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MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Mathematical
Reasoning
(Woven
throughout the
curriculum)
Standards/
Key Ideas/
Indicators
1.1.1A
1.1.2A
1.1.3A
3.1.1A
3.1.1B
Guiding Questions
How do you know?
How did you arrive at that
answer?
Why did you choose that
strategy?
What other ways could the
problem be solved?
Can you restate this
problem another way?
What’s a simpler way to say
that?
Essential Knowledge & Skills
Classroom Ideas
 Use abstraction and symbolic
representation to communicate
mathematically
 Use deductive and inductive
reasoning to reach mathematical
conclusions
 Use critical thinking skills to
solve mathematical problems
 Use mathematical reasoning to
analyze mathematical situations,
make conjectures, gather
evidence and construct an
argument
 Construct valid arguments
 Follow and judge the validity of
arguments
These ideas should be woven throughout daily
classroom instruction.
 Students use written language and/or graphic
representations to describe/illustrate problemsolving methods
 Have students respond to assignments in journals
 Have students discuss solutions and strategies in
small groups. Decide which strategies were most
efficient.
 Ask students to frequently restate problems in
own language
 Introduce complex problems with simpler
versions first
 Use graphic organizers designed to help students
think about the steps involved (step ladder or
sequence flow charts)
Assessment Ideas

Teacher
observations

Class discussions

Journal entries –
use a rubric for
level of
understanding,
clarity of
explanations, etc.
Time
How could this problem or
solution be graphically
represented?
Math A Draft; Fall 1999
1
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Fractions,
Decimals, and
Percents
(Optional
review of 8th
grade material)
Standards/
Key Ideas/
Indicators
(Intermediate
Level)
3.2.2A
3.2.2B
3.2.2D
3.3.3A
Guiding Questions
When in real life do you use
fractions, percents, and
decimals?
How are fractions,
percents, and decimals
related?
Can the same quantity be
represented by a fraction,
percent, and decimal?
Essential Knowledge & Skills
 Can understand, represent and
use numbers in variety of
equivalent forms – fractions,
percents, and decimals?
 Understands relationship
between terminating and
repeating decimals
 Calculate fractions, percents,
and decimals?
 Can use symbols (<, >, =, <, >) to
show relationships between
different fractions, percents,
and decimals.
 Knows techniques for ordering
fractions, percents, and decimals
 Can add, subtract, multiply, and
divide fractions and decimals
Classroom Ideas
 Have students interpret percent as part of 100
using variety of manipulatives (Algebra tiles,
graph paper, cubes, etc.) and show relationship to
total of 200, 300 etc.
 Popcorn activity – Pop different amounts of
kernels (25, 50, 75, etc.). Record the following
data: # kernels before popped and # kernels
after popped. Calculate # popped
# given
and express as fraction, decimal and percent. Use
some numbers that won’t come out even. Do
similar activity with M & M’s and color/package.
 Create circle graphs, bar graphs, etc. from data
collected in popcorn activity.
 Line Up activity – Sets of five cards. Put one
fraction or decimal an each card, hand out to
students line up from greatest to smallest or
smallest to largest.
 Have students can illustrate (or use
manipulatives) to show the fractions or decimals
an the line up cards.
 Using sales ads (% off), students calculate
amount saved and sale price of items to be
purchased. Role play as different consumers
(mom with young child with birthday, office
worker who needs desk supplies, kitchen
contractor looking for appliances, etc.) and have
students shop in appropriate store flyers.
Assessment Ideas
 Teacher
observations
Time
 15-20 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
2
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Ratios,
Proportions,
Similar
Triangles,
English and
Metric Units
Standards/
Key Ideas/
Indicators
3.5.5B
Guiding Questions
What are some examples of
where we use ratios in real
life?
What changes would occur if
the U.S. adopted the metric
system?
Is the English system of
measurement easier? Or just
more familiar?
Essential Knowledge & Skills
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Understanding ratios
Write and simplify ratios
Understand rate
Use ratios to express rates
Solve verbal problems using
ratios
Proportions / determine if two
ratios are equivalent
Solve proportions
Direct and indirect variation
Similar polygons
Similar triangles
Problem solving using
proportions
Solving scale drawing problems
Change units of measure in the
metric system
Change units of measure in the
metric system
Classroom Ideas

