Anchorage School District
Math Program
PROGRAM
STATEMENT
Mathematical literacy is essential for every individual in
today's technological society. A working knowledge of mathematics
is needed to deal with the qualitative, quantitative, and spatial
relationships that are encountered in everyday life. Therefore,
the overall goal of the Mathematics Program for the Anchorage
School District is to provide the opportunity for all students to
learn, use, communicate, apply, appreciate, and enjoy the
mathematics appropriate for their age, needs and ambitions.
GENERAL PROGRAM
GOALS
Students will be able to:
SEVENTH GRADE MATH PERFORMANCE STANDARDS
Each ASD mathematics course reflects the program statement and
incorporates the general program goals. In addition, each course
consists of a specific set of standards that determine the course
content and a set of performance standards that delineate what a
student should be able to do after successfully completing the
course. After satisfactorily completing the ASD Seventh Grade
mathematics curriculum, a student will be proficient in the
fourteen strands of mathematics which comprise the mathematics
curriculum. As evidence of proficiency, the student will be able
to:
7:1 Estimation:
.1 Decide when an estimate is appropriate and when an
exact answer is needed.
.2 Estimate real and scale distances on maps and globes.
.3 Estimate solutions to problems involving fractions,
decimals and percents.
.4 Estimate the total expenses of a real life experience
(e.g, a shopping trip).
.5 Use estimation to check the reasonableness of
calculator or computer results.
.6 Estimate solutions to problems to check reasonableness
of results.
.7 Apply, explain, and assess the appropriateness of a
variety of estimation strategies.
7:2 Number Sense:
.1 Use exponents to write the prime factorization of a
number.
.2 Convert between fractions, decimals, and percents, and
select the most appropriate form.
.3 Convert between standard notation and scientific
notation, and select the more appropriate form.
.4 Use rules of divisibility to determine if one number is
a factor or a multiple of another.
.5 Use prime factors to find GCF's and LCM's.
.6 Compare and order whole numbers, fractions, decimals
and integers using >, <, or =.
.7 Use models or diagrams to explain place value relations
of decimals.
.8 Explain the representations of scientific notation,
exponents, and percents.
7:3 Concepts of Number Operations:
.1 Use the commutative, associative, and distributive
properties.
.2 Use inverse operations to solve problems.
.3 Use the properties of zero and 1.
.4 Use manipulatives, diagrams, symbols, and words to
model addition, subtraction, multiplication and division of
rational numbers.
.5 Use manipulatives, diagrams, symbols and words to
describe addition and subtraction of integers.
.6 Write and solve word problems involving multiple
operations.
7:4 Computation:
.1 Select and use an appropriate method for computing
addition, subtraction, multiplication and division of rational
numbers (e.g., mental math, paper and pencil, calculator,
computer).
.2 Add, subtract, multiply, and divide fractions, and
decimals with and without a calculator or computer.
.3 Convert numbers from exponential form to standard
notation.
.4 Convert numbers between standard form and scientific
notation using positive exponents.
.5 Use proportions to solve practical problems including
scale drawings that contain whole numbers, fractions, decimals,
and percents.
.6 Write and solve practical problems that use fractions
or mixed numbers.
.7 Convert fractions to equivalent mixed numbers and
decimals.
.8 Apply the rules for order of operations to rational
numbers.
.9 Use mental math to solve problems involving basic
operations, powers of 10, and simple percents.
7:5 Geometry:
.1 Identify, classify, and compare polygons and polyhedra.
.2 Identify and use the vocabulary related to regular and
irregular polygons, circles, polyhedra, and their components.
.3 Name and classify angles formed by parallel,
perpendicular and intersecting lines
.4 Classify, construct and identify properties of angles.
.5 Describe the relationship of angles in different types
of triangles.
.6 Find the sum of the angles in any polygon.
.7 Calculate the measure of an angle in a regular polygon.
.8 Use manipulatives to construct geometric figures in two
and three dimensions.
.9 Identify and describe congruent and similar figures.
.10 Graph a figure and its image formed by a translation,
reflection, or rotation, on a coordinate plane.
.11 Identify and construct translations, rotations,
reflections and dilations of plane figures.
.12 Use characteristics of polygons to explain
tessellations.
.13 Use manipulatives to create a figure that tessellates
and explain why it tessellates.
7:6 Measurement:
.1 Measure length, weight/mass, area, and volume using the
appropriate tool in metric and in standard units.
.2 Use, compare, and convert between units in the metric
system for length, area, and volume.
.3 Use, compare, and convert between units in the standard
system for length, time, weight, area and volume.
.4 Explain the range of error that can be expected when
measuring.
.5 Find perimeter, circumference, and area of circles and
polygons, and verify the solution using a different method.
.6 Use ratios to solve problems about perimeters and areas
of similar figures.
