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8.1 Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: |
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| 8.1.A |
compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; |
5-1, 6-1
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| 8.1.B |
select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships; |
6-2
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| 8.1.C |
approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (π, √2); and |
7-4, 13-4
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| 8.1.D |
express numbers in scientific notation, including negative exponents, in appropriate problem situations using a calculator. |
6-9
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8.2 Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to: |
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| 8.2.A |
select and use appropriate operations to solve problems and justify the selections; |
1-1, 1-8, 3-8
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| 8.2.B |
add, subtract, multiply, and divide rational numbers in problem situations; |
1-8, 7-1, 7-6
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| 8.2.C |
evaluate a solution for reasonableness; and |
1-1, 3-8, 5-3, 5-7, 6-3, 7-3, 7-4, 8-5, 9-4, 9-6, 11-2, 11-6, 12-4, 12-5, 13-4
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| 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. |
9-9 |
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8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations and solves problems. The student is expected to: |
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| 8.3.A |
compare and contrast proportional and non-proportional relationships; and |
9-4
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| 8.3.B |
estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates. |
9-4, 9-9, 9-10
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| 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. |
1-10, 2-2, 4-3, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8, 8-9, 9-2, 10-1, 10-3, 11-2, 12-4, 13-2
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8.5 Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: |
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| 8.5.A |
estimate, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and |
1-1, 1-8, 2-4, 2-5, 2-7, 3-6, 3-8, 8-5, 8-7, 9-2
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| 8.5.B |
use an algebraic expression to find any term in a sequence. |
5-9, 6-8
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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; and |
MAC3 4-8
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| 8.6.B |
graph dilations, reflections, and translations on a coordinate plane. |
11-9,
MAC3 4-8 |
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8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.The student is expected to: |
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| 8.7.A |
draw solids from different perspectives; |
MAC3 7-4
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| 8.7.B |
use geometric concepts and properties to solve problems in fields such as art and architecture; |
3-5, 12-2
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| 8.7.C |
use pictures or models to demonstrate the Pythagorean Theorem; and |
13-4
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| 8.7.D |
locate and name points on a coordinate plane using ordered pairs of rational numbers. |
1-7, 2-2
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8.8 Measurement. The student uses procedures to determine measures of solids. The student is expected to: |
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| 8.8.A |
find surface area of prisms and cylinders using concrete models and nets (two-dimensional models); |
12-5
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| 8.8.B |
connect models to formulas for volume of prisms, cylinders, pyramids, and cones; and |
12-7, 12-8
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| 8.8.C |
estimate answers and use formulas to solve application problems involving surface area and volume. |
12-5, 12-6
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8.9 Measurement. The student uses indirect measurement to solve problems. The student is expected to: |
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| 8.9A |
use the Pythagorean Theorem to solve real-life problems; and |
13-5
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| 8.9B |
use proportional relationships in similar shapes to find missing measurements. |
11-6
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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; and |
MAC2 ©2004: 6-8
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| 8.10.B |
describe the resulting effect on volume when dimensions of a solid are changed proportionally. |
12-7, 12-8
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8.11 Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: |
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| 8.11.A |
find the probabilities of compound events (dependent and independent); |
10-9
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| 8.11.B |
use theoretical probabilities and experimental results to make predictions and decisions; and |
10-8
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| 8.11.C |
select and use different models to simulate an event |
10-8
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8.12 Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: |
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| 8.12.A |
select the appropriate measure of central tendency to describe a set of data for a particular purpose; |
10-4
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| 8.12.B |
draw conclusions and make predictions by analyzing trends in scatterplots; and |
8-2
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| 8.12.C |
construct circle graphs, bar graphs, and histograms, with and without technology. |
1-10, 10-3, 11-2
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8.13 Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to: |
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| 8.13.A |
evaluate methods of sampling to determine validity of an inference made from a set of data; and |
MAC3 8-7
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| 8.13.B |
recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. |
10-4
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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. The student is expected to: |
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| 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; |
1-1, 3-1, 12-4
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| 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; |
1-1, 3-8,
5-3, 5-7, 6-3, 7-3, 7-4, 8-5, 9-4, 9-6, 11-2, 11-6, 12-4, 12-5, 13-4
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| 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; and |
2-6, 3-1, 4-3,
5-8, 7-1, 8-5, 9-2, 10-5, 10-8, 12-4, 13-2
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| 8.14.D |
select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. |
1-1, 8-4, 12-4
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8.15 Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models |
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| 8.15.A |
communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and |
5-8, 8-5, 12-4
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| 8.15.B |
evaluate the effectiveness of different representations to communicate ideas. |
10-3
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8.16 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. |
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| 8.16.A |
make conjectures from patterns or sets of examples and nonexamples; and |
2-6
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| 8.16.B |
validate his/her conclusions using mathematical properties and relationships. |
5-8 |
• Chapter 1