Review if needed: English and Metric measurement
systems
 Begin discussions with real life examples that
students can connect with – for example, to
introduce ratios remind students about making
orange juice, etc. from a can (add 1 can
concentrate and 3 cans of water)
 Draw an enlarged or reduced pattern of a kite.
Measure lengths on pattern; decide on ratio of
similitude, construct real kite.
 Bring in a square inch (or square foot) of carpet.
Students count number of fibers in room’s
carpet. Can do similar activity with blades of
grass in square inch on a baseball field.
 Convert sports stats (baseball, boxing, football,
etc.) to metric
 Calculate height of buildings, trees, etc. Using
similar triangles and measuring their shadows.
Assessment Ideas
 Teacher
observations
Time
 10-13 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
3
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Integers
Standards/
Key Ideas/
Indicators
3.3.3A
Guiding Questions
What real life situations
use integers?
Essential Knowledge & Skills
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Extending the number line
Comparing integers
The opposite of a directed
number
The absolute value of a number
Addition of signed numbers
Subtraction of signed numbers
Multiplication of signed numbers
Division of signed numbers
Order of operations of signed
numbers
Using powers (exponents) of
signed numbers
Using signed numbers in
evaluating algebraic expressions
Classroom Ideas
 Use playing cards (A to 10)
1. Play “war”-red cards are positive and
black are negative-students compare.
2. Students pick 2 cards and add them.
Highest sum wins.
 Explore the use of a graphing calculator to
illustrate integer operations, have students
come up with own rules.
 Illustrate on overhead projector using + and –
symbols, pair off (cancel) to illustrate solution.
Assist students in developing rules.
2+(-3)
+ + _ = -1
A similar demonstration can be done using
algebra tiles.
 Have students write explanations of how to solve
problem, not just give the answer or don’t even
have them give the answer (reinforces to them
your interest in their thinking)
 Have students find mistakes in problems and
explain how these occurred
 Introduce subtraction…(idea of integers) “Are
you aware your elementary teacher lied to you?”
It’s not always small-large.
 Have students keep checkbook registers
 Translate words that represent negative # and
positive counterpart.
Negative – spent, lose, debit
Positive – gain, credit
Assessment Ideas

Teacher
observations

Class discussions

Journal entries

Classroom
assignment
rubrics
Time

10-12 days
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
4
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Scientific
Notation,
Powers of Ten,
and Power
Rules
Standards/
Key Ideas/
Indicators
3.3.3B
Guiding Questions
How do scientists represent
extremely large numbers
(Distance from Sun to
Earth, etc.)?
And small numbers (size of
cell)?
Essential Knowledge & Skills
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Write numbers that are powers
of ten in words
Write numbers (whole numbers
and decimals) in scientific
notation
Write powers of ten in standard
form (10 to 10 )
Write the product of a number
using exponents (8x8x8=8 )
Write decimals as exponents
(.001=1/1000=1/10 =10 )
Raise decimals to powers: (1/5)
Write word phrases as decimals
and then in scientific notation:
5 tenths = .5 = 5 x 10
Raise fractions to powers: (1/4 )
Use power rules for base 10:
10 x 10 = 10
10 / 10 = 10
Use power rules for like bases:
X X X =X
Use the scientific calculator to
solve expressions where
exponents are decimals or
integers: 5 2 8º
Use the scientific notation in
standard form
Solve word problems with
scientific notation
Classroom Ideas
 Use fraction and decimal key on a calculator to
compute 5¯ (calculator gives decimal) have
students change to fraction
 Students research using the library and the
Internet to find out when and why scientific
notation was developed
Assessment Ideas
 Teacher
observations

Class discussions

Journal entries

Classroom
assignment
rubrics
Time

12-14 days
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
5
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Square Roots,
Right
Triangles,
trigonometry,
and Formulas
Standards/
Key Ideas/
Indicators
3.3.3C
3.5.5A
Guiding Questions
How do you determine the
amount of carpet, wallpaper,
paint, etc. to buy to cover a
surface?
Essential Knowledge & Skills
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How might scientists
determine distances that
can’t be measured (Sun to
Earth, etc.)?
Why is it important to know
the angle of a staircase? A
ramp?[OSHA Standards]
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Solve perfect square roots
Simplify square root radicals
Write word phrases in standard
form: two cubed = 2 = 8
Solve right triangle problems
using the Pythagorean Formula:
A +B =C
Find the sine, cosine, and
tangent of angle using a
scientific calculator
Given the sine, cosine, and
tangent, use a scientific
calculator to find the angle
Solve word problems and/or
diagrams using trig functions
Find the perimeter of triangles,
squares, and rectangles.
Find the circumference of a
circle (Use problems where
answers may be left in terms
of “)
Find the area of triangles,
squares, rectangles,
parallelograms, rhombus,
trapezoids, circles.
Find the volume of rectangular
solids, cubes, and cylinders.
Classroom Ideas

