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Pre-K Through 12 Mathematics Curriculum

  Pre-K Kindergarten Primary Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Pre-algebra 1.5 years
Grade 6/7		 Pre-Algebra 1 yr
Grade 6/7		 Algebra 1
Grade 7/8		 Geometry Advanced Algebra FST PDM   ADDITIONAL
COURSES:
AP Calculus AB,
AP Calculus BC,
AP Statistics,
Linear Algebra
Time & Money     Intro to telling time:
analog and digital; on the
hour; intervals; identify
coins-by name and value
Count groups of coins by
1s, 2s, 5s, 10s		 Money: identify, sort,
count coins; add coins
up to 50 cents; analog &
digital clocks (1/2 hour
intervals)		 Counting money; making
change; telling time		 Review, assess, reteach
time & money concepts		 Money operations; time Money operations; time   Integrated into problemsolving;
I=prt; Stock
Market (7th gr)		 Integrated into problemsolving Word
problems;exponential
growth		   Stock project, word problems,
exponential growth		 Exponential growth of money      
Counting Counting orally:
dice, calendar,
games		 Recognizing events
happening in sequential
order; counting by 2’s,
5’s, 10’s; Mathland		 Counting forward and
backwards 2’s, 5’s, 10’s		 Counting by 2’s, 5’s, 10’s
(count 1-120)		 Skip counting; counting by
3’s, 4’s, 10’s, 20’s		 Skip counting;
multiplication		 Skip counting; Number systems:
roman numerals,binary
numbers		 Decimals; square roots GCF, LCM, prime
factorization, multiples,
decimals; square roots		 GCF, LCM, prime
factorization, multiples,
decimals; square roots		 Multiples & factors   Introduction to complex
numbers		 Complex numbers Proofs involving integers Number Sets  
Computation     Addition & subtraction
(including computations
with 10); doubling
numbers; square roots;
ratio & proportion;
Begin to use equations
to describe a math
operation		 Addition & subtraction to
10; open equations; skip
counting		 Subtraction, addition;
skip-counting; place-value
& regrouping addition		 Plus & minus; placevalue;
multiplication
by repeated addition;
Addition up to 4 digit
numbers; subtraction
with re-grouping;
multiplications facts to 10;
concept of division		 4-digit addition &
subtaction with
borrowing and
carrying; multiplication:
different methods;
mental math		 Multiplication and long
division; fraction &
decimal operations		 Operations for whole
numbers; math facts;
money operations; adding
& subtracting on number
line; order of operations;
operations with negative
numbers; exponents,
powers of 10 and of
negative numbers		 Operations for whole
numbers; & fractions;
math facts; adding &
subtracting on number
line; order of operations;
operations with negative
numbers; exponents,
powers of 10; absolute
value		 Basic computation; order
of operations; operations
with fractions; square
roots; exponents		 Positive & negative
numbers; order of
operations; absolute value
on number line; simplifying
radicals; exponents		 Side measures; angles, area,
perimeter,		 Square roots;absolute value;
rational functions; complex
numbers		 Complex numbers;
combinatorics		      
Reading, Writing,
Understanding,
Numbers		 Number
recognition; write
numerals 1-10		 How to write (draw)
numerals		 Understand the meaning
of two digit numbers,
i.e. a digit’s placement
determines its value,
intro to three digit
numbers		 Number recognition; odd
& even; place-value: 1,
10, 100		 Place value Place value   Reading large numbers
& decimal numbers		 Writing numbers like
millions		 Writing numbers like
millions; Associative,
commutative, distributive,
transitive properties		 Associative,
commutative,
distributive, transitive
properties		 Associative, commutative,
distributive, transitive
properties		 Associative, commutative,
distributive, transitive
properties; proofs; conditional
statements; logic		 Associative, commutative,
distributive, transitive
properties		 Solving and factoring over
different number sets		 Mathematical induction Axioms,
Properties,
Theorems, Proofs		  
Number Sense Estimate number
of objects in
container; 1-1
correspondence		 1-1 Correspondence used
for counting; comparing
height, weight, shapes;
pre-adding; number
appearance; arrangement
of objects		 Compare and contrast
numbers; explore greater
than, less than, equal
to through estimation
activities, counting
games, etc.		 Determine number in a
group; more vs. less vs.
