The Number System
Students will know…
Operations and properties related to real numbers.
The properties that apply to addition extend to include addition of negative numbers.
Vocabulary related to the real number system.
The relative magnitude of numbers.
Operations can be modeled using concrete, symbolic, and pictoral methods.
The properties that apply to multiplication extend to include addition of negative numbers. Numbers can be represented in many ways and these equivalent forms facilitate computation.
The subsets of the Real Number system.
Students will be able to…
Represent integer operations with concrete models and connect the actions with the models to standardized algorithms.
Add and subtract integers.
Solve multi-step problems involving integers.
Multiply and Divide Integers fluently.
Use the order of operations to solve multi-step problems involving integers.
Convert, Compare, and Order rational numbers.
Perform operations with rational numbers.
Create a Venn diagram illustrating the subsets of the real number system
Ratios and Proportional Relationships
Ratios, Rates, Unit Rates, and Constants of Proportionality. Understand the equivalence of unit rates and constants of proportionality.
Vocabulary related to percents. Values can be represented as percents, fractions, and decimals.
Represent and solve proportional relationships.
Calculate unit rates from rates.
Represent constant rates of change from a table, verbal description, equation, or graph.
Determine constant of proportionality in real-world situations.
Use rates to solve problems.
Represent and solve problems involving proportional relationships.
Solve problems involving percent increase, percent decrease, and percent of change.
Solve mark up and mark down problems.
Use percents to find sales tax, tips, total cost, and simple interest.
Covert units within a measurement system.
Convert between percents, fractions, and decimals and determine which form is best to use in different situations.
Use proportions, equations, and models to answer percent questions.
QUARTERLY 1
Expressions, Equations, and Inequalities
The difference between expressions and equations.
Balance is a required condition for equations.
The limitations of a solution.
The properties related to expressions and equations.
Properties related to inequalities.
The difference between equations and inequalities.
Write and solve two-step equations to represent real-world problems.
Model situations involving linear relationships.
Use algebraic properties to simplify expressions and solve equations.
Write and solve two-step inequalities to represent real-world problems.
Model situations involving inequalities.
Use algebraic properties to solve inequalities.
Geometry
The relationship between different types of angle pairs.
The criteria for similar and congruent figures.
The meaning of a scale factor.
The equivalence of scale factor, constant of proportionality, and unit rate.
The criteria to create two-dimensional shapes.
The different parts of a circle and the relationship between them.
Area formulas for different shapes.
The relationship between the different methods for finding surface area.
Use ratios to determine if two figures are similar.
Use similar shapes to find unknown measures.
Construct triangles given three measures of angles or sides and determine when no triangle can be made.
Write and solve equations using formulas and geometry concepts.
Find the circumference of a circle.
Find the area of a circle or a partial circle.
Find the area of composite figures.
Determine missing measurement given area or circumference.
Find the surface area of a simple or composite figure using a net or a formula.
Find the volume of prisms and composite solids.
Statistics
Vocabulary related to data analysis.
The difference between a population and a sample.
The difference between a random and non-random sample.
Compare two sets of data displayed in dot plots or box plots.
Find Mean Absolute Deviation.
Use a sample to gain information about a population using random and non-random sampling.
Make inferences from dot plots and box plots.
Use data about a sample and proportional reasoning to make inferences or predictions about a population.
Determine if an inference or prediction is valid.
QUARTERLY 2
Probability
Probability is a value between zero and one that expresses the relative likelihood of an event occurring.
The difference between theoretical and experimental probability.
Find the probability of a simple event and its complements.
Find the experimental probabilities of simple and compound events.
Use experimental probability to make a prediction.
Create a sample space for an event.
Find theoretical probability for simple and compound events.
Compare theoretical and experimental probabilities.
Use theoretical probability and proportional concepts to make predictions.
Compare a prediction to results of an experiment.
Use technology to conduct different simulations for simple and compound events and model events using diagrams, sample spaces, and symbols.
Real Numbers, Exponents, and Scientific Notation
The relationship between subsets of real numbers.
Square roots are the inverse of squaring and cube roots are the inverse of cubing.
The square root of a non-perfect square is an irrational number.
Numbers can be expressed in different forms and the different forms can be useful to answer questions in different contexts.
The properties of exponents.
Express a rational number as a decimal and approximate the value of an irrational number.
Compare and order rational and irrational numbers.
Apply properties of integer exponents to evaluate expressions.
Convert between standard notation and scientific notation.
Add, Subtract, Multiply and Divide numbers which are expressed in Scientific Notation.
Use properties to simplify exponential expressions.
Compare and order values expressed in Scientific Notation.
Linear Relations and Equations
The difference between proportional and non-proportional relationships.
The equivalence of rate of change, constant of proportionality, unit rate, scale factor, and slope.
Changes in slope and y-intercept affect the form of the graph.
Equations can have no solutions, one solution, a limited number of solutions, or an infinite number of solutions.
Represent linear situations with tables, graphs, and equations.
Use data from a table or a graph to determine the rate of change or slope and y-intercept in mathematical and real-world situations.
Graph linear relationships interpreting the unit rate as the slope of the line that models the relationship.
Model linear relationships in graphs, tables, and equations.
Comparing unit rates using tables, graphs, and equations.
Change a graph by changing slope and/or y-intercept.
Create a graphs, equations, tables, and situations given any one as a starting point.
Determine if a point is a solution to an equation using a graph, table, or equation.
Distinguish between proportional and non-proportional situations using tables, graph, and equations.
Determine if a point is a solution to an equation using a graph, table, or equation using different methods.
Model equations using concrete, pictoral, and symbolic methods.
Write complex equations given real-world situations or tables.
QUARTERLY 3
Transformational Geometry
Properties of orientation and congruence of transformations in a coordinate plane.
Transformations can be modeled using algebraic representations.
The equivalence of scale factor, unit rate, slope, constant of proportionality, and rate of change.
The relationship of the measures of angles and side lengths in similar figures.
Model transformations using algebraic representations.
Perform transformations in the coordinate plane.
Write a series of transformations to create a given image from a pre-image.
Compare and contrast the attributes of a shape and its dilation on a coordinate plane.
Represent algebraically the effect of a scale factor applied to two-dimensional figure on a coordinate plane with the origin as the center of dilation.
Write a series of transformations including dilation to create a given image from a pre-image.
Find missing measures in similar figures.
Determine if two shapes are similar given a diagram, measurements, or an equation.
Find scale factor.
Measurement Geometry
The sum of the measures of the interior angles of a triangle is 180 degrees.
Vocabulary related to parallel lines that are cut by a transversal.
The volume of a Cylinder can be found using V=Bh where B is the area of the base and h is the height.
The volume of a cone is 1/3 the volume of a cylinder with the same height and radius.
The volume of a sphere is 2/3 the volume of a cylinder with the same radius and the height of twice the radius.
Identify angle relationships in situations with parallel lines that are cut by a transversal.
Find angle measures in situations involving parallel lines that are cut by a transversal.
Determine the measures of the interior and exterior angels of a triangle.
Determine if two triangles are similar or congruent given side lengths or angle measures.
Use concepts of similar triangles to find missing measurements.
Find the volume of a cylinder, cone, and sphere.
Model the relationship between the volumes of cylinders, cones, and spheres.
QUARTERLY 4