Number & Operations (N)

5.N.1 Divide multi-digit numbers and

solve real-world and mathematical

problems using arithmetic.

5.N.1 Divide multi-digit numbers and solve real-world and mathematical

problems using arithmetic. 

5.N.1.2 Divide multi-digit numbers, by one- and two-digit 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 real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit 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 real-world

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, base-ten 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.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 real-world 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)

6.A.1 Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems. 

6.A.1.1 Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.  

6.A.1.2 Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations. 

6.A.1.3 Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false. 

6.A.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers. 

6.A.2.1 Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems. 

6.A.3 Use equations and inequalities to represent real-world and mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context. 

6.A.3.1 Represent real-world or mathematical situations using expressions, equations, and inequalities involving variables and rational numbers. 

6.A.3.2 Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the formx+p=q and px=q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. 

Geometry & Measurement (GM)

6.GM.1 Calculate area of squares, parallelograms, and triangles to solve real-world and mathematical problems. 

6.GM.1.1 Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.

6.GM.1.2 Develop and use formulas to determine the area of triangles.

6.GM.1.3 Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.

6.GM.2 Understand and use relationships between angles in geometric figures. 

6.GM.2.1 Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines. 

6.GM.2.2 Develop and use the fact that the sum of the interior angles of a triangle is 180 ̊ to determine missing angle measures in a triangle. 

6.GM.3 Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems. 

6.GM.3.1 Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.

6.GM.3.2 Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.

6.GM.4 Use translations, reflections, and rotations to establish congruency and understand symmetries. 

6.GM.4.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure. 

6.GM.4.2 Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent. 

6.GM.4.3 Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. 

6.GM.4.4 Identify and describe the line(s) of symmetry in two-dimensional shapes. 

Data & Probability (D)

6.D.1 Display and analyze data. 

6.D.1.1 Calculate the mean, median, and mode for a set of real-world data.

6.D.1.2 Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.

6.D.1.3 Create and analyze box and whisker plots exploring how each segment contains one quarter of the data.

6.D.2 Use probability to solve real-world and mathematical problems; represent probabilities using fractions and decimals.

6.D.2.1 Represent possible outcomes using a probability continuum from impossible to certain.

6.D.2.2 Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

6.D.2.3 Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.