Number, Operation, and Quantitative Reasoning 
6.1 Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of
equivalent forms. 
6.1.A  compare and order nonnegative rational numbers 
6.1.B  generate equivalent forms of rational numbers, including whole numbers, fractions, and decimals 
6.1.C  use integers to represent reallife situations 
6.1.D  write prime factorizations using exponents 
6.1.E  identify factors and multiples, including common factors and common multiples 
6.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve
problems and 
6.2.A  model addition and subtraction situations involving fractions with objects, pictures, words, and numbers

6.2.B  use addition and subtraction to solve problems involving fractions and decimals 
6.2.C  use multiplication and division of whole numbers to solve problems, including situations involving equivalent
ratios and rates 
6.2.D  estimate and round to approximate reasonable results and to solve problems where exact answers are not
required 

Patterns, Relationships, and Algebraic Thinking 
6.3 Patterns, relationships, and algebraic thinking. The student solves problems involving proportional
relationships. 
6.3.A  use ratios to describe proportional situations 
6.3.B  represent ratios and percents with models, fractions, and decimals 
6.3.C  use ratios to make predictions in proportional situations 
6.4 Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical
expressions to describe how one quantity changes when a related quantity changes. 
6.4.A  use tables and symbols to represent and describe proportional and other relationships involving conversions,
sequences, perimeter, area, etc. 
6.4.B  generate formulas to represent relationships involving perimeter, area, volume of a rectangular prism, etc.,
from a table of data. 
6.5 Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation.
The student is expected to formulate an equation from a problem situation. 
6.5.A  formulate an equation from a problem situation 
6.6 Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and
circles. 
6.6.A  use angle measurements to classify angles as acute, obtuse, or right 
6.6.B  identify relationships involving angles in triangles and quadrilaterals 
6.6.C  describe the relationship between radius, diameter, and circumference of a circle 

Geometry and Spatial Reasoning 
6.7 Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The
student is expected to locate and name points on a coordinate plane using ordered pairs of nonnegative rational numbers.

6.7.A  locate and name points on a coordinate plane using ordered pairs of nonnegative rational numbers 
6.8 Measurement. The student solves application problems involving estimation and measurement of length, area, time,
temperature, capacity, weight, and angles. 
6.8.A  estimate measurements and evaluate reasonableness of results 
6.8.B  select and use appropriate units, tools, or formulas to measure and to solve problems involving length
(including perimeter and circumference), area, time, temperature, capacity, and weight 
6.8.C  measure angles 
6.8.D  convert measures within the same measurement system (customary and metric) based on relationships between
units 

Probability and Statistics 
6.9 Probability and statistics. The student uses experimental and theoretical probability to make predictions.

6.9.A  construct sample spaces using lists, tree diagrams, and combinations 
6.9.B  find the probabilities of a simple event and its complement and describe the relationship between the
two 
6.10 Probability and statistics. The student uses statistical representations to analyze data.

6.10.A  draw and compare different graphical representations of the same data 
6.10.B  use median, mode, and range to describe data 
6.10.C  sketch circle graphs to display data 
6.10.D  solve problems by collecting, organizing, displaying, and interpreting data 

Underlying Processes and Mathematical Tools 
6.11 Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected
to everyday experiences, investigations in other disciplines, and activities in and outside of school. 
6.11.A  identify and apply mathematics to everyday experiences, to activities in and outside of school, with other
disciplines, and with other mathematical topics 
6.11.B  use a problemsolving model that incorporates understanding the problem, making a plan, carrying out the
plan, and evaluating the solution for reasonableness 
6.11.C  select or develop an appropriate problemsolving strategy from a variety of different types, including
drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler
problem, or working backwards to solve a problem. 
6.12 Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal
and mathematical language, representations, and models. 
6.12.A  communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical,
physical, or algebraic mathematical models. 
6.13 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify
conclusions. 
6.13.A  make conjectures from patterns or sets of examples and nonexamples 
6.13.B  validate his/her conclusions using mathematical properties and relationships 