• 6
Top Mathematicians
• Number & Operations
• 6.N.1.1
Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.
• 6.N.1.2
Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.
• 6.N.1.3
Explain that a percent represents parts "out of 100" and ratios "to 100."
• 6.N.1.4
Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.
• 6.N.1.5
Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
• 6.N.1.6
Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.
• 6.N.2.1
Estimate solutions to addition and subtraction of integers problems in order to assess the reasonableness of results.
• 6.N.2.2
Illustrate addition and subtraction of integers using a variety of representations.
• 6.N.2.3
Add and subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms.
• 6.N.3.1
Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different.
• 6.N.3.2
Determine the unit rate for ratios.
• 6.N.3.3
Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.
• 6.N.3.4
Use multiplicative reasoning and representations to solve ratio and unit rate problems.
• 6.N.4.1
Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.
• 6.N.4.2
Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.
• 6.N.4.3
Multiply and divide fractions and decimals using efficient and generalizable procedures.
• 6.N.4.4
Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.
• Geometry & Measurement
• 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.2.1
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.3.1
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.4.1
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.
• Algebraic Reasoning & Algebra
• 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.2.1
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.3.1
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 form x + p = q and px = q, where x, 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.
• Data & Probability
• 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 observing how each segment contains one quarter of the data.
• 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.