1
Solve problems involving operations (+, -, x, ÷) with whole numbers, decimals (through thousandths) and fractions (avoid complicated LCDs) - straight computation or word problems.
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M6.B
Measurement
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M6.B.1
Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.
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M6.B.1.1
Compare and/or determine elapsed time.
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M6.B.1.1.1
Determine and/or compare elapsed time to the minute (time may cross AM to PM or more than one day).
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M6.B.2
Apply appropriate techniques, tools and formulas to determine measurements.
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M6.B.2.1
Choose or use appropriate tools and/or units to determine measurements within the same system.
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M6.B.2.1.1
Use or read a ruler to measure to the nearest 1/16 inch or millimeter.
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M6.B.2.1.2
Choose the more precise measurement of a given object (e.g., smaller measurements are more precise).
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M6.B.2.1.3
Measure angles using a protractor up to 180° - protractor must be drawn - one side of the angle to be measured should line up with the straight edge of the protractor.
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M6.B.2.2
Solve problems involving length, perimeter, area and/or volume of geometric figures.
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M6.B.2.2.1
Find the perimeter of any polygon (may include regular polygons where only the measure of one side is given - same units throughout).
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M6.B.2.3
Identify, label, and/or list properties of angles or triangles.
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M6.B.2.3.1
Define, label and/or identify right, straight, acute and obtuse angles.
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M6.C
Geometry
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M6.C.1
Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.
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M6.C.1.1
Define and/or use basic properties of triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, decagons and circles.
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M6.C.1.1.1
Identify, classify and/or compare polygons (up to ten sides.)
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M6.C.1.1.2
Identify and/or describe properties of all types of triangles (scalene, equilateral, isosceles, right, acute, obtuse).
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M6.C.1.1.3
Identify and/or determine the measure of the diameter and/or radius of a circle (when one or the other is given).
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M6.C.1.1.4
Identify and/or use the total number of degrees in a triangle, quadrilateral and/or circle.
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M6.C.1.2
Represent and/or use concepts and relationships of lines and line segments.
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M6.C.1.2.1
Identify, describe and/or label parallel, perpendicular or intersecting lines.
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M6.C.1.2.2
Identify, draw and/or label points, planes, lines, line segments, rays, angles and vertices.
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M6.C.3
Locate points or describe relationships using the coordinate plane.
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M6.C.3.1
Identify, plot or match points given an ordered pair.
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M6.C.3.1.1
Plot, locate or identify points in Quadrant I and/or on the x and y axes with intervals of 1, 2, 5 or 10 units - up to a 200 by 200 grid. Points may be in-between lines.
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M6.D
Algebraic Concepts
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M6.D.1
Demonstrate an understanding of patterns, relations and functions.
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M6.D.1.1
Create or extend patterns.
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M6.D.1.1.1
Create, extend or find a missing element in a pattern displayed in a table, chart or graph (pattern must show at least 3 repetitions - may use up to 2 operations with whole numbers).
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M6.D.1.2
Analyze patterns.
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M6.D.1.2.1
Determine a rule based on a pattern or illustrate a pattern based on a given rule (displayed on a table, chart or graph; pattern must show at least 3 repetitions).
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M6.D.2
Represent and/or analyze mathematical situations and structures using algebraic symbols, words, tables, and graphs.
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M6.D.2.1
Select and/or use appropriate strategies to solve number sentences.
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M6.D.2.1.1
Identify the inverse operation needed to solve a one-step equation.
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M6.D.2.1.2
Solve a one-step equation (i.e., using the inverse operation -whole numbers only).
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M6.D.2.2
Create and/or interpret expressions or equations that model problem situations.
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M6.D.2.2.1
Match an equation or expression involving one variable, to a verbal math situation (one operation only).
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M6.E
Data Analysis and Probability
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M6.E.1
Formulate questions that can be addressed with data and/or collect, organize, display, and analyze data.
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M6.E.1.1
Interpret data shown in frequency tables, histograms, circle, bar or double bar graphs, line or double line graphs or line plots.
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M6.E.1.1.1
Analyze data and/or answer questions pertaining to data represented in frequency tables, circle graphs, double bar graphs, double line graphs or line plots (for circle graphs, no computation with percents).
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M6.E.1.1.2
Choose the appropriate representation for a specific set of data (choices should be the same type of graph).
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M6.E.1.1.3
Display data in frequency tables, circle graphs, double-bar graphs, double line graphs or line plots using a title, appropriate scale, labels and a key when needed. Circle graphs for open-ended items must show a center point and tic marks.
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M6.E.2
Select and use appropriate statistical methods to analyze data.
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M6.E.2.1
Describe data sets using mean, median, mode and/or range.
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M6.E.2.1.1
Determine/calculate the mean, median, mode and/or range of displayed data (data can be displayed in a table or line plot - use whole numbers only up to 2 digits).
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M6.E.3
Understand and apply basic concepts of probability.
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M6.E.3.1
Determine all possible combinations, outcomes and/or calculate the probability of a simple event.
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M6.E.3.1.1
Define and/or find the probability of a simple event (express as a fraction in lowest terms).
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M6.E.3.1.2
Determine/show all possible combinations involving no more than 20 total arrangements (e.g., tree diagram, table, grid).
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