Download MATH PHILOSOPHY

MATH PHILOSOPHY
In order to become life-long problem solvers with an understanding of the relevance to real
life situations, our students need to have a solid foundation of math which will meet the
NJCCCS. By providing a positive approach, we will build confidence to attain success for
all learners at all levels. Educators will challenge students to use mathematical concepts in
real life situations by offering a variety of problem solving strategies. Educators will use a
spiraling curriculum to build on concepts that are developmental. Through the sequential and
broad-based study of mathematical concepts, all students will reach a level of mathematics to
prepare them for a rapidly changing technological society. Because of this rapid change,
family involvement will be encouraged so parents too can build confidence in order to assist
their children.
SIXTH
GRADE
CURRICULUM
Numeration
Standard 4.1 Number and Numerical Operations
Standard 4.5 Mathematical Processes (Problem Solving)
Reading, writing, and comparing whole numbers, negative numbers, fractions, decimals, and
percents; reading, writing, and interpreting integer powers of 10; converting between
scientific and standard notation and among fractions, decimals, percents, and mixed
numbers; renaming fractions and mixed numbers in simplest form.
Goal 1: Understand the meanings, uses, and representations of numbers with and
without the calculator.
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Positive and negative powers to 10
Add and subtract positive and
negative numbers
Place value; whole numbers,
decimals
Scientific notation
Square roots
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Appropriate use of fractions, decimals,
percents
Compare and order fractions and mixed
numbers
Compare, order, read, and write numbers
through trillions; millionths
Goal 2: Understand equivalent names for numbers with and without the calculator.
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Equivalent fractions, mixed
numbers, decimals, percents
Convert numbers in exponential to
standard notation
Find equivalent fractions
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Rename mixed numbers as fractions;
express in simplest form
Goal 3: Understand common numerical relations.
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Compare and order positive and
negative numbers
Properties of number systems and
rational numbers
Rename improper fractions as
mixed numbers or whole numbers
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Fractions to express probabilities
Put numbers between 0 and 1 in decimal
and exponential notation
Operations and Computation
Standard 4.1 Number and Numerical Operations
Standard 4.5 Mathematical Processes (Problem Solving)
Using algorithms for basic operations with whole numbers, fractions, and decimals; using
mental arithmetic to compute exact answers and to estimate; performing operations with
integers and with numbers in scientific notation; solving problems using unit rates and
ratios; solving proportions; rounding to any specified place adding and subtracting fractions
and mixed numbers; multiplying and dividing fractions; finding least common multiples,
greatest common factors, and prime factors.
Goal 1: Compute accurately with and without the calculator.
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Multiply with fractions, decimals,
and percents
Find reciprocal of a number
Find squares of numbers and
square roots
Put fractions in simplest form
Add, subtract, multiply, and divide
decimals
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Add and subtract positive and negative
numbers
Add and subtract fractions
Find percent of a number
Rename fractions as decimals
Goal 2: Make reasonable estimates.
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Estimate products of decimals and
whole numbers
Estimate square roots
Estimate sums of fractions
Estimate percents and fractions of
a circle
Estimate a fraction and a percent of
a whole
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Estimate products and quotients of
fractions with positive and negative
numbers
Estimate products of decimals
Round decimals to a given place
Estimate quotients: whole numbers;
decimals
Goal 3: Understand meanings of operations.
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Calculate exponents and multiples
of 10 (scientific notation)
Use mental arithmetic: squares
and square roots
Multiply or divide by powers of 10
Extend multiplication and division
facts
Find least common multiple;
greatest common factors
Determine multiples of numbers
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Find prime and composite numbers
Identify dividend, divisor, quotient,
remainder
Use order of operations
Apply distributive property
Convert data tables to fractions and
percents
Find common denominators
Multiply and divide fractions and mixed
numbers
Patterns, Functions, and Algebra
Standard 4.3 Patterns and Algebra
Standard 4.5 Mathematical Processes (Problem Solving)
Recognizing, continuing, and describing complex patterns; finding the nth term in a
sequence; using variables and open number sentences to represent problem situations;
writing equations to fit given tables of number; evaluating algebraic expressions; solving
linear equations; representing linear functions as equations, in tables and graphs, and
verbally as rules; understanding and applying the order of operations and the distributive
property.
Goal 1: Understand patterns and functions.
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Find a pattern and continue a
number sequence
Use multiplication patterns
Apply formulas and rules in tables
Calculate formulas for distance and
speed
Calculate formula for finding an
average
Utilize computer spreadsheets
using formulas
Calculate and solve problems using
formulas for area and volumes
Pythagorean Theorem
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Use, relate, and apply formulas and
number patterns to solve problems
Solution sets of inequalities
Rewrite expressions using the distributive
property
Calculate, identify, and apply rates of
change
Compare rates (unit prices)
Find Equivalent ratios
Compare ratios
Goal 2: Use algebraic notation to represent and analyze situations and structures.
