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5.M1
Numbers and Operations
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5.M.1a
identify verbally and in writing the place value for each digit in decimals through millionths;
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5.M.1b
identify and represent equivalent forms of fractions with denominators of 12 or less, decimals, and percents;
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5.M.1c
explain how decimals and percents are parts of a whole;
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5.M.1d
use models to show the ratio interpretation of a fraction as part-to-part and part-to-whole;
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5.M.1e
represent and compare numbers less than zero by extending the number line and using familiar applications (e.g., temperature), to demonstrate the usefulness of negative numbers;
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5.M.1f
identify and use the distributive property to simplify and/or perform computations;
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5.M.1g
use order of operations, including the use of parentheses, to simplify numerical expressions;
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5.M.1h
explain why fractions need common denominators to be added or subtracted;
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5.M.1i
use models to show an understanding of the concept of multiplication and division of fractions with denominators of 12 or less;
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5.M.1j
understand and compute positive integer powers of nonnegative integers as repeated multiplication;
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5.M.1k
divide whole numbers with two-digit divisors;
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5.M.1l
use models and equivalent forms to add and subtract fractions with like and unlike denominators up to 12, expressing answers in simplest form;
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5.M.1m
use estimation strategies for the results of computations involving whole numbers, fractions with denominators of 12 or less, and decimals through millionths;
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5.M.1n
compute and perform multiplication and division of fractions with denominators of 12 or less and decimals;
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5.M.1o
understand and apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10;
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5.M2
Algebra
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5.M.2a
express a general rule for a pattern by using visual representations, words, tables, graphs, or mathematical symbols;
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5.M.2b
explain the concept of variable (e.g., a letter standing for all numbers of a specific set, such as integers);
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5.M.2c
use variables to represent unknown quantities in general rules when describing mathematical patterns and relationships;
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5.M.2d
apply order of operations and the commutative, associative properties for addition and multiplication and the distributive property to simplify algebraic expressions, equations, and inequalities;
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5.M.2e
construct tables and graphs that accurately represent the relationship between two variables;
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5.M.2f
identify, describe, and compare situations that represent constant or varying rates of change;
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5.M3
Geometry
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5.M.3a
identify, describe and compare the properties of a three-dimensional objects (e.g., cylinder, cone, cube, square pyramid, and rectangular prism) by the number of faces, edges, or vertices;
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5.M.3b
identify and graph ordered pairs in the first quadrant of a coordinate system;
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5.M.3c
create patterns that result from drawing a combination of reflections (flips), rotations, and translations (slides) of geometric figures, including rotational symmetry;
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5.M.3d
visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids;
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5.M4
Measurement
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5.M.4a
identify volume as the space inside a three-dimensional object as a measured in cubic units and use strategies to determine the surface areas and volumes of rectangular solids;
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5.M.4b
convert standard units of measurement within both customary and metric systems of measurement, e.g., inches to feet, centimeters to meters, etc.;
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5.M.4c
develop and use strategies for estimating the volume of various three-dimensional objects;
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5.M.4d
use standard measurement tools and units to measure volume;
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5.M5
Data Analysis and Probability
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5.M.5a
explain sampling techniques for gathering data;
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5.M.5b
select and use a graph that is appropriate for the type of data to be displayed;
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5.M.5c
describe the role of the mean as a balance point for the data set;
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5.M.5d
recognize samples as subsets of larger populations;
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5.M.5e
use a sample to make projections for a larger population;
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5.M.5f
use common fractions to represent the probability of events that are neither certain nor impossible;
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5.M.5g
compare theoretical and experimental outcomes in an experiment when the total number of possible outcomes is 12 or less;
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5.M.5h
make predictions based on experimental and theoretical probabilities.
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