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Mathematics and the World We Live In

Key	Numbers and Operations
M	Identify the place value of a given digit.
I	Develop meaning for perfect squares (e.g., 1, 4, 9, and 16).
I	Develop meaning for square roots.
I	Use exponential notation for powers of whole numbers.
I	Use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs).
A	Represent numbers using a variety of equivalent forms (i.e., mixed numbers, fractions, decimals, percents, and integers). http://www.mathgoodies.com/puzzles2004/ http://www.coolmath4kids.com/calculators/alcohol.html http://www.coolmath4kids.com/calculators/percentage.html http://www.coolmath4kids.com/calculators/salestax.html http://www.gamequarium.com/geometry.html
A	Compare rational numbers using the appropriate symbol (<, >, and =). http://www.gamequarium.com/math.htm
A	Connect rational numbers to locations on a number line.
A	Connect percents greater than 100 and percents less than one to real-world situations.
A	Use ratios to represent quantitative relationships.
D	Understand and use ratios and proportions to represent quantitative relationships.
A	Identify the opposite and the reciprocal of a rational number.
D	Use concrete, pictorial, and symbolic representations for integers, including locations on a number line.
D	Apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime numbers, prime factorization, and relatively prime).
A	Identify prime and composite numbers up to 50. http://www.mathgoodies.com/puzzles2004/ http://www.coolmath4kids.com/calculators/prime.html http://www.gamequarium.com/division.html
A	Compute efficiently and accurately with whole numbers, fractions, and decimals. http://www.coolmath4kids.com/calculators/payment.html http://www.coolmath4kids.com/fractions/index.html
D	Understand the meaning and effects of arithmetic operations with fractions and decimals.
D	Use models to demonstrate meaning and effects of arithmetic operations with integers.
M	Apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals.
A	Apply order of operations when computing with whole numbers (no more than two parentheses and no exponents). http://www.gamequarium.com/prealgebra.html
D	Apply order of operations when computing with decimals and fractions.
M	Understand and use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems.
D	Select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, percents, and integers in problem solving situations (e.g., mental computation, estimation, calculators, number line, computers, and paper and pencil).
D	Analyze procedures for computing with fractions, decimals, and integers.
D	Estimate the results of rational number computations in real-world situations.
A	Use estimation strategies to select a reasonable solution to a computation involving rational numbers.
D	Determine if the results of rational number estimates and computations are reasonable.
A	Select a reasonable solution to a real-world division problem in which the remainder must be considered.
A	Solve one- and two-step real-world problems involving whole numbers, fractions, and decimals. http://www.fema.gov/kids/dizmath.htm http://www.gamequarium.com/prealgebra.html
D	Solve two-step real-world problems involving percents.
D	Develop methods for solving problems involving proportions (e.g., scaling, and finding equivalent ratios).

Algebraic Thinking

D	Represent, analyze, and extend geometric and numerical patterns.
A	Extend geometric and numerical patterns.
I	Develop understanding for arithmetic sequences.
A	Generalize patterns in data represented in tables and graphs.
A	Extend rate charts to solve real-world problems.
A	Apply function rules.
D	Create function rules.
D	Demonstrate understanding of different uses of variables.
A	Represent mathematical statements and real-world situations using symbols.
I	Translate one-variable verbal and written expressions into algebraic expressions.
A	Evaluate algebraic expressions given the value of two or more variables. http://www.mathgoodies.com/puzzles2004/
A	Solve one-step linear equations.
A	Identify whole numbers that satisfy a given one-variable inequality.
D	Model algebraic equations with manipulatives, technology, and paper and pencil.
A	Solve real-world problems involving one-step linear equations. http://www.gamequarium.com/prealgebra.html
I	Explore relationships between symbolic expressions and graphs of lines.
A	Select a scatterplot to represent data presented in tabular form.
D	Create a scatterplot to represent data presented in a tabular form.
D	Describe the relationship between two quantities represented in a scatterplot.
D	Describe how changes in one quantity or variable result in changes in another.
A	Interpret graphs which represent rates of change.
D	Use unit rates to solve problems (e.g., miles per hour, and words per minutes).