equal; fast vs. slow		 Predicting and estimating;
compare & order numbers		 Great than; lesser than;
equal to; estimating		 Estimates Place value, estimation,
negative numbers		 Number sense; scientific
notation		 Number sense; scientific
notation; estimation &
reasonableness		 Square roots; estimation
& reasonableness		 Scientific notation;
exponents; estimation;
radicals		 Estimation; nth terms Asymptotic behavior;
Estimation		 Asymptotic behavior;
Estimation; conceptualizing
infinity		 Conceptualizing infinity;
Asymptotic behaviour;
estimation		    
Reasoning &
Problem-solving		   Logical thinking: concept
of 1 more; sorting;
distinguishing between
groups; more vs. less		 Explore a variety of
math story problems;
practice problem solving
strategies i.e. draw
pictures, diagrams, lists,
etc.		 Story problems involving
addition & subtraction;
reading & following
directions; sorting
treasures by 1 or 2
attributes		 Problem-solving
strategies; logical thinking;
classification and sorting;
making groups		 Strategies such as: Make
a list; Draw a picture or
diagram; logical thinking;
working backwards		 Story problems; Math
Olympiads		 Math Olympiads; logic
problems		 Recognizing key words;
logic puzzles, Math
Olympiads		 Recognizing key words;
logic puzzles, Math
Olympiads		 Problem-solving; writing
verbal models; interpret
word problems into
algebraic equations		 Problem-solving
strategies; growth &
decay (exponents); word
problems		 Logic puzzles; problemsolving
strategies		 Problem-solving strategies;
direct and inverse variation		 Problem-solving strategies Problem-solving strategies;
logic, truth tables		    
Patterns, Sequences,
Series		   Recognize, create,
extend patterns		 Build, repeat and extend
patterns in two and three
dimensions.
Explore patterns in our
base ten number system,
counting by 2’s, 5’s, 10’s		 Patterns on the 100-
board: create and label		 Pattern & sequences;
extending and
transforming patterns		 Skip counting   Patterns & sequences Sequences Sequences; perfect
squares; fractals;
Fibonacci		 Fibonacci series;
triangular numbers;
perfect numbers		 Exponential patterns Inductive logic; basic
sequences; nth term		 Series Arithmetic and geometric;
sequences (honors)		 Sequences & series    
Measuring     Explore non-standard
and standard
measurement; linear,
solids and liquids through
real life projects, i.e.
cooking, arts and crafts,
etc.		 Explore non-standard
and standard
measurement; linear,
solids and liquids
through real life projects,
i.e. cooking, arts and
crafts, etc.		 Measurement: length,
weight		 Area, perimeter, volume,
length as it relates to
fractions		 Length, weight,
temperature		 Inches, cm, temperature Customary unit conversion Dream Backyard Project;
area; perimeter; volumev		 Area; perimeter   Area, length, angles,
perimeter		 Distance, magnitude; 2D
representation		        
Fractions &
Decimals		     Intro to fractions
through measurement
explorations and use of
decimal in money		 Introduction to basic
fractions & decimals in
money		 Fractions: 1/2, 3/4, 1/3,
1/4		 Explore fractions Adding and subtracting
fractions		 Fractions, decimals,
percents (how they
relate); the four
operations		 Ratios; rates Ratios; rates; computation;
place value; converting		 computation, place
value, converting		 Fractions: order,
compuations		 Similar triangles; ratios Simplifying rational
expressions; complex
fractions; rational functions		 Rational functions Partial fractions Rational
Functions		  
Graphing     Intro to data collection
and how to record data
on a simple bar graph		 Intro to data collection
and how to record data
on a simple bar graph		 Bar graphs, plot graphs How to record/interpret
data on a graph		   4 quadrants; types of
graphs		 Graphing Line plots, bar graphs,
scatter plots; coordinate
graphing		 Line plots, bar graphs,
scatter plots; coordinate
graphing		 Graphs & solving;
graphing inequalities		 Graphing shapes; parallel &
perpendicular lines		 Graphing quadratics;absolute
value functions, piecewise
functions; systems of linear
inequalities; parent functions		 all elementary functions;
parent functions; parametric
equations (honors)		 Trigonometric, polar,
polynomial functions;
parametric equations		    
Transformations     Explore symmetry in art
and nature		   Introduction to concept of
symmetry		 Congruency, symmetry Identify symmetrical
objects, lines of
symmetry		 Flip, slide, & rotational
transformations		       Graphing lines Transformations Transformations; parent
functions		 Transformations; parent
functions		 Transformations; parent
functions		    
Statistics &
Probability		     Collect, sort and interpret
data using graphs and
charts		 Gathering, organizing,
reporting data; drawing
conclusions; games of
chance; dice, coins,
spinners; simple
probability		 Collection, analysis,
interpretation graphing
data (bar & plot graphs);