Review if needed: the three trig functions (sine,
cosine, and tangent)
 Pythagorean Theorem - distance from home
plate to second place
 Interior design projects - how much
wallpaper/carpet, etc. to cover wall or floor in
your bedroom? the classroom?
 Bring in gift boxes, cans, etc.…to discuss volume
and the differences
 Take two 5 X 8 note cards. Tape one note card
into a short fat cylinder and one into a tall
skinny cylinder. Place the tall, skinny, cylinder
inside the short fat cylinder. Fill the tall, skinny
cylinder with rice or beans, etc. Ask students to
predict how high the material filling the tall
cylinder will be when poured into the short fat
cylinder. Check predictions by lifting the tall
cylinder and letting the material pour into the
short, fat cylinder. Discuss the results.
 Use kites made when doing similarity-fly kites,
use hand sextant to measure angle, use trig to
calculate height of kite. (Students can measure
string as they wind it in).
 Simulate installation of in-ground pool…how much
soil to remove? How much concrete, etc.
Assessment Ideas
 Teacher
observations
Time
 20-25 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
6
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Algebraic
Expressions
and Simple
Equations
Standards/
Key Ideas/
Indicators
3.4.4A
3.7.7H
Guiding Questions
Essential Knowledge & Skills
What are some examples of
inverses in real life?
(on/off switch,
drive/reverse, etc.)
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What are some simple
algebraic expressions to
represent every day things?
(number of eyes /number of
people, number of
sides/number of triangles,
etc.)
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Use letters to represent
variables
Evaluate algebraic expressions
Use order of operations to solve
algebraic expressions
Understand the meaning of
vocabulary words used in
algebra (Monomial, binomial,
trinomial, polynomial, etc.)
Translate verbal phrases into
algebraic language
Prepare to solve an equation
Solve simple equations by using
division or multiplication
postulates
Solve two-step equations with
whole numbers, fractions, and
decimals
Use the distributive law with
variables
Solve equations with the
distributive law
Identify like or similar terms
Collect like terms and simplify
algebraic expressions
Solve equations with like terms
by using several operations
Solve word problems – one step
i.e. number, consecutive integer
Classroom Ideas
 Graphic organizer for key words used in
translating phrases into algebraic expressions
 Translate verbal problems into algebraic
equations
 In math journals, have students explain process
used in solving one-step equations, two-step
equations, equations with variable on both sides.
Assessment Ideas
 Teacher
observations
Time
 15-20 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
7
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Laws,
Equations, and
Inequalities
Standards/
Key Ideas/
Indicators
3.4.4A
3.7.7H
Guiding Questions
Why do we have the number
zero?
Essential Knowledge & Skills
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Identify and memorize field
properties used in solving
equations:
Additive Identity
Additive Inverse
Commutative Property
Property of Zero
Multiplicative Identity
Multiplicative Inverse
Associative Property
Distributive Property
Solve equations that have
variables on both sides
Solve equations containing
parentheses, like terms, and/or
the distributive law
Properties of Inequalities
Solve inequalities and graph the
solution sets
EXAMPLES:
X+5>2
2n – 7 13
Solve compound inequalities and
graph the solution set:
EXAMPLES:
5 2X – 9 7
2X + 2 -4 or
2X-5>10
Classroom Ideas
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Crossword puzzle for names of properties-clues
are examples of properties
Use properties to illustrate why x + 6 = 10 means
x = 4. (Use properties to prove steps used in
solving equations.)
Use examples of inequalities:
2x – 3 > 5
2x>8
x>4
Graph and check
Do several examples until students discover
when –X , reverse sign
Writing exercise: compare and contrast solving
equations and solving inequalities
Assessment Ideas
 Teacher
observations
Time
 12-15 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
8
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Geometry and
Measurement,
Part 1
Standards/
Key Ideas/
Indicators
3.4.4A
Guiding Questions
What are examples of
angles, parallel, and
perpendicular in real life?
Essential Knowledge & Skills
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Solve formulas and literal
equations
EXAMPLE: Using the formula
d= rt, solve for t when d = 200
and r = 50.
EXAMPLE: Solve the following
equation for x: ax + by = c.
Undefined terms: point, line and
plane
Define: collinear and coplanar
Sum of the interior angles of a
triangle = 180º
Study of triangles:
classifications of scalene,
isosceles and equilateral, acute,
right and obtuse
Define congruent triangles and
corresponding parts of a
congruent triangle
Study of quadrilaterals:
classification and properties of
parallelograms, rectangles,
rhombi, and trapezoids
Sum of the interior angles of a
quadrilateral = 360º
Solve word problems involving
polygons
Study of solids: classification of
prism, rectangular solid, pyramid,
right circular cylinder, cone and
sphere
Classroom Ideas
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Review if needed:
-types of lines (intersecting, parallel, and
perpendicular)
-naming angles
-degree measure
-types of angles (acute, right, obtuse,
straight, reflex, supplementary,
complementary, vertical, alternate interior,
alternate exterior, interior and
corresponding)
-simple closed curves (polygons and circles)
-definition of regular polygon
Use Venn diagram to illustrate relationships of
quadrilaterals (also tree diagram)
Crossword puzzle with terms and definitions
“Bingo”-write terms on game board, flashcard
with pictures to review terms
Have students plot coordinates for triangles or
quadrilaterals then have students name shapes
and give their definitions
Translate verbal phrases into algebraic
expressions. (“supplementary adds to 180º”)
Assessment Ideas
 Teacher
observations
Time
 15-20 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
9
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Coordinate
Plane and Venn
Diagrams
