Download Common Curriculum Map Discipline: Math Course: AP Prep Algebra I

Common Curriculum Map
Discipline: Math
Course: AP Prep Algebra I
Teacher: Renee Hunt
Semester 1:
Standards:
6A.e.1: Placed mixed numbers and decimals on the number line
6A.f.2: Represent, order, compare and graph integers
6A.f.4: Compare and order fractions and decimals efficiently and find their approximate
on the number line
6A.g.2: Show relationships between sets of numbers, including rational numbers, whole
numbers, natural numbers and integers
6A.h.2: Represent, order, and compare rational numbers using a variety of methods
6A.h.3: Place rational numbers on a number line
6A.i.3: Represent, order, and compare real numbers
6A.i.4: Place real numbers on the number line
6B.g.5: Simplify arithmetic expressions using the field properties and the order of operations
6B.g.7: Solve multi-step number sentences and word problems with rational numbers using the four basic
operations
6B.h.3: Simplify arithmetic expressions containing integers using the field properties and order of
operations
6B.i.1: Compare and contrast the properties of numbers and number systems including rational and the
real numbers
6B.j.2: Simplify expressions using the field properties, order of operations, and properties of equality for
the
set of real numbers
6D.e.1: Identify and express rations using appropriate notation
6D.f.1: Solve number sentences and word problems using percents
6D.f.5: Determine equivalent ratios
6D.g.2: Create and explain ratios and proportions that represent quantitative relationships
6D.g.4: Develop, use, analyze and explain methods for solving numeric or word problems involving
proportions
6D.h.2: Solve problems that involve percents, including percent increase and decrease, regardless of the
piece of info that is missing
7C.g.4: Solve simple problems involving rate, distance, and time
8A.f.2: Evaluate algebraic expressions for given values
8A.f.3: Express properties of numbers and operations using variables
8A.f.4: Simplify algebraic expressions involving like terms
8A.i.1: Write equivalent forms of inequalities
8A.i.2: Represent and explain mathematical relationships using symbolic algebra
8A.i.9: Represent relationships arising from various contexts
8A.i.10: Rewrite absolute value inequalities in terms of two separate equivalent inequalities with the
appropriate connecting phrase, and or or
8B.e.3: Demonstrate how the change in one quantity affects the other in a functional relationship
involving
whole numbers and unit fractions
8B.f.1: Graph simple inequalities on a number line
8B.f.2: Create a table of values that satisfy a simple linear equation and plot the points on the Cartesian
Plane
8B.f.3: Describe verbally, symbolically and graphically a simple relationship presented by a set of
ordered
pairs of numbers
8B.g.2: Graph two inequalities with a single variable including the intersection or union of these
inequalities on a number line
8B.h.1: Graph linear equations and inequalities on the Cartesian plane
8B.h.2: Graph a set of points and describe the relationship as linear or nonlinear
8B.i.1: Describe the relationships of independent and dependant variables from a graph
8B.j.4: Analyze functions by investigating domain and range
8B.j.11: Use a variety of symbolic representations for functions and relations
8C.f.1: Identify and explain incorrect uses of the commutative, associative and distributive properties
8C.f.2: Identify and provide examples of the identity property of add/mult
8C.h.1: Solve arithmetic and simple algebraic equations using properties of real numbers, equalit, and
inequality and justify the procedures
8C.h.2: Solve simple algebraic equations for a give variable
8D.h.1: Solve algebraic equations or word problems using algebraic or graphical representation
8D.h.2: Solve absolute value inequalities in one variable using algebraic or graphical representations
8D.i.1: solve equivalent forms of equations
8D i.3: Solve simple quadratic equations using algebraic or graphical representations
9C.j.2: Extend the ideas of formal and informal proof to non-geometric situations
Essential Questions:
Describe the relationship between a set and subsets of that set.
How are disjoint and equal sets similar? different?
Describe the Cartesian Product. How does it relate to relations and functions?
What is the purpose of the Order of Operations? Why is it crucial to the study of mathematics?
How do you use the Order of Operations to simplify an expression? To solve an equation?
Why do we need the properties of equality?
How are the different real number sets related?
What roles do the domain and range play in determining whether a relation is a function? whether a
relation is an equivalence relation? whether a function is injective, surjective or bijective.
When solving an equation, what is it that you are finding (not just x!)?
Why do we use the vertical line test? Why does it NOT work 100% of the time?
What is the purpose of function notation?
What does an argument need to be logically equivalent?
