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5.A
Mathematical Process
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5.A.a
Reasoning
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5.A.a.1
Use reasoning and logic to:
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5.A.a.1.a
Perceive patterns
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5.A.a.1.b
Identify relationships
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5.A.a.1.c
Formulate questions
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5.A.a.1.d
Pose problems
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5.A.a.1.e
Make conjectures
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5.A.a.1.f
Justify strategies
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5.A.a.1.g
Test reasonableness of results
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5.A.b
Communication
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5.A.b.1
Communicate mathematical ideas and 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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5.A.c
Connections
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5.A.c.1
Connect mathematics to the real world, as well as within mathematics.
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5.A.d
Representation
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5.A.d.1
Create and use representations to organize, record, and communicate mathematical ideas.
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5.A.e
Problem Solving
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5.A.e.1
Solve and analyze routine and non-routine problems.
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5.B
Number Operations and Relationships
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5.B.a
Concepts
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5.B.a.1
Recognize and apply place-value concepts to whole numbers less than 1,000,000
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5.B.a.2
Read, write, and represent numbers using words, numerals, pictures (e.g.,. base ten blocks), number lines, , arrays, expanded forms (243=200+40+3) and symbolic renaming e.g., 243=250-7.
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5.B.a.3
Compare and order numbers less than 10,000 represented in numbers, arrays, symbols (<, > , =) and words.
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5.B.a.4
Use basic facts to determine the first ten multiples of 2-10 and determine factors for numbers up to 100.
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5.B.a.5
Recognize the divisibility potential of numbers (divisors of 2, 5, 10, 25)
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5.B.a.6
Count using whole numbers less than 10,000 and by any number 1-12 and 'friendly numbers' through 100. (ex. 20, 25, etc.)
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5.B.a.7
Read, write, represent, count, compare and order, and make change using a collection of coins and bills equal to and less than $20.00.
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5.B.a.8
Read, write and identify, equivalent fractions (1/4s, 1/2s, 1/8s, 1/10s, 1/16s)
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5.B.a.9
Represent fractions (1/4s, 1/2s, 1/8s, 1/10s, 1/16s) using numbers, pictures (e.g. drawings or base ten blocks), and number lines.
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5.B.a.10
Order and compare fractions (1/4s, 1/2s, 1/8s, 1/10s, 1/16s)represented numerically or as models (including parts of a set and parts of a whole)
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5.B.a.11
Rename improper fractions to mixed numbers.
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5.B.b
Computation
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5.B.b.1
Use all operations in everyday situations to solve single or multi-step word problems.
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5.B.b.2
Solve three-and four-digit addition and subtraction with regrouping; multiplication of two-digit by one-digit numbers; division with single-digit divisors and two-digit dividends and with two-step or mixed operation problems with single-digit numbers.
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5.B.b.3
Add and subtract decimals in the context of money.
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5.B.b.4
Solve problems using basic multiplication and division facts.
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5.B.b.5
Add and subtract fractions with like denominators.
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5.B.b.6
Estimate: multiplication of two-digit by one-digit problems, addition and subtraction of decimals using money, and division in context
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5.B.b.7
Determine reasonableness of answers.
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5.C
Geometry
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5.C.a
Describing Figures
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5.C.a.1
Identify, describe and compare properties of 2-and 3-dimensional figures, comparing sides, faces, vertices and edges of regular figures including parallel and perpendicular lines and line segments.
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5.C.a.2
Determine the number of faces, edges and vertices given an illustration of a 3-dimensional figure.
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5.C.b
Spatial Relationships and Transformations
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5.C.b.1
Use pattern blocks and dot paper (geoboards) to describe, model and construct plane figures.
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5.C.b.2
Identify cubes, rectangular and triangular prisms and rectangular and triangular pyramids from simple nets (flat patterns).
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5.C.b.3
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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5.C.b.4
Discern a shape with one line of symmetry.
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5.C.b.5
Identify and describe 3-dimensional figures from multiple perspectives.
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5.C.c
Coordinate Systems
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5.C.c.1
Use simple 2-dimensional coordinate systems to identify or plot locations on maps and to represent points and simple figures with coordinates using letters and numbers, (e.g., (E, 3)).