Standards/
Key Ideas/
Indicators
3.7.7B
Guiding Questions
Where are coordinates used
in real life?
Essential Knowledge & Skills
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Ordered number pairs and points
in a plane
Linear equations in two variables
using charts
Graph triangles and
quadrilaterals
Solve word problems with Venn
diagrams
Classroom Ideas
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Play “Battleship” on a coordinate plane.
Students plot ships on graphing paper and
opponent guesses coordinates.
Plotting vertices of 2-dimensional figures.
Name figure. Find perimeter and area.
Students create a drawing on graph paper, list
the coordinates, and then give coordinates for
another student to try and draw.
Students (in groups) list characteristics and
draw Venn diagram illustrating their group and
present their diagram to class.
Assessment Ideas
 Teacher
observations
Time
 3-5 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
10
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Probability and
Statistics
Standards/
Key Ideas/
Indicators
3.6.6A
3.6.6C
3.6.6D
Guiding Questions
What are your chances of
winning…’the lottery
sweepstakes?
Essential Knowledge & Skills
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How many possible phone
numbers?
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Evaluating simple probabilities
The probability of A or B, of Not
A, and of A and B
Counting principle and sample
spaces
Many-stage experiments
Factorials
Permutations
Read charts and graphs (bar
graphs, line graphs, circle graphs,
double bar graphs, and double
line graphs)
Collection of data and organize
tables, charts or graphs
Histograms
Determine and know the
significance of mean, median,
mode, and range
Classroom Ideas
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Find heights (anonymously) of class members
determine mean, median, and mode for students
in class.
Using NY #’s, lotto, casino gambling, to calculate
odds of winning. Use counting principle to
determine # of possibilities.
Use examples of sweepstakes (1 in 4 wins – if I
buy four, will I get one free?)
Collect data (ex. birth dates) from several
classes, graph data and compare
Graph results of sale [FFA citrus, Girlscout
cookies] using double/triple line, bar, circle
graphs
Take one of lottery games and calculate odds of
winning
Writing exercise: describe an example of an
unfair sample space
Assessment Ideas
 Teacher
observations
Time
 12-15 days
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
11
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Number and
Numeration
Operations
Standards/
Key Ideas/
Indicators
3.2.2A
3.2.2B
3.2.2C
3.3.3A
3,3,3D
Guiding Questions
How many different sets of
numbers can you identify?
Can you name a member of
each set?
Can a number belong to
more than one set?
Can numbers be rational and
irrational?
What are the properties of
the set of real numbers?
What is a monomial,
binomial, and trinomial?
How do you recognize and
combine like terms?
Using the rules of signed
numbers, how would you
apply them to adding and
subtracting polynomials?
How do you multiply and
divide a polynomial by a
monomial?
Essential Knowledge & Skills
Understand and use rational and
irrational numbers:
 Rational & irrational numbers
 Oorder of real numbers
 Know and apply the properties
of real numbers to various
subsets of number
(closure, prop. of 0, additive
identity, additive inverse, mult.
identity, mult. Inverse,
commutative, associative,
distributive)
 Scientific notation
Operations with monomials and
polynomials:
 Identify monomials, binomials,
trinomials
 Add/subtract like monomials
 Add/subtract polynomials
 Multiply monomials by
monomials, polynomials by
monomials, and binomials by
binomials
 Divide monomials by monomials
and polynomials by monomials
Factoring:
 Prime factorization
 GCF
 Factoring polynomials – GCF( )
 Factoring trinomials of the
form: ax + bx + c
Classroom Ideas
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Discuss real numbers and apply to word problems
Use Venn diagrams to illustrate real sets of
numbers
Given examples of numbers, students identify
the set to which they belong
Match properties with examples of properties
Flashcard games to help students recognize
monomials, binomials, and trinomials
In small groups, have students generate
examples of monomials with like and unlike
terms. Compare their lists with other groups to
add or revise.
Writing activity – explain why 5x and 5x can be
multiplied but not added
Progress from factoring numbers to variable
expressions
Review adding , subtracting, and simplifying
rational expressions
Have students explain the field properties used
in solving linear equations, ex. 2(x-5) + 3 = x + 7
Give students equations that were solved
incorrectly to identify where mistakes were
made and then to solve correctly. Trade with
partners to correct.
Assessment Ideas
 Teacher
observations
Time
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 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
12
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Number and
Numeration
Operations
(con’t)
Standards/
Key Ideas/
Indicators
Guiding Questions
How do you multiply a
polynomial by a polynomial?
How do you use
multiplication to simplify
algebraic expressions
containing grouping
symbols?
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
Use field properties to justify
mathematical procedures:
 Techniques for solving equations
and inequalities
 Solve linear equations with
integral, fraction, or decimal coefficients
 Solve literal equations
How do you determine the
GMF?
How do you factor
polynomials?
Can you identify the
properties used in solving
linear equations?
Math A Draft; Fall 1999
13
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Transformations
Standards/
Key Ideas/
Indicators
3.3.3B
3.4.4F
Guiding Questions
What is point and line
symmetry?
What are line and point
reflections?
What is translation,
rotation, and dilation?
Essential Knowledge & Skills
Recognize and identify symmetry and
transformations on figures:
 intuitive notions of line
reflection, translation, rotation,
and dilation
 line and point symmetry
Use transformations in the
coordinate plane:
 reflection in a line and in a point
 translations
 dilations
Classroom Ideas