Geometry

D	Describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
A	Classify types of two- and three-dimensional objects using their defining properties. http://www.quia.com/jg/65535.html http://www.quia.com/jg/65535.html http://www.aplusmath.com/cgi-bin/games/geomatho
A	Identify relationships among the angles (i.e., complementary, supplementary, interior, exterior, vertical, and corresponding).
D	Understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, and corresponding).
A	Solve problems using angle relationships (i.e., complementary, supplementary, interior, exterior, vertical, and corresponding).
A	Determine the measure of an angle of a triangle given the measures of the other two angles.
A	Apply relationships among the angles and side lengths of similar geometric figures.
A	Recognize similar geometric figures.
D	Determine congruence of line segments, angles, and polygons by direct comparison of given attributes.
D	Develop an understanding of the Pythagorean theorem and use it to solve real-world problems.
D	Graph points in the coordinate system.
A	Use ordered pairs to describe given points in a coordinate system.
D	Describe sizes, positions, and orientations of shapes under transformations (e.g., rotations, translations, reflections, and dilations).
D	Relate symmetry and congruence to reflections about a line.
D	Use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, and angle measure).
D	Use two-dimensional representations of three-dimensional objects to visualize.
A	Apply spatial reasoning and visualization to solve real-world problems.
A	Apply geometric ideas and relationships in areas outside the mathematics classroom (i.e., art, science, and everyday life).

Measurement

M	Understand both metric and customary systems of measurement.
A	Convert from one unit to another within the same system. http://www.aaamath.com/mea.html http://www.mathcats.com/explore/convert.html
A	Select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. http://www.shodor.org/interactivate/activities/sa_volume/index.html
A	Estimate length, perimeter, circumference, area, and volume using a variety of strategies. http://www.aaamath.com/geo.html
D	Select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision.
A	Apply formulas to find the circumference and area of circles.
A	Apply formulas to find the area of triangles, parallelograms, and trapezoids. http://www.aaamath.com/geo.html http://www.funbrain.com/poly/
A	Estimate or find the area of irregular and complex shapes.
I	Apply given formulas to find volume of selected prisms and cylinders.
D	Compare and contrast the volumes of a variety of geometric solids.
A	Solve real-world problems involving rate/time/distance (i.e., d = rt).
A	Solve problems involving scale factors using ratios and proportion.
A	Solve real-world problems using the Pythagorean theorem (no radicals).
D	Construct tables and graphs to represent rates of change.
D	Find measures using proportional relationships and properties of similar figures.
D	Determine the measures of angles by applying angle relationships (e.g., complementary, supplementary, interior, exterior, and vertical corresponding).

Data Analysis and Probability

D	Formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g., random sampling and simulations).
A	Interpret appropriate graphical representations of data (i.e., histograms, box plots, and scatterplots).
D	Select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, and scatterplots).
D	Determine and interpret measures of center and spread (e.g., mean, median, and interquartile range).
A	Determine the mean of a given set of real-world data.
A	Determine the median of a given set of real-world data (even number of data).
I	Develop meaning for frequency, distribution, and outliers.
A	Connect data sets and their graphical representations (i.e., histograms, stem-and-leaf plots, box plots, and scatterplots).
D	Connect data sets and their graphical representations (e.g., bar graphs, line graphs, and circle graphs).
A	Make conjectures and predictions based on data.
A	Recognize misleading presentations of data.
I	Develop meaning for lines of best fit.
A	Identify an appropriate sample to test a given hypothesis.
D	Make conjectures to formulate new questions for future studies.
I	Develop meaning of mutually exclusive events.
A	Connect the symbolic representation of a probability to an experiment.
D	Use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, and/or area models).
I	Distinguish between theoretical and experimental probability.
D	Find the probability of dependent and independent events.