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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