.7 Write and solve rate problems and use appropriate units
for the solutions.
7:7 Statistics:
.1 Compute the mean, median, mode, and range for a given
set of data and justify one as the best representation of the
data.
.2 Explain which measure of central tendency best
represents a given data set.
.3 Sample and record data systematically.
.4 Present data as a scatter plot, stem & leaf, circle
graph, line plot, and bar graph; make an argument for which graph
best represents the data.
.5 Use technology and a spread sheet or data table to
create a graph.
.6 Interpret a broken axis bar graph and use it to show
how data can be misrepresented.
.7 Identify and communicate trends based on statistics
from data.
.8 Analyze data for validity and misrepresentation.
7:8 Probability:
.1 Express the probability of a single event as a
fraction, decimal, or percent.
.2 Predict the outcome of an independent event, design an
experiment to test the probability, compute the actual outcome
and compare the results to the prediction.
.3 Explain why experimental (actual) results may be
different from theoretical (expected) probabilities in 50 coin
flips.
.4 Explain how to determine probability if the odds are
known.
.5 Predict the probability of a future event, using a
table of evidence from the past, and defend your conclusion.
7:9 Patterns:
.1 Identify, describe, and extend arithmetic, geometric,
or other patterns.
.2 Use an arithmetic or geometric rational number pattern
to find an unknown value.
.3 Use symbols to describe number patterns.
.4 Determine the nth term in a sequential pattern.
.5 Explain the patterns found in tables, graphs, rules and
formulas.
.6 Use a pattern from a table or graph to predict an
outcome.
.7 Explain how to use patterns as a strategy for problem
solving.
7:10 Algebra:
.1 Translate word problems into symbolic expressions,
equations, or inequalities.
.2 Substitute values for a variable and evaluate the
expression, equation, or inequality.
.3 Combine like terms to simplify expressions.
.4 Graph inequalities on a number line.
.5 Describe linear data with tables, graphs, and lines of
best fit.
.6 Substitute values into a linear equation to make a
table of ordered pairs; graph the points on a coordinate plane.
.7 Use order of operations including grouping symbols and
exponents to solve problems.
.8 Solve one step equations using inverse operations and
check the solutions.
.9 Use ratios and proportions to solve problems.
.10 Use equations to solve problems.
.11 Write and solve real life problems that require the
use of a variable.
7:11 Problem solving:
.1 Select, modify, and apply a variety of problem-solving
strategies.
7:12 Communication:
.1 Explain the methods and results of various mathematical
efforts, orally and in writing.
7:13 Reasoning:
.1 Justify solutions or use counter examples to disprove
statements.
7:14 Connections:
.1 Apply mathematical skills and processes to other
disciplines.
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EIGHTH GRADE MATH PERFORMANCE STANDARDS
Each ASD mathematics course reflects the program statement and
incorporates the general program goals. In addition, each course
consists of a specific set of standards that determine the course
content and a set of performance standards that delineate what a
student should be able to do after successfully completing the
course. After satisfactorily completing the ASD Eighth Grade
mathematics curriculum, a student will be proficient in the
fourteen strands of mathematics which comprise the mathematics
curriculum. As evidence of proficiency, the student will be able
to:
8:1 Estimation:
.1 Estimate solutions to problems to check reasonableness
of results.
.2 Estimate probability of an event from random samples or
experimental data.
.3 Use estimation to compare metric and standard units.
.4 Explain when an estimate is appropriate and when an
exact answer is needed.
.5 Use estimation to check calculator or computer
accuracy.
.6 Estimate the square root of a number by finding the two
square numbers between which it lies.
8:2 Number Sense:
.1 Solve problems using ratio, proportion, and percent.
.2 Describe and model the relationship between equivalent
fractions, decimals, percents, or ratios when solving problems.
.3 Use manipulatives, diagrams, or symbols to explain how
to solve different types of percent problems.
.4 Use mental math to calculate discounts, taxes,
interest, commissions and gratuities.
.5 Compare and order real numbers using >, <, and =.
.6 Write and solve problems that use primes, factors, and
multiples .
.7 Explain the relationship between the subsets of the
real number system.
.8 Model counting in a different base system.
.9. Explain order of operations.
8:3 Concepts of Number Operations:
.1 Use manipulatives or diagrams to explain how to
approximate a square root.
.2 Write and solve problems involving multiple operations.
.3 Use manipulatives, diagrams, symbols, and words to
describe addition, subtraction, multiplication and division of
integers.
.4 Use manipulatives or a diagram to explain absolute
value.
.5 Use the commutative, associative, and distributive
properties to solve problems with variables and rational numbers.
.6 Use inverse operations and the properties of zero and 1
to solve problems with variables and rational numbers.
.7 Use and explain prime factorization.