Content:
1. Fundamental Counting Principle
2. Combinations
3. Permutations
4. Basic Set Theory
5. Cartesian Product
6. Open sentences
7. Field Properties
8. Rational Numbers
9. Relations
10. Equivalence Relations
11. Equations
12.. Functions
- graphing and mapping
- injective, surjective and bijective
13. Logic
- compositions
- truth tables
- logical equivalence
- tautologies
- laws of logic
14. Inequalities
- Solving and graphing
- multi-step inequalities
- conjunctions and disjunctions
15. Ratios/Proportions
- rates, simple interest
- percent of change
- mixture problems
- uniform motion
- direct and indirect variation
16. Equations
- solving and graphing
- linear and quadratic
Skills:
1. Understand what sets, elements, empty, finite and infinite sets are
2. Understand and know the difference of what proper and subsets are
3. create the intersection and union of sets (both venn diagrams and set notation)
4. understand what a Cartesian Product is
5. Translate verbal expressions into mathematical expressions
6. use the order of operations to evaluate expressions
7. Solve open sentences by performing arithmetic operations
8. recognize and use the properties of identity and equality
9. use the distributive property to simplify expressions
10. Recognize and use the commutative and associate properties when simplifying expressions
11. translate verbal expressions into equations and formulas
12. state the coordinate of a point on a number line
13. graph integers on the number line
14. Add integers using the number line
15. Find the absolute value of a number
16. add/subtract/multiply and divide integers
17. compare numbers
18. write inequalities for graphs on a number line
19. graph inequalities on a number line
20. write rational numbers in increasing or decreasing order
21. find a number between two rational numbers
22. add/subtract/multiply and divide rational numbers
23. Define variables and write equations for verbal problems
24. Multiply and divide rational numbers without a calculator
25. understand the concept of the Cartesian Product
26. recognize a relation as a subset of the cartesian product
27. Use set selector, mapping, graphing, and listing methods to determine relations
28. understand the concept of an equivalence relation
29. Identify a relation as symmetric, reflexive and transitive
30. be able to determine if a relation is an equivalence relation
31. Solve multi-step equations involving all four operations
32. determine whether a relation is a function
33. students are able to differentiate between a relation and a function
34. students can identify the characteristics of function with respect to its domain
35. students are able to represent functions by mapping, listing, set selector method and graphing on the
cartesian plane
36. students are able to apply the vertical line test and are able to explain in detail why this method
doesn't
always work
37. students can identify an injective, surjective and bijective function and understand the characteristics
of
each
38. students can identify the 4 main connectors of logic thought
39. students justify the validity of a statement using a truth table
40. students can determine whether two statements are logically equivalent
41. students are able to identify and describe a tautology
42. students can solve and graph linear inequalities
43. students are able to solve and graph conjunctions and disjunctions
44. students can connect linear conjunctions and disjunctions to the logical connectors
45. Students are able to compute simple interest
46. students are able to recognize percent inc. and dec. and calculate the percent of change in word
problems
47. students are able to set up and solve mixture problems involving two or more variables
48. students are able to use uniform motion to find either the distance, rate or time
49. students can differentiate between inverse and direct variation and can set up and solve each
50. students can write equations from relations
51. student can graph linear relations
52. students can graph inequalities with two variables
53. Work with the Fundamental Counting Principle
54. Apply formula for Permutations
55. Apply formula for Combinations
Assessment:
