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 real-life problems, including those involving
proportional relationships |
8.1.C - approximate (mentally) the value of irrational numbers as they arise from problem situations (pie , 2)
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8.1.D - express numbers in scientific notation, including negative exponents, in appropriate problem situations
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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 |
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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 non-proportional 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 |
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Geometry and Spatial Reasoning |
8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.
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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.
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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 |
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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 (two-dimensional 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 real-life 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.
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8.10.A - describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally
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8.10.B - describe the resulting effect on volume when dimensions of a solid are changed proportionally |
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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
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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.
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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 |
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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 problem-solving 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 problem-solving 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 |