8:4. Computation:
.1 Use paper and pencil, mental math, or a calculator to
efficiently and accurately solve problems with real numbers.
.2 Apply order of operations to real numbers.
.3 Use percent to create circle graphs.
.4 Add, subtract, multiply and divide fractions, decimals
and integers with and without a calculator.
.5 Solve problems using percent of increase or decrease.
.6 Write and solve practical problems that use real
numbers.
.7 Convert numbers between standard form and scientific
notation using both positive and negative exponents.
8:5 Geometry:
.1 Identify, classify, and compare polygons and polyhedra.
.2 Identify and use the vocabulary related to regular and
irregular polygons, circles, polyhedra, and their components.
.3 Use the relationships of angles formed by parallel,
perpendicular and intersecting lines to solve problems.
.4 Describe the relationship of angles in different types
of polygons.
.5 Construct or draw geometric figures in three
dimensions.
.6 Identify corresponding parts in similar and congruent
geometric figures using a scale factor.
.7 Use similarity and congruence to find missing angles or
sides of figures.
.8 Graph translations, rotations, reflections and
dilations of plane figures and describe the transformation in
words and symbols.
.9 Describe the use of translations, reflections and
rotations in a tessellation (e.g., Escher drawing).
.10 Draw a polygon that will not tessellate and explain
why.
.11 Model and apply the Pythagorean Theorem.
8:6 Measurement:
.1 Use, compare, and convert between units in the metric
system for length, mass, area, and volume.
.2 Use, compare, and convert between units in the standard
system for length, time, weight, area and volume.
.3 Use multiple strategies, including formulas, to find
rates and to find volume and surface area; use correct units.
.4 Explain what precision can be expected when measuring.
.5 Use indirect measurement to solve problems.
.6 Explain what happens to ratios when changes are made to
one or more dimensions of a figure.
.7 Use manipulatives or diagrams to explain the
Pythagorean Theorem.
.8 Solve practical problems involving proportions, the
Pythagorean Theorem, and ¹
8:7 Statistics:
.1 Present data as a scatter plot, stem & leaf, circle
graph, line graph, histogram, box & whiskers, and bar graph;
make an argument for which graph best represents the data.
.2 Find a line of best fit or trend line for a given set
of data and use it to predict future outcomes.
.3 Analyze data using patterns or trends and make
decisions or defend a conclusion.
.4 Explain or demonstrate how statistics are used to
influence decisions.
.5 Conduct an experiment or simulation that leads to a
generalization or formula.
.6 Identify rules and formulas, based on multiple
experiments and observed outcomes.
8:8 Probability:
.1 Express the theoretical and experimental probabilities
of dependent, independent and multiple (compound) events as a
ratio or percent.
.2 Predict the probability of a dependent event occurring,
design an experiment to test the probability, compute the
outcome, and compare it to the original prediction.
.3 Use a variety of strategies to determine the number of
possible outcomes.
8:9 Patterns:
.1 Identify and explain a classic pattern (e.g. Pascal's
Triangle, Fibonacci Numbers, Pythagorean Triples, etc.).
.2 Translate an arithmetic or geometric pattern into a
rule.
.3 Find a rule from a sequential pattern and translate it
into symbolic form to determine the nth term.
.4 Use patterns from tables or graphs to predict an
outcome.
.5 Use patterns as a strategy for solving problems.
.6 Find a missing item in an arithmetic and geometric
sequence, with and without a calculator, and predict the graph of
each function.
.7 Use tables of ordered pairs, graphs on coordinate
planes, and linear equations as tools to represent and analyze
patterns.
8:10 Algebra:
.1 Translate word problems into numerical expression,
inequalities, or equations.
.2 Write word problems from symbolic statements.
.3 Solve and graph two-step equations and inequalities.
.4 Graph the equation of a line that is in slope/intercept
form.
.5 Identify slopes as positive, negative, zero, or
undefined.
.6 Combine like terms to simplify expressions.
.7 Use order of operations including grouping symbols and
exponents to solve problems.
.8 Use the commutative, associative, and distributive and
properties of 0 and 1 to solve two-step equations and check the
solutions.
.9 Represent a linear function as a table and a graph.
8:11 Problem Solving:
.1 Evaluate, interpret, and justify solutions to problems.
8:12 Communication:
.1 Explain and use a variety of problem solving
strategies.
.2 Represent a problem numerically, graphically,
symbolically, and translate between these alternative
representations.
.3 Use math vocabulary, symbols, and notations to explain,
justify, and defend mathematical ideas.
8:13 Reasoning:
.1 Recognize and apply deductive and inductive reasoning
in both concrete and abstract contexts.
8:14 Connections:
.1 Use mathematical ideas from one area of mathematics to
explain an idea from another area of mathematics (e.g., algebra
to geometry).
.2 Translate between various representations of equivalent
representations.
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