(a) Introduction.

(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 8 are using

basic principles of algebra to analyze and represent both proportional and non-proportional

linear relationships and using probability to describe data and make predictions.

(2) Throughout mathematics in Grades 6-8, students build a foundation of basic understandings in

number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking;

geometry and spatial reasoning; measurement; and probability and statistics. Students use

concepts, algorithms, and properties of rational numbers to explore mathematical relationships

and to describe increasingly complex situations. Students use algebraic thinking to describe

how a change in one quantity in a relationship results in a change in the other; and they connect

verbal, numeric, graphic, and symbolic representations of relationships. Students use geometric

properties and relationships, as well as spatial reasoning, to model and analyze situations and

solve problems. Students communicate information about geometric figures or situations by

quantifying attributes, generalize procedures from measurement experiences, and use the

procedures to solve problems. Students use appropriate statistics, representations of data,

reasoning, and concepts of probability to draw conclusions, evaluate arguments, and make

recommendations.

The provisions of this subchapter were adopted by the State Board of Education in February 2005 to be implemented beginning

with the 2006-2007 school year.

10

(3) Problem solving in meaningful contexts, language and communication, connections within and

outside mathematics, and formal and informal reasoning underlie all content areas in

mathematics. Throughout mathematics in Grades 6-8, students use these processes together with

graphing technology and other mathematical tools such as manipulative materials to develop

conceptual understanding and solve problems as they do mathematics.

(b) Knowledge and skills.

(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:

(A) compare and order rational numbers

in various forms including integers,

percents, and positive and negative

fractions and decimals;

(B) select and use appropriate forms of

rational numbers to solve real-life

problems including those involving

proportional relationships;

(C) approximate (mentally and with

calculators) the value of irrational

numbers as they arise from problem

situations (such as π, √2); and

(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.

The student is expected to:

(A) select appropriate operations to solve

problems involving rational numbers

and justify the selections;

(B) use appropriate operations to solve

problems involving rational numbers

in problem situations;

(C) evaluate a solution for

reasonableness; and

(D) use multiplication by a constant

factor (unit rate) to represent

proportional relationships.

(8.3) Patterns, relationships, and

algebraic thinking. The student

identifies proportional or nonproportional

linear relationships in

problem situations and solves

problems.

The student is expected to:

(A) compare and contrast proportional

and non-proportional linear

relationships; and

(B) estimate and find solutions to

application problems involving

percents and other 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 of data given

another 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.

The student is expected to:

(A) predict, find, and justify solutions to

application problems using

appropriate tables, graphs, and

algebraic equations; and

(B) find and evaluate an algebraic

expression to determine any term in

an arithmetic sequence (with a

constant rate of change).

(8.6) Geometry and spatial reasoning.

The student uses transformational

geometry to develop spatial sense.

The student is expected to:

(A) generate similar figures using

dilations including enlargements and

reductions; and

(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.

The student is expected to:

(A) draw three-dimensional figures from

different perspectives;

(B) use geometric concepts and

properties to solve problems in fields

such as art and architecture;

(C) use pictures or models to demonstrate

the Pythagorean Theorem; and

(D) locate and name points on a

coordinate plane using ordered pairs

of rational numbers.

(8.8) Measurement. The student uses

procedures to determine measures of

three-dimensional figures.

The student is expected to:

(A) find lateral and total surface area of

prisms, pyramids, and cylinders using

concrete models and nets (twodimensional

models);

(B) connect models of prisms, cylinders,

pyramids, spheres, and cones to

formulas for volume of these objects;

and

(C) estimate measurements and use

formulas to solve application

problems involving lateral and total

surface area and volume.

(8.9) Measurement. The student uses

indirect measurement to solve

problems.

The student is expected to:

(A) use the Pythagorean Theorem to

solve real-life problems; and

(B) use proportional relationships in

similar two-dimensional figures or

similar three-dimensional figures to

find missing measurements.

(8.10) Measurement. The student describes

how changes in dimensions affect

linear, area, and volume measures.

The student is expected to:

(A) describe the resulting effects on

perimeter and area when dimensions

of a shape are changed

proportionally; and

(B) describe the resulting effect on

volume when dimensions of a solid

are changed proportionally.

(8.11) Probability and statistics. The

student applies concepts of

theoretical and experimental

probability to make predictions.

The student is expected to:

(A) find the probabilities of dependent

and independent events;

(B) use theoretical probabilities and

experimental results to make

predictions and decisions; and

(C) select and use different models to

simulate an event.

(8.12) Probability and statistics. The

student uses statistical procedures to

describe data.

The student is expected to:

(A) select the appropriate measure of

central tendency or range to describe

a set of data and justify the choice for

a particular situation;

(B) draw conclusions and make

predictions by analyzing trends in

scatterplots; and

(C) select and use an appropriate

representation for presenting and

displaying relationships among

collected data, including line plots,

line graphs, stem and leaf plots, circle

graphs, bar graphs, box and whisker

plots, histograms, and Venn

diagrams, with and without the use of

technology.

(8.13) Probability and statistics. The

student evaluates predictions and

conclusions based on statistical data.

The student is expected to:

(A) evaluate methods of sampling to

determine validity of an inference

made from a set of data; and

(B) recognize misuses of graphical or

numerical information and evaluate

predictions and conclusions based on

data analysis.

(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:

(A) identify and apply mathematics to

everyday experiences, to activities in

and outside of school, with other

disciplines, and with other

mathematical topics;

(B) use a problem-solving model that

incorporates understanding the

problem, making a plan, carrying out

the plan, and evaluating the solution

for reasonableness;

(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

(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.

(8.15) Underlying processes and

mathematical tools. The student

communicates about Grade 8

mathematics through informal and

mathematical language,

representations, and models.

The student is expected to:

(A) communicate mathematical ideas

using language, efficient tools,

appropriate units, and graphical,

numerical, physical, or algebraic

mathematical models; and

(B) evaluate the effectiveness of different

representations to communicate ideas.

(8.16) Underlying processes and

mathematical tools. The student

uses logical reasoning to make

conjectures and verify conclusions.

The student is expected to:

(A) make conjectures from patterns or

sets of examples and nonexamples;

and

(B) validate his/her conclusions using

mathematical properties and

relationships.

## Wednesday, March 12, 2008

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