Explore the letters of the alphabet for lines of
symmetry. Draw them. What are the
characteristics of those letters with more than
one?
Use points on a coordinate plane and apply the
rules of transformations
Use diagrams with various inscribed figures for
students to draw all the lines of symmetry
Identify and justify why it is the type of
transformation on the various diagrams
presented
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
14
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Geometry and
Measurement,
Part 2
Standards/
Key Ideas/
Indicators
3.4.4A
3.4.4E
3.5.5A
3.5.5F
Guiding Questions
Essential Knowledge & Skills
What are complementary,
supplementary, vertical and
adjacent angles and how do
you apply them to a given
situation?
Represent problem situations
symbolically by using algebraic
expressions, sequences,
geometric figures, and graphs.
 Recognize symbolic
representations of: infinity,
perpendicular, parallel, angle,
measure of an angle, congruent,
and similar
Study of triangles:
 Classification of triangles:
scalene, isosceles, equilateral,
acute, right, obtuse
 Sum of interior angles of a
triangle = 180º
 Median, altitude, and angle
bisector of a triangle
 Relationship between sides and
angles of triangles: sum of 2
sides is > than 3rd side, largest
angle of triangle is opposite the
longest side
 Properties of exterior angles:
ext. angle = sum of the 2
remote int. angles, ext. angle is
always > than either remote int.
angle
What special relationships
are formed when a
transversal intersects
parallel lines and how do you
apply them to a give
situation?
What are the various
characteristics of polygons?
Given two polygons, how can
you determine whether they
are congruent or similar?
How can you find the
missing angle (s) of a
polygon?
How do you find the area,
perimeter, or circumference
of a triangle, quadrilateral,
or circle?

