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M5.A
Numbers and Operations
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M5.A.1
Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.
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M5.A.1.1
Express numbers in equivalent forms.
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M5.A.1.1.1
Use expanded notation to represent whole numbers or decimals (whole numbers less than 10,000,000 and decimals through hundredths).
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M5.A.1.2
Demonstrate understanding of place value of whole numbers and decimals.
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M5.A.1.2.1
Match the standard form to the word form of decimal numbers through the hundredths.
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M5.A.1.2.2
Identify the place value of a digit (from millions through hundredths).
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M5.A.1.3
Compare quantities or magnitudes of numbers.
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M5.A.1.3.1
Compare whole numbers through 9 digits using the words more, less, equal, least, most, greater than, less than or the symbols <, >, =.
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M5.A.1.3.2
Compare and/or order decimals through the hundredths. (Limit sets for ordering to no more than 4 numbers.)
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M5.A.1.3.3
Compare proper fractions through 16ths with like and unlike denominators.
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M5.A.1.4
Use simple applications of negative numbers (number line, counting, temperature).
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M5.A.1.4.1
Locate/Identify integers on a number line (greater than or equal to -20).
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M5.A.1.4.2
Identify negative temperatures on a thermometer (through -20°C or °F).
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M5.A.1.5
Use or develop models to represent fractions and/or mixed numbers.
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M5.A.1.5.1
Use or develop regions and/or sets (e.g., circle graph, base ten blocks) to model fractions and mixed numbers through hundredths (may include reducing the fractions).
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M5.A.1.6
Apply number theory concepts (i.e., primes, factors, multiples, composites).
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M5.A.1.6.1
Define/list/identify prime and composite numbers less than or equal to 100.
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M5.A.1.6.2
Define/list/identify factors and/or multiples of a given whole number less than or equal to 50.
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M5.A.2
Understand the meanings of operations, use operations and understand how they relate to each other.
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M5.A.2.1
Solve problems involving decimals, fractions and/or whole numbers (straight computation or word problems).
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M5.A.2.1.1
Solve problems involving addition, subtraction, multiplication and division of whole numbers (multipliers up to 2 digits - divisors one digit) and decimals including money (answer through hundredths - no divisors with decimals).
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M5.A.2.1.2
Solve problems involving addition and subtraction of fractions (through 16ths - like and unlike denominators - for unlike denominators, the LCD must be one of the given denominators).
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M5.A.2.1.3
Choose the correct operation(s) to solve a problem (no more than 2 operations).
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M5.A.3
Compute accurately and fluently and make reasonable estimates.
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M5.A.3.1
Apply estimation strategies to a variety of problems.
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M5.A.3.1.1
Round whole numbers through millions and decimals through hundredths.
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M5.A.3.1.2
Use estimation to solve problems involving whole numbers and/or decimals (up to 2-digit multipliers, single-digit divisors or multiples of 10; whole numbers through thousands and decimals through hundredths).
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M5.A.3.2
Compute accurately without the use of a calculator (straight computation or 1 operation word problems).
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M5.A.3.2.1
Use addition, subtraction, multiplication and division to compute accurately without a calculator (multipliers up to 2 digits, single-digit divisors or multiples of 10 - whole numbers through thousands and decimals through hundredths - no division with decimals).
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M5.B
Measurement
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M5.B.1
Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.
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M5.B.1.1
Select appropriate units (customary or metric) to measure specific attributes of objects.
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M5.B.1.1.1
Select the appropriate unit for measuring weight (mass), capacity, length, perimeter and area.
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M5.B.1.2
Solve problems using simple conversions and/or add and subtract measurements.
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M5.B.1.2.1
Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below - use a conversion chart or a "hint" with problems e.g., hint: 16oz = 1lb).
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M5.B.1.2.1.a
Metric using mm, cm, m and km; mL and L; g and kg
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M5.B.1.2.1.b
Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb
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M5.B.1.2.2
Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form).
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M5.B.1.3
Estimate and/or compare the perimeters or areas of 2 figures without computation.
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M5.B.1.3.1
Estimate which polygon (shown on a grid) has a greater perimeter or area (compare either area to area or perimeter to perimeter).
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M5.B.1.3.2
Estimate the area of an irregular figure shown on a grid.
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M5.B.2
Apply appropriate techniques, tools and formulas to determine measurements.
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M5.B.2.1
Use appropriate tools to determine measurements.