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Use variables to state the properties
Substitute a given value and
evaluate expressions
Write number sentences: relation,
operation, and grouping symbols
Write and solve simple equations
(open sentences)
Use order of operations
Simplify and solve equations
Evaluate and write algebraic
expressions for word problems
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Use substitution to evaluate formulas for
given values
Find, compute, and apply ratios
Apply rates as comparisons, word rules,
formulas, tables, and graphs
Create rate tables and find per-unit rates to
solve problems
Develop and apply rules for operations for
positive and negative numbers
Solve Venn diagram problem
Geometry
Standard 4.2 Geometry and Measurement
Standard 4.5 Mathematical Processes (Problem Solving)
Comparing and contrasting properties of 2-dimensional and 3-dimensional figures;
understanding congruence and similarity; visualizing, describing, and using translations,
reflections, rotations, and size-change transformations; using formulas to compute areas,
volumes, perimeters, circumferences, and surface areas; measuring, drawing, and classifying
angles; identifying angle relationships in triangles and quadrilaterals, in parallel lines cut by
a transversal, and in intersecting and perpendicular lines; understanding and applying basic
concepts in topology; classifying tessellations.
Goal 1: Investigate characteristics and properties of two- and three-dimensional
geometric shapes.
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Congruence
Regular polygons
Circle; interior, sector, radius,
diameter
Descriptions and properties of
polygons
Types of triangles and
quadrilaterals
Construct polygons using tools
Ratios and corresponding side and
angles of similar polygons
Rectangular prisms, cylinders,
spheres
Pythagorean Theorem: meaning
and proof
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Midpoint of a line segment
Endpoints and midpoints: lines, line
segments, rays
Parallel and perpendicular lines
Transversals
Types of angles
Sum of the measures of interior angles of a
triangle
Relationships between angles formed by
two parallel lines and a transversal
Relationships among angles and sides of a
parallelogram
Goal 2: Apply transformations and symmetry in geometric situations.
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Tessellations
Isometric transformations:
reflections, translations, rotations
Symmetry: line, rotation, point,
order of rotation symmetry
Cross sections of solids: cube,
cylinder, cone, pyramid, prism,
torus
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Topological transformations: genus,
properties, equivalence
Perspective drawing
Enlargements, reductions, and similar
figures
Measurement and Reference Frames
Standard 4.2 Geometry and Measurement
Standard 4.5 Mathematical Processes (Problem Solving)
Measuring and estimating length, area, volume, weight, and capacity; converting and
computing with common units of measure; creating scale drawings.
Goal 1: Understand the systems and processes of measurement; use appropriate
techniques, tools, units, and formulas in making measurement.
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Use estimation strategies
Draw, classify; estimate and
measure angles
Use area and notation for square
units
Find perimeter, circumference, and
area
Compare measures of volume and
capacity
Find volume and notation for cubic
units
Measure to nearest gram
Measure to find sum of angles in a
polygon
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Measure length in US customary and
metric
Measure and draw line segments
Fractions and linear measure
Equivalent measures
Highest/lowest elevations
Measure in fractions of inches
Fractions, decimals, positive and negative
numbers on the number line
Time equivalents
Convert units of time
Temperature change and negative numbers
Celsius/Fahrenheit equivalents
Goal 2: Use and understand reference frames.
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Locate, plot, and read ordered pairs on a coordinate grid
Use parts of map
Data and Chance
Standard 4.4 Data, Analysis, Probability, and Discrete Mathematics)
Standard 4.5 Mathematical Processes (Problem Solving)
Expressing probabilities as fractions, decimals, and percents; using tree diagrams to analyze
simple probabilistic situations; understanding that the sum of the probabilities for all
possible outcomes of an experiment is 1; making predictions based on theoretical
probabilities and understanding why actual outcomes may differ from predicted outcomes;
constructing and interpreting circle graphs; understanding how changing the scale on the
axis affects a graph; using measures of central tendency (mean, median, mode) to
characterize data sets; understanding how changes in a data set may affect the mean,
median, and mode; formulating a question, carrying out a survey or experiment, recording
data, and communicating results.
Goal 1: Select and create appropriate graphical representations of collected or given
data.
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Analyze shapes and graph data on
coordinate grids
Use data from a diagram and a
table
Collect data
Match line plots with statements
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Use and interpret tree diagrams
Construct stem-and-leaf plots
Use computer spreadsheets
Convert data to fractions/percents
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Identify and use landmarks: minimum,
maximum, mean, median, mode, range
Understand the effect of sample size on
outcome distribution
Compare mean and median
Goal 2: Analyze and interpret data.
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Collect, analyze, and display data
Use data to evaluate a diagram
Construct, read, and interpret
graphs
Interpret and analyze misleading
ways of presenting data
Discuss and interpret Venn
diagrams
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Goal 3: Understand and apply basic concepts of probability.
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Vocabulary and concepts of
probability
Probability for situations with
equally-likely outcomes
Tree diagrams to find expected
outcomes
Fair and unfair games
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Strategies for guessing on multiple-choice
tests
Probability when rolling number cubes
Estimate chances of various outcomes of
an event