Classroom Ideas

Review if needed:
-undefined terms: point, line and plane
-types of lines: intersecting, parallel, and
perpendicular
-collinear and coplanar
-angles
-simple closed curves: polygons, regular
polygons, and circles
-congruent triangles and corresponding parts
-reflexive, symmetric, and transitive
properties
-ways to prove two triangles congruent (SAS,
SSS, ASA, HL, AAS)
 Use word problems to solve side and angle
relationships with isosceles and equilateral
triangles
 Create classroom or individual glossaries of
geometric symbols and terms with information on
derivations and origins
 Using any triangle, examine the relationship
between the angles and sides.
 Have students find the measurements of missing
angles in different types of triangles and have
them develop the rules of exterior angles
 Have students divide a polygon into triangles to
determine the sum of the interior angles of a
polygon
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
15
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Geometry and
Measurement,
Part 2
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
What are the basic
geometric concepts and how
are they defined or
explained?
How do you prove two
triangles congruent?
What are the special
properties of an isosceles
triangle?
What is the Triangle Angle
Sum Theorem and how do
you apply it?
What are the properties of
special quadrilaterals?
Why is the sum of 2 sides
of a triangle greater than
the length of the 3rd side?
Essential Knowledge & Skills


Classroom Ideas
Assessment Ideas
Time
Formulas for sum of interior
and exterior angles of polygons
Solve word problems involving
polygons
Quadrilaterals:
 Classification and properties of
parallelograms, rectangles,
rhombi, squares, and trapezoids
Solids:
 classification of prism,
rectangular solid, pyramids,
right circular cylinder, cone and
sphere
Apply formulas to find measurements
of length, area, volume, weight, time
and angle in real world contexts
 perimeter of polygons
 circumference of circles
 area of polygons and circles
 volume of solids
What is the relationship
between the measures of
angles of a triangle and the
sides opposite them?
What is an exterior angle of
a triangle?
Math A Draft; Fall 1999
16
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Geometry and
Measurement,
Part 2
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
How does the measurement
of an exterior angle relate
to the measurement of the
interior angles?
How do you find the sum of
the interior and exterior
angles of polygons?
Math A Draft; Fall 1999
17
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Similarity and
Measurement
Standards/
Key Ideas/
Indicators
3.5.5B
3.5.5C
3.5.5H
3.5.5I
Guiding Questions
How do you solve a
proportion involving an
algebraic expression?
What is a direct variation
and how do you find the
solution?
Given two similar triangles,
how do you find the missing
length of a side?
How does the ratio of the
perimeters of two similar
polygons compare to the
ratio of their corresponding
sides? (area, volume)
What is the constant of
proportionality?
What comparisons can be
made to show that two
triangles are similar?
(extend to polygons)
Essential Knowledge & Skills
Similarity
 Review ratios
 Solve proportions
 Solve percent problems
 Solve direct variation problems
Use geometric relationships in
relevant measurement problems
involving geometric concepts
 Find lengths and altitudes of
corresponding sides of polygons
 Similar polygons
 Comparison of volumes of
similar solids
 Triangle Proportionality
Theorem
Choose and apply appropriate units
and tools in measurement situations
 Convert equivalent measures
within metric measurement
system
 Convert equivalent measures
within English measurement
system
 Direct and indirect measure
Classroom Ideas





Using word problems that mirror real life
contexts, have students find the ratio of
perimeters and areas.
Have students measure the height of trees: by
measuring shadow of tree, their height, and
shadow AND/OR by using mirrors to find the
distance and forming similar triangles.
Map drawing and scale drawing
Categorize polygons by similarities
Using rulers and both English and metric
systems of measurement
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
How is the triangle
proportionality theorem
related to similar triangles?
Math A Draft; Fall 1999
18
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Similarity and
Measurement
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
How would you relate real world situations to similar
triangles?
What are the units in the
English and metric systems
of measurement?
Why do you need to know
the relationship between
the two?
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
Role of error in measurement and its
consequence on subsequent
calculations involving:
 Perimeter of polygons
 Circumference of circles
 Area of polygons and circles
 Volumes of solids

Percent of error in
measurements
Why can’t you combine
inches and centimeters?
Why is it important to
convert to only one unit of
measurement?
Math A Draft; Fall 1999
19
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Construction
and Locus
Standards/
Key Ideas/
Indicators
3.4.4F
3.4.4H
Guiding Questions
What is locus?
How would you describe the
seven fundamental loci?
What is the process for
finding the points where
two or more loci intersect?
What are the basic
constructions and their
justifications?
How would you apply your
construction skills to
construct other geometric
figures? (i.e. equilateral
triangle, inscribe,
circumscribe...)
Essential Knowledge & Skills
Justify the procedures for basic
geometric constructions
 Do basic constructions:
congruent line segment and
congruent angle, bisect line
segment and angle,
perpendicular lines and
parallel lines.
Develop and apply the concept of
basic locus to compound loci.
 Define locus.
 Find the locus at a fixed
distance from a point.
 Find the locus at a fixed
distance from a line.
 Find the locus equidistant
from two points.
 Find the locus equidistant
from two parallel lines.
 Find the locus equidistant
from two intersecting lines.
 Find compound loci.
Classroom Ideas



