| Lesson |
Concept |
Objectives |
Hours |
|
Topic F1: Whole Numbers |
| F1.1 Whole Numbers I |
Adding and Subtracting |
a) Number line and ordering symbols
b) Place value
c) Adding whole numbers
d) Subtracting whole numbers
e) Solving x ± a = b
f) Applications |
2 hours |
Multiplying and
Dividing |
a) Multiplying whole numbers
b) Dividing whole numbers
c) Prime factorization
d) Solving ax = b
e) Applications |
2 hours |
Rounding and
Divisibility |
a) Rounding and estimating
b) Divisibility
c) Applications |
3 hour |
| Explore |
a) Magic Squares
b) Working with 11
c) How many Soda Cans? |
1 hour |
| |
|
Lesson Total |
6-8 hours |
| F1.2 Whole Numbers II |
Exponential Notation |
a) Base
b) Exponent
c) Roots
d) Applications |
3 hours |
| Order of Operations |
a) Grouping symbols
b) Order of operations
c) Distributive property and other properties of whole
numbers
d) Combining similar terms
e) Applications |
2 hours |
| Explore |
a) Double Double
b) The Four 4’s Game |
1 hour |
| |
|
Lesson Total |
4-6 hours |
|
Topic F2: Proportional Reasoning I |
| F2.1 Fractions I |
Equivalent Fractions |
a) Fraction notation
b) Equivalent fractions (with larger or smaller denominators)
c) Simplify fractions ( reducing to lowest terms)
d) Greatest common factor (GCF)
e) Applications |
3 hours |
Multiplying and
Dividing |
a) Mixed numerals and improper fractions
b) Multiplying fractions
c) Finding reciprocals
d) Dividing fractions
e) Solving px = q
f) Applications |
2 hours |
| Explore |
a) Daily Fractions
b) Fractions and Triangles |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F2.2 Fractions II |
Common
Denominators |
a) Least common multiple (LCM)
b) Common denominators
c) Least common denominator (LCD)
d) Ordering fractions
e) Applications |
2 hours |
Adding and
Subtracting |
a) Fractions with the same denominators
b) Fractions with different denominators
c) Mixed numerals
d) Order of operations
e) Properties of rational numbers
f) Combining similar terms
g) Solving x ± p = q
h) Applications |
3 hours |
| Explore |
a) Stock Prices
b) A Survey |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F2.3 Decimals I |
Notation |
a) Place value
b) Ordering decimals
c) Rounding and estimating
d) Applications |
2 hours |
| Converting |
a) Converting decimals to fractions
b) Converting fractions to decimals
c) Irrational numbers
d) Applications |
3 hours |
| Explore |
a) Using Decimals to Compare Data
b) The Dewey Decimal System |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F2.4 Decimals II |
Adding and
Subtracting |
a) Adding decimals
b) Subtracting decimals
c) Combining similar terms
d) Solving x ± r = s
e) Applications |
2 hours |
Multiplying and
Dividing |
a) Multiplying decimals
b) Dividing decimals
c) Multiplying and dividing by powers of 10
d ) Converting fractions to decimals
e) Irrational numbers
f) Order of operations
g) Properties of real numbers
h) Solving rx = s
i) Applications |
3 hours |
| Explore |
a) A Calculator Game
b) A Target Game |
1 hour |
| |
|
Lesson Total |
4-6 hours |
|
Topic F3: Proportional Reasoning II |
| F3.1 Ratio and Proportion |
Ratios |
a) Notation
b) Equivalent ratios
c) Rates
d) Applications |
2 hours |
| Proportions |
a) Setting up a proportion
b) Solving a proportion
c) Similar triangles
d) Applications |
3 hours |
| Explore |
a) Inverting Ratios
b) Similar Figures |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F3.2 Percent |
Definition |
a) Percent as a fraction
b) Percent as a decimal
c) “Benchmark” percents
d) Applications |
2 hours |
| Converting |
a) Converting among fractions, decimals and percents
b) Percent increase and decrease
c) Applications |
3 hours |
Solving Percent
Problems |
a) Setting up and solving proportions
b) Setting up and solving other equations
c) Applications |
