Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
Course Title
Algebra Readiness
School
Sinaloa MS, Hill MS, San Jose MS
District
Novato Unified School District
City
Novato, California 94945
Contact Person
Department or Discipline
 History/Social Studies
 English/Language Arts
 Mathematics
 Laboratory Science
 Language other than English
 Visual & Performing Arts (for 2003)
 College Preparatory Elective:
Subject Area: __________________
Grade Level(s) for which course is
intended
8
Length of Course
 Semester
 Year
 Other
Director of Secondary Instruction
Contact Information
Phone: 415-897-4288
Unit Value
 0.5 (half year equivalent)
 1.0 (one year equivalent)
 2.0 (two year equivalent)
 Other: two one-year equivalent courses
Fax: 415-892-1622
Seeking “Honors” distinction?
 Yes
 No
Date of School Board Approval:
April 7, 2009
Course Number Assigned:
Was this course previously approved by UC?  Yes
If so, in what year?
Under what course title?
 No
Pre-Requisites
7th grade math
Co-Requisites
See course description, credits earned as math requirement and math elective
D:\533566096.doc 2/17/2016
1
Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
Brief Course Description for Academic Planning Guide (student friendly)
This course is a double period course designed for students who are two to three years behind in
mathematics and not ready for Algebra. The curriculum has been designed to help students
overcome weak preparation in mathematics. It utilizes an approach that accelerates student
learning up to the level needed for advanced mathematics courses. The curriculum scaffolds
mathematics standards to prepare for the fundamental principles of Algebra.
COURSE CONTENT
A.
Course goals and/or major student outcomes
● The goal of this course is to have an explicit and cohesive curriculum based on
mathematical concepts.
● Instruction will reinforce and strengthen concepts and skills introduced in 2nd
through 7th grades.
● Emphasis will be placed on 13 of the 7th grade standards and 3 of the Algebra 1
standards.
● Students will gain confidence by working at levels appropriate to their abilities
while raising their content knowledge and strengthening their skills.
● Students will be better prepared for college-prep mathematics at the high school
level.
● Students will use mathematical language to express their understanding of the
material
B.
Course Objectives-specific student learning objectives
Objectives.
Students will Understand
1. the foundations of
algebra using
appropriate diagrams,
numbers and letters and
basic number
properties
2. various properties of
Standards
Grade 5 – Algebra and Functions
1.0 Students use variables in simple expressions, compute the value of the
expression for specific values of the variable, and plot and interpret the results
1.2 Use a letter to represent an unknown number; write and evaluate simple
algebraic expressions in one variable by substitution.
1.3 Understand and compute positive integer powers of nonnegative integers;
compute examples as repeated multiplication.
Grade 5 – Mathematical Reasoning
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
Grade 6 – Algebra and Functions
1.3 Apply algebraic order of operations and the commutative, associative, and
distributive properties to evaluate expressions; and justify each step in the
process.
Grade 4 – Number Sense
D:\533566096.doc 2/17/2016
2
Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
the number system,
including place value,
number lines, rational
numbers, percents, and
operations
3. factors and fractions
with the ability to
simplify through
knowledge of prime
factors, common
multiples, GCF and
LCM as well as
operations using
fractions
4. concepts, properties
and operations of
positive and negative
numbers including
integers, fractions and
decimals
5. comparing quantities in
1.0 Students understand the place value of whole numbers and decimals to two
decimal places and how whole numbers and decimals relate to simple fractions.
Students use the concepts of negative numbers:
3.2 Demonstrate an understanding of, and the ability to use, standard algorithms
for multiplying a multi digit number by a two-digit number and for dividing a
multi digit number by a one-digit number; use relationships between them to
simplify computations and to check results.
Grade 6 – Mathematical Reasoning
1.2 Formulate and justify mathematical conjectures based on a general
description of the mathematical question or problem posed.
Grade 7 – Number Sense
1.3 Convert fractions to decimals and percents and use these representations in
estimations, computations, and applications
1.5 Know that every rational number is either a terminating or repeating decimal
and be able to convert terminating decimals into reduced fractions.
Grade 4 – Number Sense
1.7 Write the fraction represented by a drawing of parts of a figure; represent a
given fraction by using drawings; and relate a fraction to a simple decimal on a
number line.
Grade 5 – Number Sense
2.0 Students perform calculations and solve problems involving addition,
subtraction, and simple multiplication and division of fractions and decimals
2.4 Understand the concept of multiplication and division of fractions.
Grade 6 – Number Sense
2.2 Explain the meaning of multiplication and division of positive fractions and
perform the calculations (e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 = 2/3).
2.4 Determine the least common multiple and the greatest common divisor of
whole numbers; use them to solve problems with fractions (e.g., to find a
common denominator to add two fractions or to find the reduced form for a
fraction).
Grade 6 – Mathematical Reasoning
2.5 Express the solution clearly and logically by using the appropriate
mathematical notation and terms and clear language; support solutions with
evidence in both verbal and symbolic work.
Grade 4 – Number Sense
1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in
temperature, in "owing").
Grade 5 – Number Sense
2.1 Add, subtract, multiply, and divide with decimals; add with negative integers;
subtract positive integers from negative integers; and verify the reasonableness of
the results.
Grade 6 – Number Sense
2.3 Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers and
combinations of these operations.
Grade 6 – Mathematical Reasoning
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
Grade 6 – Algebra and Functions
1.3 Apply algebraic order of operations and the commutative, associative, and
distributive properties to evaluate expressions; and justify each step in the
process.
Grade 6 – Algebra and Functions
2.0 Students analyze and use tables, graphs, and rules to solve problems
D:\533566096.doc 2/17/2016
3
Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
a variety of contexts
using ratios, solving
proportions, connecting
scale factor and
similarity of figures,
and represent these
concepts with a variety
of methods including
diagrams, charts and
tables
6. slope as a constant
ratio, graphing linear
equations with an
emphasis on real
applications. Students
will also discover
connections between
parallel and
perpendicular lines and
other geometric
relationships.
7. variables, expressions,
equations and
exponents, both
positive and negative,
as an introduction to
algebra.
8. the interpretation of
solutions to real life
involving rates and proportions
Grade 6 – Number Sense
1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/
21, find the length of a side of a polygon similar to a known polygon). Use crossmultiplication as a method for solving such problems, understanding it as the
multiplication of both sides of an equation by a multiplicative inverse.
Grade 7 – Algebra and Functions
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the
number of an item, feet to inches, circumference to diameter of a circle). Fit a line
to the plot and understand that the slope of the line equals the quantities.
4.2 Solve multi step problems involving rate, average speed, distance, and time or
a direct variation.
Grade 7 – Mathematical Reasoning
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
Grade 4 – Algebra and Functions
1.5 Understand that an equation such as y = 3 x + 5 is a prescription for
determining a second number when a first number is given.
Grade 5 – Algebra and Functions
1.5 Solve problems involving linear functions with integer values; write the
equation; and graph the resulting ordered pairs of integers on a grid.
Grade 5 – Statistics, Data Analysis, and Probability
1.4 Identify ordered pairs of data from a graph and interpret the meaning of the
data in terms of the situation depicted by the graph.
Grade 7 – Algebra and Functions
3.3 Graph linear functions, noting that the vertical change (change in y- value)
per unit of horizontal change (change in x- value) is always the same and know
that the ratio ("rise over run") is called the slope of a graph.
Grade 7 – 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 in both verbal and symbolic work.
Grade 7 – Algebra and Functions
1.1 Use variables and appropriate operations to write an expression, an equation,
an inequality, or a system of equations or inequalities that represents a verbal
description (e.g., three less than a number, half as large as area A).
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 include exponents.
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.
Grade 7 – Mathematical Reasoning
1.2 Formulate and justify mathematical conjectures based on a general
description of the mathematical question or problem posed.
Algebra 1
2.0 Students understand and use such operations as taking the opposite, finding
the reciprocal, taking a root, and raising to a fractional power. They understand
and use the rules of exponents.
4.0 Students simplify expressions before solving linear equations and inequalities
in one variable, such as 3(2x-5) + 4(x-2) = 12.
Grade 7 – Measurement and Geometry
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed
as products (e.g., person-days) to solve problems; check the units of the solutions;
D:\533566096.doc 2/17/2016
4
Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
situations and problem
solving.
and use dimensional analysis to check the reasonableness of the answer.
Grade 7 – Mathematical Reasoning
1.3 Determine when and how to break a problem into simpler parts.
2.2 Apply strategies and results from simpler problems to more complex
problems.
3.2 Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
Algebra 1
5.0 Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for each
step.
C.
Outline
Topics/Units/Themes
Foundations of Algebra
Number System
Factors and Fractions
Positive and Negative
Numbers
Ratio and Proportionality
Showing Relationships
with Graphs
Key Activities/Assignments/
Standard(s) addressed in Key Activities




