Students use written language and/or graphic
representations to describe/illustrate problemsolving methods
Students show understanding of mathematical
concepts using manipulatives
“Round Robin” activity - students in small groups
practice all constructions – one student begins a
construction and passes on paper for next
student to do next step , etc. until completed.
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
20
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Coordinate
Geometry
Standards/
Key Ideas/
Indicators
3.4.4J
3.5.5G
3.7.7B
3.7.7C
3.7.7E
Guiding Questions
How do you graph a linear
equation?
How do you determine the
slope and the intercept of a
given linear equation?
Using a set of real data,
how do you write the
equation of a line?
How do you solve a system
of linear equations and
inequalities graphically?
How do you solve a system
of linear equations
algebraically?
How do you apply you
knowledge of system of
equations to solve real world problems?
How do you find the area of
a figure formed by a given
set of vertices?
What are the distance,
midpoint and slope
formulas?
Essential Knowledge & Skills
Relate absolute value, distance
between two points, and the slope of
a line to the coordinate plane.
 Using the distance formula
and/or absolute value, find the
length of a segment.
 Using the midpoint formula, find
the midpoint of a line segment.
 Find the slope of a line.
 Graph a line using slopeintercept form.
 Graph a system of linear
equations in two variables, list
solution, and check the answer.
 Graph a system of inequalities.
 Write the equation of a line in
two forms: point slope form and
slope-intercept form.
 Compare parallel and
perpendicular lines:
-Parallel lines have the same
slope
-Perpendicular lines/one slope
is the negative reciprocal of
the other
 Algebraic solution of systems of
simultaneous linear equations by
using the addition and/or
subtraction method.
Classroom Ideas



Randomly put class scores on board from
assignments and ask students to calculate
mean, median, made, range.
Use graphing calculators to show 3 cases of
systems
1. if they intersect
2. if they’re parallel
3. or if they coincide
On graph paper, students draw a variety of
irregular shapes to pass to peers to determine
the area
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
21
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Coordinate
Geometry
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
How is the slope related to
the orientation of lines?
What is the point - slope
form of a line?
How would you compare and
contrast point - slope form
and slope- intercept form of
a line?
How can you determine the
roots of a quadratic by
using a graph?
How do you find the vertex
and the axis of symmetry of
a quadratic equation?
What is the process for
solving a linear quadratic
system and how do you
determine its solution?
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
 Algebraic solution of systems of
simultaneous linear equations by
the substitution method.
 Solution of word problems using
systems of linear equations.
 Graph the parabola (quadratic
equation) Y = ax + bx + c
 Recognize the roots of the
parabola.
 Using the graph of the parabola,
find the vertex point and axis of
symmetry.
 Using the equation x = -b/2a,
find the axis of symmetry.
 Graph a quadratic-linear system
of equations. (parabola, line)
 Algebraically solve a quadraticlinear system of equations.
 Solve word problems with
quadratic equations.
 Model real-world problems with
systems of linear equations
and/or inequalities.
Math A Draft; Fall 1999
22
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Radicals and
Right Triangle
Trigonometry
Standards/
Key Ideas/
Indicators
3.3.3A
3.5.5D
3.5.5E
Guiding Questions
What is a radical?
How do you know the
difference between a
perfect root and a nonperfect root?
What does it mean to be in
simplest radical form?
How do you add, subtract,
multiply and divide radical
expressions?
How do you solve quadratic
equations and related word
problems by factoring?
What is the zero product
property and when is it
used?
Essential Knowledge & Skills
Operations with radicals
 Finding rational square roots
 Finding irrational square roots
 Simplifying radicals
 Addition and subtraction of
radicals
 Multiplication and division of
radicals
 The quadratic formula-solving
equations
 Solving word problems using
quadratic equation
Use trigonometry as a method to
measure indirectly.
 Right triangle trigonometry
1) Special Right Triangles:
a) 30º - 60º - 90º
b) 45º - 45º - 90º
2) The Pythagorean Theorem.
3) Using trigonometry to solve
word problems
Classroom Ideas


