Number, Operation, and Quantitative Reasoning 
8.1 Number, operation, and quantitative reasoning. The student understands that different forms of numbers are
appropriate for different situations. 
8.1.A  compare and order rational numbers in various forms, including integers, percents, and positive and negative
fractions and decimals 
8.1.B  select and use appropriate forms of rational numbers to solve reallife problems, including those involving
proportional relationships 
8.1.C  approximate (mentally) the value of irrational numbers as they arise from problem situations (pie , 2)

8.1.D  express numbers in scientific notation, including negative exponents, in appropriate problem situations

8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to
solve problems and justify solutions. 
8.2.A  select and use appropriate operations to solve problems and justify the selections 
8.2.B  add, subtract, multiply, and divide rational numbers in problem situations 
8.2.C  evaluate a solution for reasonableness 
8.2.D  use multiplication by a constant factor (unit rate) to represent proportional relationships; for example, the
arm span of a gibbon is about 1.4 times its height, a = 1.4h 

Patterns, Relationships, and Algebraic Thinking 
8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in
problem situations and solves problems. 
8.3.A  compare and contrast proportional and nonproportional relationships 
8.3.B  estimate and find solutions to application problems involving percents and proportional relationships, such
as similarity and rates 
8.4 Patterns, relationships, and algebraic thinking. The student makes connections among various
representations of a numerical relationship. The student is expected to generate a different representation given one
representation of data such as a table, graph, equation, or verbal description. 
8.4  generate a different representation given one representation of data, such as a table, graph, equation, or
verbal description 
8.5 Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic
representations to make predictions and solve problems. 
8.5.A  estimate, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic
equations 
8.5.B  use an algebraic expression to find any term in a sequence 

Geometry and Spatial Reasoning 
8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.

8.6.A  generate similar shapes using dilations, including enlargements and reductions 
8.6.B  graph dilations, reflections, and translations on a coordinate plane 
8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.

8.7.A  draw solids from different perspectives 
8.7.B  use geometric concepts and properties to solve problems in fields such as art and architecture 
8.7.C  use pictures or models to demonstrate the Pythagorean Theorem 
8.7.D  locate and name points on a coordinate plane using ordered pairs of rational numbers 

Measurement 
8.8 Measurement. The student uses indirect measurement to solve problems. 
8.8.A  find surface area of prisms and cylinders using concrete models and nets (twodimensional models) 
8.8.C  estimate answers and use formulas to solve application problems involving surface area and volume 
8.9 Measurement. The student uses indirect measurement to solve problems. 
8.9.A  use the Pythagorean Theorem to solve reallife problems 
8.9.B  use proportional relationships in similar shapes to find missing measurements 
8.10 Measurement. The student describes how changes in dimensions affect linear, area, and volume measures.

8.10.A  describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally

8.10.B  describe the resulting effect on volume when dimensions of a solid are changed proportionally 

Probability and Statistics 
8.11 Probability and statistics. The student applies concepts of theoretical and experimental probability to
make predictions. 
8.11.A  find the probabilities of compound events (dependent and independent) 
8.11.B  use theoretical probabilities and experimental results to make predictions and decisions 
8.12 Probability and statistics. The student uses statistical procedures to describe data. 
8.12.A  select the appropriate measure of central tendency to describe a set of data for a particular purpose

8.12.B  draw conclusions and make predictions by analyzing trends in scatterplots 
8.12.C  construct circle graphs, bar graphs, and histograms, [with and] without technology 
8.13 Probability and statistics. The student evaluates predictions and conclusions based on statistical data.

8.13.A  evaluate methods of sampling to determine validity of an inference made from a set of data 
8.13.B  recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on
data analysis 

Underlying Processes and Mathematical Tools 
8.14 Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems
connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. 
8.14.A  identify and apply mathematics to everyday experiences,to activities in and outside of school,with other
disciplines,and with other mathematical topics 
8.14.B  use a problemsolving model that incorporates understanding the problem, making a plan, carrying out the
plan, and evaluating the solution for reasonableness 
8.14.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 
8.15 Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through
informal and mathematical language,representations,and models. 
8.15.A  communicate mathematical ideas using language,efficient tools,appropriate units,and
graphical,numerical,physical,or algebraic mathematical models 
8.16 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and
verify conclusions. 
8.16.A  make conjectures from patterns or sets of examples and nonexamples 
8.16.B  validate his/her conclusions using mathematical properties and relationships 