Number & Operations (N)

5.N.1 Divide multidigit numbers and solve realworld and mathematical problems using arithmetic.

5.N.1.1 Divide multidigit numbers and solve realworld and mathematical
problems using arithmetic.

5.N.1.2 Divide multidigit numbers, by one and twodigit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

5.N.1.3 Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution.

5.N.1.4 Solve realworld and mathematical problems requiring addition, subtraction, multiplication, and division of multidigit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

5.N.2 Read, write, represent, and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in realworld and mathematical situations.

5.N.2.1 Represent decimal fractions (e.g., 1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, rational number wheel, baseten blocks, meter stick) and make connections between fractions and decimals.

5.N.2.2 Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions.

5.N.2.3 Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line.

5.N.2.4 Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts. 
5.N.3 Add and subtract fractions with like and unlike denominators, mixed numbers and decimals to solve realworld and mathematical problems.

5.N.3.1 Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.

5.N.3.2 Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g., fraction strips, area models, number lines, fraction rods).

5.N.3.3 Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve realworld and mathematical problems including those involving money, measurement, geometry, and data.

5.N.3.4 Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a
number and 0.001 less than a number.

Algebraic Reasoning & Algebra (A)

5.A.1 Describe and graph patterns of change created through numerical patterns.

5.A.1.1 Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about realworld and mathematical problems.

5.A.1.2 Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.

5.A.2 Understand and interpret expressions, equations, and inequalities involving variables and whole numbers, and use them to represent and evaluate realworld and mathematical problems.

5.A.2.1 Generate equivalent numerical expressions and solve problems involving whole numbers by applying the commutative, associative, and distributive properties and order of operations (no exponents).

5.A.2.2 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. 
5.A.2.3 Evaluate expressions involving variables when values for the variables are given. 
Geometry & Measurement (GM)

5.GM.1 Describe, classify, and draw representations of two and threedimensional figures.

5.GM.1.1 Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts.

5.GM.1.2 Describe and classify threedimensional figures including cubes, rectangular prisms, and pyramids by the number of edges, faces or vertices as well as the shapes of faces.

5.GM.1.3 Recognize and draw a net for a threedimensional figure (e.g., cubes, rectangular prisms, pyramids).

5.GM.2 Understand how the volume of rectangular prisms and surface area of shapes with polygonal faces are determined by the dimensions of the object and that shapes with varying dimensions can have equivalent values of surface area or volume.

5.GM.2.1 Recognize that the volume of rectangular prisms can be determined by the number of cubes (n) and by the product of the dimensions of the prism (a×b×c = n). Know that rectangular prisms of different dimensions (p, q, and r) can have the same volume if a×b×c = p×q×r = n.

5.GM.2.2 Recognize that the surface area of a threedimensional figure with rectangular faces with whole numbered edges can be found by finding the area of each component of the net of that figure. Know that threedimensional shapes of different dimensions can have the same surface area.

5.GM.2.3 Find the perimeter of polygons and create arguments for reasonable values for the perimeter of shapes that include curves.

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