Group or Individual activity:
1. Give a word problem and an answer
2. State whether answer is right or wrong
3. Work through problem and verify if their
hypothesis is correct. Note: Can give an
answer that needs to be rejected to see if
student(s) remembers to follow through with
check.
Lab activity using yarn to find lengths of sides of
triangles.
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Other than factoring, how
can you solve quadratic
equations?
How do you apply the
concepts of similar triangles
to right triangles?
Math A Draft; Fall 1999
23
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Radicals and
Right Triangle
Trigonometry
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
How would you apply the
Pythagorean Theorem to
special quadrilaterals?
What is the ratio of the
lengths of the sides of the
45º-45º-90º & 30º-60º- 90º
triangles and how can they
be related to real - world
situations?
Given right triangle ABC,
what are the sine, cosine
and tangent of each acute
angle?
How would you find a
missing side of a right
triangle, using an
appropriate trigonometric
function?
How are the angles of
elevation and depression
trigonometrically applied?
Math A Draft; Fall 1999
24
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Measurement
and
Uncertainty
Standards/
Key Ideas/
Indicators
3.6.6A
3.6.6E
3.7.7G
Guiding Questions
What is the meaning of
statistics and how is it
used?
How do you calculate the
mean, median, and mode for
a set of data?
How do you determine
percentile / quartile?
What does probability mean
to you?
How do you use probability
to predict the chance of an
event occurring?
How do you find the
probability of dependent
and independent events?
What is the counting
principle and how do you use
it to determine the number
of outcomes of a given
event?
Essential Knowledge & Skills
Classroom Ideas
Use statistical methods including the
measures of central tendency to
describe and compare data.
 Measures of central tendency:
mean, median, and mode.
 Quartiles and percentiles
 Review if needed:
-collecting and organizing data: sampling,
tally, chart, frequency table, circle graphs,
broken line graphs, frequency histogram,
and cumulative frequency histogram.
-sample spaces, counting principle, and tree
diagrams
Determine probabilities, using
permutations and combinations, tree
diagrams
 Evaluate simple probabilities
 Review factorials, permutations,
& combinations
 Define empirical and theoretical
probabilities








Use calculator to review factorials,
permutations (nPn and nPr), combinations nCn
and nCr)
Explore empirical and theoretical probabilities
through word problems
Randomly put class scores on board from
assignments and ask students to calculate
mean, median, made, range.
Make a histogram of class mean; continue
through out the year for complete histogram
Store data on computer, at end of year
(semester) extend to calculating percentiles,
quartiles, etc.
Drawing Venn diagrams
Use students to physically show different ways
of lining up.
Making tree diagrams related to age
appropriate situations (clothing, cars)
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
What does permutation
mean?
Math A Draft; Fall 1999
25
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Measurement
and
Uncertainty
(con’t.)
Standards/
Key Ideas/
Indicators
Guiding Questions
Essential Knowledge & Skills
Classroom Ideas
Assessment Ideas
Time
When are two events
mutually exclusive?
How do mutually exclusive
and intersecting events
differ?
What is the compliment of
an event?
How do you determine the
probabilities of events with
and without replacement?
What is a combination and
how does it differ from a
permutation?
Math A Draft; Fall 1999
26
MATH
REGIONAL PRIORITIZED CURRICULUM
MATH A Draft
Topic
Logic
Standards/
Key Ideas/
Indicators
3.1.1A
3.1.1B
3.1.1D
Guiding Questions
What is an open and closed
sentence?
What is the difference
between a replacement and
a solution set?
What does negation,
conjunction, disjunction,
conditional, and
bi-conditional mean?
After reading a sentence,
how do you translate the
sentence into symbolic logic
notations?
What does logically
equivalent mean?
Essential Knowledge & Skills
Simple Proofs
Classroom Ideas

Truth value of simple sentences
 Closed sentences

Replacement set and solution
set
 Negations
Truth values, compound sentences,
and symbolic representation
 Conjunction
 Disjunction
 Conditional
 Biconditional
 Negation
Related conditional and truth values
 Converse
 Inverse
 Contrapositive

“Commercials” – Ask students when watching T. V.
to pay close attention to the commercials. Pick
out and write down any conditional statements
you hear. Share statements and write the
converse, inverse, and contra-positive of each
conditional. Compare these statements to
original, has it changed the meaning of the
commercial? (Variation - Tape commercials and
do activity in class.)
Logic Puzzles
Assessment Ideas
Time
 Teacher
observations
 Class discussions
 Journal entries
 Classroom
assignment rubrics
 Quizzes/tests
(Should incorporate
open-ended problemsolving situations
requiring students to
show work and/or
explain the
mathematics they
used)
Math A Draft; Fall 1999
27