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5.C.c.2
Identify and use relationships among figures (e.g., location, position and intersection).
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5.D
Measurement
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5.D.a
Measurable Attributes
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5.D.a.1
Identify appropriate units to measure length, liquid capacity, volume, weight/mass, time, temperature. Units include: inches, feet, yards, miles, millimeters, centimeters, meters, kilometers, ounces, cups quarts, gallons, liters, seconds, minutes, hours, days, months, years, ounces, pounds, grams, kilograms and degrees Fahrenheit/Celsius.
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5.D.a.2
Compare attributes of length and weight by direct observation or when given actual measurements.
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5.D.a.3
Make measurement conversions within a system between units (e.g., feet and yards; inches and feet; quarts and gallons; meters and centimeters; minutes and hours; hours and days; months and years).
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5.D.b
Direct Measurement
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5.D.b.1
Read, interpret and use measuring instruments to determine the measurement of objects with non- standard and standard units to the nearest ΒΌ- inch or centimeter.
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5.D.b.2
Read thermometers to the nearest five degrees F/C and read a scale to the nearest ounce or five grams.
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5.D.b.3
Translate time on an analog clock to a digital clock and vice versa.
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5.D.b.4
Determine and compare elapsed time in problem-solving situations.
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5.D.c
Indirect Measurement
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5.D.c.1
Estimate measurement using U.S customary and metric measurements.
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5.D.c.2
Determine perimeter and area of regular shapes and the area of plane rectangular shapes.
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5.D.c.3
Determine perimeter and area of irregular shapes when given a reference tool such as a grid.
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5.E
Statistics and Probability
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5.E.a
Data Analysis and Statistics
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5.E.a.1
Formulate questions to collect, organize and display data.
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5.E.a.2
Collect, organize and display data in appropriate graphs or charts.
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5.E.a.3
Draw reasonable conclusions based on contextual data.
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Data, charts, and graphs: Read a table (Fifth grade - R.1)
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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.E.a.4
Use data to predict outcomes or trends from graph or table.
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5.E.a.5
Read and interpret information from single bar graphs, line plots, picture graphs and Venn diagrams.
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5.E.a.6
Describe a given set of data of seven items/numbers or fewer using the terms range, mode and median in problems with and without context.
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5.E.b
Probability
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5.E.b.1
Determine if future events are more, less or equally likely, impossible or certain to occur.
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5.E.b.2
Choose or design an event that is fair or unfair.
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5.E.b.3
Predict the outcomes of a simple event using words to describe probability and test predictions using data from a variety of sources.
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5.E.b.4
Describe and determine the number of combinations for choosing 2 out of 4 items Ex: What are the possible combinations when selecting 2 items from a menu of 4 items (chips, cookie, pizza, banana, etc.)?
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5.F
Algebraic Relationships
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5.F.a
Patterns, Relations and Functions
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5.F.a.1
Recognize, extend, describe, create and replicate a variety of patterns including attribute, numeric and geometric patterns.
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5.F.a.2
Represent patterns and relationships with pictures, tables and charts.
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5.F.a.3
Describe a rule that explains a functional relationship or pattern using addition, subtraction or multiplication rules.
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5.F.a.4
Determine a future event in a pattern up to the eighth item when given the first five.
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5.F.b
Expressions, Equations and Inequalities
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5.F.b.1
Solve simple one-step open sentences involving all operations in context.
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5.F.b.2
Demonstrate a basic understanding of equality and inequality using symbols (<, >, =) with all operations.
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5.F.b.3
Solve simple one-step open sentences including missing factor in problems with and without context e.g., "box" or letter variable and whole number coefficients.
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5.F.b.4
Represent problem situations with one-step equations involving multiplication and division with simple open sentences.
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5.F.b.5
Represent problem situations with one-step equations or expressions using one of the four operations.
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5.F.c
Properties
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5.F.c.1
Use the commutative property of multiplication with positive single digits.
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5.F.c.2
Use the inverse relationship of division and multiplication with single digit, whole numbers.
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5.F.c.3
Demonstrate understanding of order of operations by solving two-step open sentences involving all operations.
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