Expressions, Equations
and Exponents
Using Equations to Solve
Problems






Use diagrams to show two amounts are equal
Learn strategies for interpreting, representing and solving word problems
Use the various identities and properties of operations
Represent addition, subtraction, multiplication, and division on number lines
Recognize and write equivalent fractions
Convert fractions to decimals and decimals to fractions
Use inverse operations
Use concepts of prime and composite numbers
Use exponents to express a prime factorization of a number, greatest common
factors, and least common multiple
Order decimals or fractions and place them on the number line
Use the distributive property in relation to negative and positive numbers
Add, subtract, multiply and divide positive and negative numbers
Use inequalities in comparing rational numbers
Use ratio to compare numbers using division
Use proportionality to model problems
Solve problems using dimensional analysis
Explore similar polygons
Draw a line given two points
Show that relationships between quantities can be represented using tables,
graphs, and formulas
Solve word problems that describe situations modeled by arithmetic
operations
Use the number properties to write equivalent expressions that represent the
same quantity
Use algebraic terminology correctly
Evaluate expressions with negative exponents
Apply the Pythagorean Theorem
Apply cumulative concepts to real world situations
Communicate the results of problem solving investigations in written form
and in oral discussion
D:\533566096.doc 2/17/2016
5
Novato Unified School District
Initial Draft
Course Description
Algebra Readiness
D. Texts and supplemental instructional materials
America's Choice: Ramp-Up to Algebra, California Algebra Readiness Program
E. Instructional methods and strategies
 Direct Instruction
 Problem solving activities
 Math note-taking and journal writing
 Student modeling of problem solving strategies
 Independent practice
 Cooperative learning groups
F. Assessment methods and/or tools






Publisher tests / assessments
Math notebook and journals
Class participation
Homework
Teacher designed tests / assessments
Class discussion and oral response
G. Assessment criteria
 Students will be using standards-based assessments aligned to the California Mathematics
Frameworks
 Mastery of course content standards
 Completion and accuracy of work
 Thoroughness of work
 Ability to think critically and problem solve
D:\533566096.doc 2/17/2016
6