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M5.B.2.1.1
Use a ruler to measure to the nearest 1/8 inch or centimeter.
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M5.B.2.2
Solve problems involving length, time, weight (mass), capacity, temperature, perimeter and/or area.
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M5.B.2.2.1
Find the perimeter of a figure drawn and labeled (with the same units throughout).
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M5.B.2.2.2
Find the area of a square or rectangle (with the same units throughout - whole numbers only).
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M5.B.2.2.3
Solve problems involving weight, time, temperature, length and capacity (with the same units throughout - limited to 3 digits).
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M5.C
Geometry
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M5.C.1
Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.
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M5.C.1.1
Define and/or use basic properties of quadrilaterals (parallelograms, squares, rectangles, trapezoids, rhombi), triangles, circles, pyramids, cubes, and/or prisms.
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M5.C.1.1.1
Identify, and/or classify cubes, rectangular prisms or pyramids using faces, vertices and edges.
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M5.C.1.1.2
Identify and/or describe properties of all types of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid).
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M5.C.1.2
Represent and/or use properties of lines, line segments, rays, points and planes.
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M5.C.1.2.1
Identify, draw and/or label points, lines, line segments and rays.
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M5.C.2
Identify and/or apply concepts of transformations or symmetry.
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M5.C.2.1
Analyze transformations and/or use symmetry to analyze mathematical situations.
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M5.C.2.1.1
Draw or identify a translation (slide), reflection (flip) or rotation (turn) of a 2-dimensional shape.
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M5.C.2.1.2
Identify the number of lines of symmetry and/or draw all lines of symmetry in a two-dimensional polygon.
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M5.C.3
Locate points or describe relationships using the coordinate plane.
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M5.D
Algebraic Concepts
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M5.D.1
Demonstrate an understanding of patterns, relations and functions.
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M5.D.1.1
Create or extend patterns.
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M5.D.1.1.1
Extend or find a missing element in a numerical or simple geometric pattern (+, -, x or ÷ of whole numbers). Pattern must show 3 repetitions.
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M5.D.1.1.2
Create or replicate a numerical or geometric pattern showing 3 repetitions of that pattern (+, -, x or ÷ of whole numbers may be used).
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M5.D.1.2
Analyze patterns.
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M5.D.1.2.1
Form a rule based on a given pattern, or illustrate a pattern based on a given rule (+, -, x or ÷ of whole numbers may be used). Patterns must show 3 repetitions.
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M5.D.2
Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.
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M5.D.2.1
Select and/or use appropriate strategies, including concrete materials, to solve or represent expressions or number sentences.
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M5.D.2.1.1
Solve for a missing number (blank, question mark, variable) in an equation involving a single operation whole numbers only.
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M5.D.2.1.2
Match a realistic situation to an equation, expression, inequality (<, >, =), table or graph (variable must be isolated, e.g., 17 + 39 = n).
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M5.E
Data Analysis and Probability
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M5.E.1
Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.
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M5.E.1.1
Organize, display and/or interpret data using pictographs, tallies, tables, charts, line, bar graphs.
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M5.E.1.1.1
Display and/or interpret data shown in tallies, tables, charts, pictographs, bar graphs, line graphs and using a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs.
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Data, charts, and graphs: Read a table (Fifth grade - R.1)
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Data, charts, and graphs: Line graphs (Fifth grade - R.2)
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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: Circle graphs (Fifth grade - R.7)
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Data, charts, and graphs: Histograms (Fifth grade - R.8)
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Data, charts, and graphs: Choose the best type of graph (Fifth grade - R.9)
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M5.E.2
Select and/or use appropriate statistical methods to analyze data.
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M5.E.2.1
Describe data sets using mean, median, mode and/or range.
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M5.E.2.1.1
Determine the mean/average (answer is a whole number), median (answer is a whole number or average of 2 numbers) and range of data (up to 10 numbers).
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M5.E.2.1.2
Identify the mode in a set of data (up to 10 numbers).
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M5.E.3
Understand and/or apply basic concepts of probability or outcomes.
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M5.E.3.1
Predict or determine all possible combinations, outcomes and/or calculate the probability of a simple event.
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M5.E.3.1.1
Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (information could be represented by pictographs, bar graphs, charts, tables and/or spinners).
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M5.E.3.1.2
Determine the probability of an outcome (e.g., a coin toss, a roll of a number cube) and express as a fraction without reduction.
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