The provisions of this written curriculum shall be implemented beginning September 1, 1997.
(a) Introduction.
(1) Within a well-balanced mathematics curriculum, the
primary focal points at Grade 6 are using ratios
to describe proportional relationships involving
number, geometry, measurement, and probability and
adding and subtracting decimals and fractions.
(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
objects 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.
(3) Problem solving, 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 technology (at least four-function
calculators for whole numbers, decimals, and
fractions) and other mathematical tools such as
manipulative materials to develop conceptual
understanding and solve problems as they do
mathematics.
(b) Knowledge and skills.
(6.1)Number, operation, and quantitative reasoning. The
student represents and uses rational numbers in a
variety of equivalent forms. The student is
expected to:
(A) compare and order non-negative rational
numbers;
(B) generate equivalent forms of rational numbers
including whole numbers, fractions, and
decimals;
(C) use integers to represent real-life
situations;
(D) write prime factorizations using exponents;
and
(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 justify solutions. The student
is expected to:
(A) model addition and subtraction situations
involving fractions with objects, pictures,
words, and numbers;
(B) use addition and subtraction to solve problems
involving fractions and decimals;
(C) use multiplication and division of whole
numbers to solve problems including situations
involving equivalent ratios and rates; and
(D) estimate and round to approximate reasonable
results and to solve problems where exact
answers are not required.
(6.3)Patterns, relationships, and algebraic thinking.
The student solves problems involving proportional
relationships. The student is expected to:
(A) use ratios to describe proportional
situations;
(B) represent ratios and percents with concrete
models, fractions, and decimals; and
(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.
The student is expected to:
(A) use tables and symbols to represent and
describe proportional and other relationships
involving conversions, sequences, perimeter,
area, etc.; and
(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.
(6.6)Geometry and spatial reasoning. The student uses
geometric vocabulary to describe angles, polygons,
and circles. The student is expected to:
(A) use angle measurements to classify angles as
acute, obtuse, or right;
(B) identify relationships involving angles in
triangles and quadrilaterals; and
(C) describe the relationship between radius,
diameter, and circumference of a circle.
(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 non-
negative rational numbers.
(6.8)Measurement. The student solves application
problems involving estimation and measurement of
length, area, time, temperature, capacity, weight,
and angles. The student is expected to:
(A) estimate measurements and evaluate
reasonableness of results;
(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;
(C) measure angles; and
(D) convert measures within the same measurement
system (customary and metric) based on
relationships between units.
(6.9)Probability and statistics. The student uses
experimental and theoretical probability to make
predictions. The student is expected to:
(A) construct sample spaces using lists, tree
diagrams, and combinations; and
(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. The
student is expected to:
(A) draw and compare different graphical
representations of the same data;
(B) use median, mode, and range to describe data;
(C) sketch circle graphs to display data; and
(D) solve problems by collecting, organizing,
displaying, and interpreting data.
(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. 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.
(6.12) Underlying processes and mathematical tools.
The student communicates about Grade 6 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.
(6.13) 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.
(a) Introduction.
(1) Within a well-balanced mathematics curriculum, the
primary focal points at Grade 7 are using
proportional relationships in number, geometry,
measurement, and probability; applying addition,
subtraction, multiplication, and division of
decimals, fractions, and integers; and using
statistical measures to describe data.
(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
objects 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.
(3) Problem solving, 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 technology (at least four-function
calculators for whole numbers, decimals, and
fractions) and other mathematical tools such as
manipulative materials to develop conceptual
understanding and solve problems as they do
mathematics.
(b) Knowledge and skills.
(7.1)Number, operation, and quantitative reasoning. The
student represents and uses numbers in a variety of
equivalent forms. The student is expected to:
(A) compare and order integers and positive
rational numbers;
(B) convert between fractions, decimals, whole
numbers, and percents mentally, on paper, or
with a calculator; and
(C) represent squares and square roots using
geometric models.
(7.2)Number, operation, and quantitative reasoning. The
student adds, subtracts, multiplies, or divides to
solve problems and justify solutions. The student
is expected to:
(A) represent multiplication and division
situations involving fractions and decimals
with concrete models, pictures, words, and
numbers;
(B) use addition, subtraction, multiplication, and
division to solve problems involving fractions
and decimals;
(C) use models to add, subtract, multiply, and
divide integers and connect the actions to
algorithms;
(D) use division to find unit rates and ratios in
proportional relationships such as speed,
density, price, recipes, and student-teacher
ratio;
(E) simplify numerical expressions involving order
of operations and exponents;
(F) select and use appropriate operations to solve
problems and justify the selections; and
(G) determine the reasonableness of a solution to
a problem.