3 hours |
| Explore |
a) A Survey
b) Computing Tips
c) A Percent Question |
1 hour |
| |
|
Lesson Total |
6-8 hours |
|
Topic F4: Signed Numbers |
| F4.1 Signed Numbers I |
Adding |
a) Signed numbers
b) Ordering signed numbers
c) Absolute value
d) Adding signed numbers
e) Applications |
2 hours |
| Subtracting |
a) Subtracting signed numbers
b) Solving x ± a = b
c) Applications |
3 hours |
| Explore |
a) Tracking Temperatures
b) Efficient Calculating |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F4.2 Signed Numbers II |
Multiplying and
Dividing |
a) Multiplying signed numbers
b) Dividing signed numbers
c) Solving ax = b
d) Applications |
2 hours |
| Combining Operations |
a) Order of operations
b) Distributive property and other properties of real numbers
c) Combining similar terms
d) Applications |
3 hours |
| Explore |
a) Ups and Downs
b) 2’s and 4’s |
1 hour |
| |
|
Lesson Total |
4-6 hours |
|
Topic F5: Geometry |
| F5.1 Geometry I |
Geometric Figures |
a) Point, line, line segment, ray
b) Polygons
c) Measuring angles
d) Angles: acute, right, obtuse, straight
e) Relationships between angles: complementary,
supplementary, adjacent, vertical
f) Applications |
3 hours |
| Explore |
a) Tiling with Polygons
b) What’s the Sum? |
1 hour |
| |
|
Lesson Total |
4 hours |
| F5.2 Geometry II |
Perimeter and Area |
a) Perimeter of a polygon
b) Area of a polygon
c) Area of a rectangle, square, parallelogram, triangle,
trapezoid
d) Circumference of a circle
e) Area of a circle
f) Perimeter and area of composite figures
g) Applications |
2 hours |
Surface Area and
Volume |
a) Surface area of a solid
b) Volume of a solid
c) Surface area and volume of a rectangular prism
d) Surface area and volume of a cylinder
e) Volume of a cone
f) Volume of a sphere
g) Composite figures
h) Applications |
3 hours |
| Explore |
a) Don’t Fence Me In
b) Why π?
c) Packaging Products |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F5.3 Geometry III |
Triangles and
Parallelograms |
a) Angle sum of a triangle
b) Congruent triangles
c) Isosceles and equilateral triangles
d) Right triangles
e) The Pythagorean Theorem
f) Parallel lines and transversals
g) Properties of parallelograms
h) Applications |
2 hours |
| Similar Polygons |
a) Similar polygons
b) Similar triangles
c) Applications |
3 hours |
| Explore |
a) Congruent Triangles
b) Door to Door |
1 hour |
| |
|
Lesson Total |
4-6 hours |
|
Topic F6: Interpreting Data |
| F6.1 Units of Measurement |
US/English Units |
a) Measures: length, weight, time, volume
b) Converting from one unit to another
c) Adding and subtracting measurements
d) Applications |
2 hours |
| The Metric System |
a) The metric system: length, mass, volume
b) Fahrenheit and Celsius scales
c) Converting between US and metric units
d) Applications |
3 hours |
| Explore |
a) Sizing it Up
b) Choosing Units |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F6.2 Interpreting Graphs |
Data and Graphs |
a) Reading data from graphs
b) Graphing data
c) Pictographs
d) Bar graphs
e) Circle graphs
f) Line graphs
g) Applications |
2 hours |
| Explore |
a) Collecting and Picturing Data
b) Graphs in the News |
1 hour |
| |
|
Lesson Total |
2-3 hours |
F6.3 Introduction to
Statistics |
Statistical Measures |
a) Mean
b) Median
c) Mode
d) Box-and-whisker plots
e) Applications |
2 hours |
| Explore |
a) Collecting Data
b) Where’s the Middle? |
1 hour |
| |
|
Lesson Total |
2-3 hours |
|
Topic 1: Real Numbers |
| 1.1 The Real Numbers |
Number Line and
Notation |
a) Sets
b) Subsets of real numbers: natural numbers, integers, rational,
irrational
c) Graphing real numbers on a number line
d) Ordering symbols: =, <, >, ≤, ≥
e) The absolute value of a real number
f) Grouping symbols
g) Exponents |
2 hours |
| |
|
Lesson Total |
2 hours |
1.2 Factoring and
