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Middle School Pre-Algebra

Course Description:

In this two-semester course, students will study Pre-Algebra and its application to the real
world. Students will be required to demonstrate proficiency in the content to pass the
course.

The standards for this course are the California Grade 7 Mathematics Standards as
approved by the California Board of Education. The curriculum for this course prepares
students for both the annual state testing and for High School Exit Exam.
This course is a pre-requisite for both Algebra 1 and Algebra 1A/1B.

Content Standards:

Standard 1: Number Sense and Operations

Benchmarks
Students will:
Performances
Students who meet the standard will:
1. Students will know
the properties of, and
compute with,
rational numbers
expressed in a variety
of forms
1.1 Read, write, and compare rational numbers in scientific notation with
approximate numbers using scientific notation. (exposure)
1.2 Add, subtract, multiply, and divide rational numbers and take positive
rational numbers to whole number powers.

1.3 Convert fractions to decimals and percents and use these representations in
estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating
decimal and be able to convert terminating decimals into reduced
fractions
.
1.6 Calculate the percentage of increase and decreased of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit
and
compute simple and compound interest.
 
2. Students use
exponents, powers,
and roots and use
exponents in working
with fractions.
2.1 Understand negative whole number exponents. Multiply and divide
expressions involving exponents with a common base .
2.2 Add and subtract fractions by using factoring to find common
denominators.
2.3 Multiply, divide and simplify rational numbers by using exponent rules.

2.4 Use the inverse relationship between raising to a power and extracting the
root of a perfect square integer ; for an integer that is not a square, determine
without a calculator the two integers between which its square root lies and
explain why.
2.5 Understand the meaning of the absolute value of a number ; interpret the
absolute value as the distance of the number from zero on a number line; and
determine the absolute value of real numbers.
 

Standard 2: Algebra and Functions

Benchmarks
Students will:
Performances
Students who meet the standard will:
1. Students express
quantitative
relationships by
using algebraic
terminology,
expressions,
equations,
inequalities, and
graphs.
1.1 Use variables and appropriate operations to write an expression, an equation,
an inequality, or a system of equations or inequalities that represent a verbal
description (exposure)
1.2 Use the correct order of operations to evaluate algebraic expressions.
1.3 Simplify numerical expressions by applying properties of rational
numbers and justify the process used.

1.4 Use algebraically terminology correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a
specific part of a graph in the situation represented by the graph.
2. Students interpret
and evaluate
expressions
involving integer
powers and simple
roots
 
2.1 Interpret positive whole-number powers as repeated multiplication and
negative whole-number powers as repeated division or multiplication by the
multiplicative inverse. Simplify and evaluate expressions that involve
exponent (exposure)
2.2 Multiply and divide monomials; extent the process of taking powers and
extracting roots to monomials when the latter results in a monomial with an
integer exponent.
3. Students graph and
interpret linear and
some nonlinear
functions.
3.1 Graph functions of the form y=nx3 and y=nx2 and use in solving problems
(exposure)
3.2 Plot the values from the volumes of three-dimensional shapes for various
values of the edge lengths (exposure)
3.3 Graph linear functions, noting that the vertical change per unit of
horizontal change is always the same and know that the ratio (“rise” over
“run”) is called the slope of the graph.

3.4 Plot the values of quantities whose ratios are always the same. Fit the line to
the plot and understand that the slope of the line equals the quantities.
 
4. Students solve
simple linear
equations and
inequalities over the
rational numbers
.
4.1 Solve two-step linear equations and inequalities in one variable over the
rational numbers, interpret the solution or solutions in the context from
which they arose, and verify the reasonableness of the results.

4.2 Solve multi-step problems involving rate, average speed, distance and time or
a direct variation.

Standard 3: Geometry and Measurement

Benchmarks
Students will:
Performances
Students who meet the standard will:
1. Students choose
appropriate units of
measure and use
ratios to convert
within and between
measurement
systems in solve
problems.
1.1 Compare weights, capacities, geometric measures, times and temperature
within and between measurement systems.
1.2 Construct and read drawings and models made to scale (exposure)
1.3 Use measures expressed as rates and measures expressed as products to solve
problems: check the units of the solutions; and use dimensional analysis to
check the reasonableness of the answer.