(7.3)Patterns, relationships, and algebraic thinking.
The student solves problems involving proportional
relationships. The student is expected to:
(A) estimate and find solutions to application
problems involving percent; and
(B) estimate and find solutions to application
problems involving proportional relationships
such as similarity, scaling, unit costs, and
related measurement units.
(7.4)Patterns, relationships, and algebraic thinking.
The student represents a relationship in numerical,
geometric, verbal, and symbolic form. The student
is expected to:
(A) generate formulas involving conversions,
perimeter, area, circumference, volume, and
scaling;
(B) graph data to demonstrate relationships in
familiar concepts such as conversions,
perimeter, area, circumference, volume, and
scaling; and
(C) describe the relationship between the terms in
a sequence and their positions in the
sequence.
(7.5)Patterns, relationships, and algebraic thinking.
The student uses equations to solve problems. The
student is expected to:
(A) use concrete models to solve equations and use
symbols to record the actions; and
(B) formulate a possible problem situation when
given a simple equation.
(7.6)Geometry and spatial reasoning. The student
compares and classifies shapes and solids using
geometric vocabulary and properties. The student is
expected to:
(A) use angle measurements to classify pairs of
angles as complementary or supplementary;
(B) use properties to classify shapes including
triangles, quadrilaterals, pentagons, and
circles;
(C) use properties to classify solids, including
pyramids, cones, prisms, and cylinders; and
(D) use critical attributes to define similarity.
(7.7)Geometry and spatial reasoning. The student uses
coordinate geometry to describe location on a
plane. The student is expected to:
(A) locate and name points on a coordinate plane
using ordered pairs of integers; and
(B) graph translations on a coordinate plane.
(7.8)Geometry and spatial reasoning. The student uses
geometry to model and describe the physical world.
The student is expected to:
(A) sketch a solid when given the top, side, and
front views;
(B) make a net (two-dimensional model) of the
surface area of a solid; and
(C) use geometric concepts and properties to solve
problems in fields such as art and
architecture.
(7.9) Measurement. The student solves application
problems involving estimation and measurement.
The student is expected to estimate measurements and
solve application problems involving length
(including perimeter and circumference), area, and
volume.
(7.10) Probability and statistics. The student
recognizes that a physical or mathematical model
can be used to describe the probability of real-
life events. The student is expected to:
(A) construct sample spaces for compound events
(dependent and independent); and
(B) find the approximate probability of a compound
event through experimentation.
(7.11) Probability and statistics. The student
understands that the way a set of data is displayed
influences its interpretation. The student is
expected to:
(A) select and use an appropriate representation
for presenting collected data and justify the
selection; and
(B) make inferences and convincing arguments based
on an analysis of given or collected data.
(7.12) Probability and statistics. The student uses
measures of central tendency and range to describe
a set of data. The student is expected to:
(A) describe a set of data using mean, median,
mode, and range; and
(B) choose among mean, median, mode, or range to
describe a set of data and justify the choice
for a particular situation.
(7.13) Underlying processes and mathematical tools.
The student applies Grade 7 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.
(7.14) Underlying processes and mathematical tools.
The student communicates about Grade 7 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.
(7.15) 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.
(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
proportional and non-proportional 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
objects 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.
(3) Problem solving, 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 technology (at least four-function
calculators for whole numbers, decimals, and
fractions) 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 (p, Ö2); and
(D) express numbers in scientific notation,
including negative exponents, in appropriate
problem situations using a calculator.
(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 and use appropriate operations to solve
problems and justify the selections;
(B) add, subtract, multiply, and divide 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;
for example, the arm span of a gibbon is about
1.4 times its height, a = 1.4h.
(8.3)Patterns, relationships, and algebraic thinking.
The student identifies proportional relationships
in problem situations and solves problems. The
student is expected to:
(A) compare and contrast proportional and non-
proportional relationships; and
(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.
(8.5)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) estimate, find, and justify solutions to
application problems using appropriate tables,
graphs, and algebraic equations; and
(B) use an algebraic expression to find any term
in a sequence.
(8.6)Geometry and spatial reasoning. The student uses
transformational geometry to develop spatial sense.
The student is expected to:
(A) generate similar shapes 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 solids 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 solids. The student is
expected to:
(A) find surface area of prisms and cylinders
using concrete models and nets (two-
dimensional models);
(B) connect models to formulas for volume of
prisms, cylinders, pyramids, and cones; and
(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. The student is expected to:
(A) use the Pythagorean Theorem to solve real-life
problems; and
(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. 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 compound events
(dependent and independent);
(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 to describe a set of data for a
particular purpose;
(B) draw conclusions and make predictions by
analyzing trends in scatterplots; and
(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. 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.