Fractions |
The GCF and LCM |
a) Prime factors
b) Greatest common factor
c) Least common multiple |
1 hour |
| Fractions |
a) Reducing to lowest terms
b) Multiplication and division
c) Addition and subtraction |
1 hour |
| Explore |
a) Exploring Greatest Common Factor |
1 hour |
| |
|
Lesson Total |
3 hour |
1.3 Arithmetic of
Numbers |
Operations on
Numbers |
a) Addition
b) Subtraction
c) Multiplication
d) Division
e) Order of operations
f) Commutative law
g) Associative law
h) Distributive law
i) Additive and multiplicative identities
j) Inverses |
1 hour |
| Explore |
a) Exploring Operations on Numbers |
1 hour |
| |
|
Lesson Total |
2 hour |
|
Topic 2: Solving Linear Equations and Inequalities |
| 2.1 Algebraic Expressions |
Simplifying
Expressions |
a) Constants and variables
b) Terms and coefficients
c) Combining like or similar terms
d) Parentheses
e) Evaluating expressions
f) Formulas: Substitution |
2 hours |
| |
|
Lesson Total |
2 hour |
2.2 Solving Linear
Equations |
Solving Equations I |
a) Recognizing a linear equation
b) The addition and subtraction principles for solving a
linear equation
c) The multiplication and division principles for solving a
linear equation
d) Combining the principles |
2 hours |
| Solving Equations II |
a) Equations with fractions as coefficients
b) Equations with no solutions or infinitely many solutions
c) Formulas: Solving for a particular unknown |
1 hour |
| |
|
Lesson Total |
3 hour |
| 2.3 Problem Solving |
Number and Age |
a) Translating words into algebraic expressions
b) Number problems
c) Age problems |
2 hours |
| Geometry |
a) Geometry problems |
2 hours |
| |
|
Lesson Total |
4 hour |
| 2.4 Linear Inequalities |
Solving Inequalities |
a) Recognizing solutions of linear inequalities
b) Graphing solutions of inequalities in one variable
c) The addition and subtraction principles for solving a
linear inequality
d) The multiplication and division principles for solving a
linear inequality
e) Combining the addition, subtraction, multiplication, and
division principles
f) Solving problems using inequalities |
2 hours |
| |
|
Lesson Total |
2 hour |
|
Topic 3: Introduction to Graphing |
3.1 Introduction to
Graphing |
Plotting Points |
a) The xy-plane
b) The x-axis and y-axis
c) The origin
d) Ordered pairs
e) The x-coordinate (abscissa), the y-coordinate (ordinate)
f) Plotting ordered pairs of numbers
g) Labeling the four quadrants
h) Determining the quadrant in which a point lies
i) The signs of the coordinates in each quadrant |
1 hour |
| Rise and Run |
a) Subscript notation
b) Geometric interpretation of rise and run
c) Algebraic definition of rise and run |
1 hour |
| The Distance Formula |
a) Pythagorean Theorem
b) The distance formula
c) The equation of a circle |
0.5 hours |
| Explore |
a) Plotting Points |
0.5 hours |
| |
|
Lesson Total |
3 hour |
|
Topic 6: Exponents and Polynomials |
| 6.1 Exponents |
Properties of
Exponents |
a) Definition of exponent, power, and base
b) Multiplication property
c) Division property
d) Powers raised to powers
e) Products raised to powers
f) Quotients raised to powers
g) The zero exponent |
2 hours |
6.2 Polynomial
Operations I |
Adding and
Subtracting |
a) Definition of polynomial, term, and coefficient
b) Evaluating a polynomial
c) The degree of a term and a polynomial
d) Writing the terms of a polynomial in descending order
e) Definition of a monomial, binomial , and trinomial
f) Recognizing like or similar terms
g) Combining like or similar terms
h) Polynomial addition
i) Polynomial subtraction |
2 hours |
Multiplying and
Dividing |
a) Multiplying a monomial by a monomial
b) Multiplying a polynomial by a monomial
c) Dividing a monomial by a monomial
d) Dividing a polynomial by a monomial |
2 hours |
| |
|
Lesson Total |
4 hour |