 
2. Students compute the
perimeter, area, and
volume of common
geometric objects
and use the results to
find measures of less
common objects.
They know how
perimeter, area and
volume are affected
by the change in
scale.

 
2.1 Use formulas routinely for finding the perimeter and are of basic two-dimensional
figures and the surface area and volume of basic three-dimensional
figures, including rectangles, parallelograms, trapezoids,
squares, triangles, circles, prisms and cylinders.
2.2 Estimate and compute the area of more complex or irregular two
- and
three-dimensional figures by breaking the figures down into more basic
geometric object (exposure)
2.3 Compute the length of the perimeter, the surface area of the faces, and the
volume of a three-dimensional object built from rectangular solids.
Understand that when the lengths of all dimensions are multiplied by a scale
factor, the surface are is multiplied by the square of the scale factor and the
volume is multiplied by the cube of the scale factor (exposure)
2.4 Relate the changes in measurement with a change of scale to the units used
and to conversions between units (exposure)
3. Students know the
Pythagorean theorem
and deepen their
understanding of
plane and solid
geometric shapes by
constructing figures
that meet given
conditions and by
identifying attributes
of figures.
3.1 Identify and construct basic elements of geometric figures by using a compass
and straightedge (exposure)
3.2 Understand and use coordinate graphs to plot simple figures, determine
lengths and areas related to them
and determine their image under
translations and reflection (exposure)
3.3 Know and understand the Pythagorean theorem and its converse and use
it to find the length of the missing side of a right triangle and the lengths
of the other line segments and, in some situations, empirically verify the
Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two
geometrical figures are congruent and what congruence means about the
relationships between the sides and angles of the two figures.

3.5 Construct two-dimensional patterns for three-dimensional models, such as
cylinders, prisms and cones (exposure)
3.6 Identify elements of three-dimensional geometric objects and describe how
two or more objects are related in space (exposure)
 

Standard 4: Data, Statistics and Probability

Benchmarks
Students will:
Performances
Students who meet the standard will:
1. Students collect,
organize and
represent data sets
that have one or more
variables and identify
relationships among
variables within a
data set by hand and
through the use of an
electronic
spreadsheet software
program.
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or
box-and-whisker; use the forms to display a single set of data or to compare
two sets of data (exposure)
1.2 Represent two numerical variables on a scatter plot and informally describe
how the data points are distributed and any apparent relationship that exists
between the two variables (exposure)
1.3 Understand the meaning of, and be able to compute, the minimum, the lower
quartile, the median, the upper quartile and the maximum of a data set
(exposure)
 
2. Collect and interpret
data and make
decisions based on
their interpretations.
2.1 Use experimental and theoretical probability appropriately to represent to
represent and solve problems.
2.2 Identify examples and explain impact of probability on real life.
2.3 Compute probability of independent/dependent events occurring.

Standard 5: Mathematical Reasoning

Benchmarks
Students will:
Performances
Students who meet the standard will:
1. Make decisions about
how to approach
problems.
1.1 Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information, identifying missing information, sequencing and
prioritizing information and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description
of the mathematical question or problem posed.
1.3 Determined when and how to break a problem into simpler parts.
 
2. Use strategies, skills
and concepts in
finding solutions
2.1 Use estimation to verify the reasonableness of calculated results
2.2 Apply strategies and results from simpler problems to more complex
problems.
2.3 Estimate unknown quantities graphically and solve for them b using logical
reasoning and arithmetic and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate
mathematical notation and terms and clear language; support solutions with
evidence both in verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to
problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the
context of the problem.
 
3. Determine a solution
is complete and
move beyond a
particulate problem
by generalizing to
other situations.
3.1 Evaluate the reasonableness of the solution in the context of the original
situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and
apply them to new problem situations.
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