probability		 Probability; predicting
results		 Probability; data
collection; predicting
results; displaying
data, graphs		 Statistics: data collection,
displays & analysis;
mean, median & mode		 Line plots, bar graphs,
scatter plots; probability		 Line plots, bar graphs,
scatter plots; probability;
Counting Principle;
permutations; mean,
median, mode, range		 Line plots, bar graphs,
scatter plots; probability;
Counting Principle;
permutations; mean,
median, mode, range		 Exploring data;picture
graphs, pie charts, scatter
plots; linear equations
from points; matrices
(arrays); mean, median,
mode		   Regression, scatter plots, data
analysis		 Descriptive & inferential
statistics; probability;
central tendency, variance;
distributions; hypothesis
testing; [research design;
density curves; chi-square
(honors)]		      
Equations &
Inequalities		     Intro on how to write
equations; vertically and
horizontally		 Cover each number
in a simple equation
and solve for it; writing
equations using + and
-; equations with 2 or 3
terms added		 Equations Basic equation solving;
multi-operation equations		 Fact families;
prealgebra (variables)		 Equations with 2 or 3
terms added		 Basic equation solving Basic equation solving;
solutions of inequalities		 Equations & inequalities,
2 step, variables on both
sides		 Solving equations;
systems of equations;
solving inequalities;
expression vs. equation		 Translating shapes to
equations		 Radical equations; rational
equations		 Solving and graphing linear &
quadratic inequalities		 Systems of equations; linear
programming		    
Geometry Reorganizing
geometric shapes		   Explore two and threedimensional
shapes: i.e.
squares vs. cubes, circle
vs. spheres, etc. Identify
basic two-dimensional
shapes; square,
rectangle, triangle,
diamond, circle, oval, etc.		 Record 2D patterns on
grid paper; classification
of geometric shapes by
number of sides		 Geometric shapes,
definitions, concrete
modeling, 3D shape
comparison		 Geometric investigations:
shapes, symmetry;
patterns in fractions:
rhombus, trapezoid,
hexagon		 Classifiying shapes;
build polyhedra;
division, avg, area,
perimeter		 Polygons, angles,
tesselations, circles;
shapes classified
by number of sides;
perimeter, area, volume		 Angles, lines, perimeter,
area, volume;
Pythagorean Theorem;
identifying shapes		 Angles, lines, perimeter,
area, volume;
Pythagorean Theorem;
identifying shapes		 Pythagorean theorem;
geometric constructions;
polyhedra		   Angles: measures,
properties; congruence;
similarity; construction;
perspective; area,
volume, distance;
Pythagorean Theorem;
circles & arcs;parallel line
relationships; right triangle
trigonometry		 Distance with line segments;
magnitude		 Right triangle & circular
trigonometry; trigonometic
functions & graphs; unit
circle; identities;solving
trigonometric equations; Law
of Sine & Cosines		 Analytic geometry, 3D; polar
equations; right triangle
& circular trigonometry;
trigonometric functions &
graphs; unit circle; identities;
Law of Sines and Cosines;
Vectors		 Trigonometry  
Functions             Function tables Function tables     Introduction to functions;
domain & range		 Linear and beginning
quadratic functions		   Functions; domain,
range; parent functions;
transformations		 Domain, range, operations,
inverses; all elementary
functions		 Parametric equations    
Lines                   basic linear equations linear equations Line equation forms:
slope-intercept, pointslope,
standard; find
equation of line through
two points		 Linear equations; parallel &
perpendicular lines; distance,
midpoint, slope		 Linear programming;
linear functions; linear
approximations		 Linear functions, systems of
equations (honors)		 Systems of equations, linear
programming		    
Quadratic &
polynomial functions		                       Quadratics; multiplying
polynomials; factoring
quadratics		   Factoring; roots of quadratic
equations; polynomials;
quadratic approximations		 Polynomials: long
division, synthetic division;
Fundamental Theorem of
Algebra		      
Exponential
& logarithmic
functions		             Square numbers Scientific notation;
squares and cubes		       Rules of exponents; basic
graphs		   Review rules of exponents;
exponential & logarithmic
functions		 Review exponential &
logarithmic functions		      
Conics                       Parabolas Circles (Regular): parabolas;
(honors): parabolas, ellipses,
hyperbolas		 Parabolas Parabolas, ellipses,
hyperbolas; rotations in
parametric, rectangular, and
polar form		    
Matrices                       Basic addition,
subtraction, multiplication;
data entry		   Matrix operations;
determinants, solving systems
by matrix inverse method		 Honors: Matrix operations;
determinants, solving
systems by matrix inverse
method		 Review of Matrix operations;
determinants, solving systems
by matrix inverse method