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5.M1
Numbers and Operations
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5.M1a
Understand place value and explain the relationship to addition and subtraction and multiplication and division of decimals;
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5.M1b
Identify and generate equivalent forms of fractions, decimals, and percents;
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5.M1c
Explain how decimals and percents are parts of a whole;
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5.M1d
Use models to develop the concept of ratio as part to part and part to whole;
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5.M1e
Represent and compare numbers less than zero by extending the number line and using familiar applications, like temperature, to demonstrate the usefulness of negative numbers;
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5.M1f
Identify and use the distributive properties to simplify and/or perform computations;
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5.M1g
Use order of operations, including the use of parentheses, to simplify numerical expressions;
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5.M1h
Explain why fractions need common denominators to be added or subtracted;
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5.M1i
Understand the concept of multiplication and division of fractions;
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5.M1j
Understand and compute positive integer powers of nonnegative integers as repeated multiplication;
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5.M1k
Demonstrate proficiency with two-digit divisors;
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5.M1l
Use models and equivalent forms to add and subtract fractions with like and unlike denominators expressing answers in simplest form;
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5.M1m
Estimate the results of computations involving whole numbers, fractions, and decimals, using a variety of strategies;
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5.M1n
Compute and perform simple multiplication and division of fractions and decimals.
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5.M2
Algebra
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5.M2a
Express a general rule for a pattern or a function by using visual representations, words, tables, or graphs;
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5.M2b
Explain the concept of variable;
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5.M2c
Use variables as unknown quantities in general rules when describing mathematical patterns and relationships;
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5.M2d
Apply algebraic order of operations and the commutative, associative and distributive properties to algebraic expressions, equations, and inequalities;
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5.M2e
Construct tables and graphs that accurately represent the relationship between two variables;
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5.M2f
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.M3a
Identify faces, edges, vertices and bases of three-dimensional shapes;
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5.M3b
Identify and plot ordered pairs in the first quadrant of a coordinate system;
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5.M3c
Explore patterns that result from a combination of reflections, rotations, and translations of geometric figures, including rotational symmetry;
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5.M3d
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.M4a
Extend the recognition of measurable attributes to include volume (cubic units);
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5.M4b
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.M4c
Develop strategies for estimating the volume of various shapes;
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5.M4d
Extend the use of appropriate standard tools and units to include measures of volume and angle size;
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5.M4e
Develop strategies to determine the surface areas and volumes of rectangular solids;
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5.M4f
Differentiate between units of measurement for two- and threedimensional objects and use appropriately.
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5.M5
Data Analysis and Probability
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5.M5a
Explain and conduct sampling techniques for gathering data;
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5.M5b
Select and use a graph that is appropriate for the type of data to be displayed;
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5.M5c
Read and interpret quantitative and qualitative data;
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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: 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.M5d
Investigate the role of the mean as a balance point for the data set;
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5.M5e
Recognize samples as subsets of larger populations;
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5.M5f
Use a sample to make projections for a larger population;
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5.M5g
Use common fractions to represent the probability of events that are neither certain nor impossible;
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5.M5h
Compare theoretical and experimental outcomes in a simple experiment;
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5.M5i
Make predictions based on experimental and theoretical probabilities.
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