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)

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 real-world 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

real-world 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).

Geometry & Measurement (GM)

5.GM.1 Describe, classify, and draw

representations of two- and three- dimensional

figures.

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

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.