1. Assignments from textbook.
2. Observation during group work/individual work in class.
3. Class discussions, formal and informal.
4. Chapter tests and quizzes
8 . Think/pair/share activities several times a week
9. Have students go to the board daily and verbally explain problems
10. KEL journals for each Chapter/topic presented.
11. CRISS: Think/pair/share activities once a week
12. binder check quarterly to assess organization and note taking skills
13. Computer based project on linear functions
Semester 2:
Standards:
6A.g.2: show relationships between sets of numbers
6A.h.1:Recognize and use exponential and scientific notation
6A.i.1: illustrate the relationship between second and third roots and powers of a number
6A.j.1: represent numbers in equivalent forms
6B.e.1: Determine whether a number is prime or composite
6B.e.2: Identify all whole number factors of a composite number
6B.f.2: Determine the LCM and the GCF of a set of numbers6B.g.2: Describe the relationships between
prime factorization and properties of squares, primes and composites
6B.g.5: Simplify arithmetic expressions containing exponents using the field properties and the order of
operations
6B.h.4: describe and use the inverse relationships of squaring and finding square roots to simplify
computations and solve problems
8A.f.4: Simplify algebraic expressions involving like terms
8A.h.3: Describe the relationships between symbolic expressions and graphs of lines
using the appropriate vocab for the intercepts and slope of a line
8A.h.5: Recognize and generate equivalent forms for linear equations, including
transforming linear equations into standard and slope-intercept form
8A.i.1: write equivalent forms of equations, inequalities, and systems of equations
8A.i.3: Model and describe slope as a constant rate of change
8A.i.6: Simplify algebraic expressions using a variety of methods including factoring
8B.e.2: represent and analyze patterns and functions
8B.h.1: Graph linear equations on the Cartesian plane
8B.h.5: Determine the slope of a line from a graph
8B.i.1: Describe the relationships of the independent and dependent variable from a
graph
8B.i.7: Identify slope in an equation and from a table of values
8D.i.1: solve equivalent forms of equations and systems of equations, using technology in some cases
9A.h.5: solving pictorial or word problems that involve geometric relationships, within a single geometric
shape including Pythagorean Theorem
9B.f.2: Solve problems that involve vertical, supplementary, and complementary angles
9B.h.2: Solve problems involving similar figures
9D.g.1: Analyze the relationship between sides of right triangles using Pyth. Theorem
9D.g.2: solve problems that involve the use of proportions and the pyth. thm.
Essential Questions:
Content:
1. Monomials
- product of monomials
- laws of exponents
2. Polynomials
- add/sub
- multiplying
3. Factoring
- GCF
- grouping
- factoring quadratic trinomials
- difference of squares
4 .Factoring
- perfect squares
- summary of factoring
- solving equations by factoring
5. ISAT Review
- basic geometry
- review of algebra concepts
- writing sample portion
ISAT TESTING (one week)
SPRING BREAK (one week)
6.Solving Systems of Linear Equations
- graphing, substitution, and elimination
7.Roots of Real Numbers
- square, cube and nth roots
- operations with roots
8. Graphing Linear Functions
- slope
- slope intercept form
9.Quadratics Equations
- solve by factoring
- solve by completing the square
- solve by graphing
- solve by quadratic formula
Final Exam
Skills:
1. students can write monomials in descending order
2. students can multiply monomials and apply the laws of exponents
3. students are able to divide monomials
4. students are able to add and subtract polynomials by recognizing like terms and combining them
5. students are able to multiply polynomials, binomials and monomials using the distributive property
6. students are able to recognize special products: difference of squares and perfect square trinomials
7. students are able to find the GCF of integers and monomials
8. students are able to factor a monomial out of a polynomial using the distributive property
9. students are able to factor a 4 term polynomial by grouping
10. students are able to factor a quadratic trinomial using the "chart"
11. students can reconize and use all special products when factoring
12. students can solve linear and quadratic equations using factoring
13. students are able to recognize and use the Zero Product Property
14. review several geometric concepts for ISAT
15. students can complete the free response section of the ISAT
16. use Pythagorean Theorem to find unknown side lengths
17. find the volume and surface area of triangles, rectangles, and cylinders
18. reveiwed major 8th grade algebra concepts: solving equations, combining like
terms, solving multi-step word problems
19. learned how to write a free response answer to the math portion of the ISAT
20. find the slope of a line both graphically and algebraically
21. graph linear equations on a cartesian plane using values from a table and
slope-intercept form
22. recognize and apply the slope and y-intercept from slope-intercept form
23. understand that slope is a rate of change
24. graph linear equations using the x/y intercepts
25. identify and find the x/y intercepts
26. solve problems that use the relationships of vertical, complimentary and
supplementary angles.
27. Students are able to solve systems of linear equations by graphing
28. can identify the points of intersection on a graph of two linear equations
29. students are able to distinguish between a graph that has one sol, no sol or infinitely many sol
30. students are able to solve a system by substitution
31. students can use elimination to find the points of intersection
32. students understand what it means to take the "square root"
33. students can apply the notion of square roots to problems with larger indexes
34. students can simplify a square root, while leaving it as an exact answer
35. apply the Pythagorean Theorem using radicals
36. add/sub radicals
37. derive the distance formula
38. use the distance formula to find the length of a line segment
39. students will be able to solve a quadratic equation by the following methods
- graphing
- completing the square
- quadratic formula
40. students are able to derive the quadratic formula from the standard form of the quadratic equation
41. Apply definition of factorial and manipulate terms using factorials
Assessment:
1. Assignments from textbook.
2. Observation during group work/individual work in class.
3. engaged students in class discussions, formal and informal.
4. Quartely Binder check