1.1 Understand and apply concepts and procedures from number sense.

Grade 9/10

Grade 11

Grade 12

Number and Numeration

1.1.1

Understand and apply scientific notation. W

·          Read and use scientific and exponential notation. [MC, SP, RL]

·          Identify a real-life situation to match a particular number written in scientific or exponential notation, and justify the answer. [MC, CU, SP, RL]

·          Use scientific or exponential notation to simplify a problem. [SP, RL, MC]

1.1.2

1.1 Understand and apply concepts and procedures from number sense.

Grade 9/10

Grade 11

Grade 12

Number and Numeration

1.1.3

1.1.4

Apply understanding of direct and inverse proportion to solve problems. W

·         Explain a method for determining whether a real world problem involves direct proportion or inverse proportion. [SP, RL, CU, MC]

·         Explain a method for solving a real world problem involving direct proportion. [CU, MC]

·          Explain a method for solving a real world problem involving inverse proportion. [CU, MC]

·          Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth).

1.1 Understand and apply concepts and procedures from number sense.

Grade 9/10

Grade 11

Grade 12

Computation

1.1.5

1.1.6

Apply strategies to compute fluently with rational numbers in all forms, including whole number exponents. W

·         Complete multi-step computations with combinations of rational numbers, including whole number exponents and square roots of perfect squares, using order of operations.

·         Calculate, using order of operations on all forms of rational numbers (e.g., (3·2+5)²-8, 2²+ 3²). [SP, RL]

·         Use properties to reorder and rearrange expressions to compute more efficiently.

1.1 Understand and apply concepts and procedures from number sense.

Grade 9/10

Grade 11

Grade 12

Computation

1.1.7

Estimation

1.1.8

Apply understanding of estimation to determine the reasonableness of answers in situations involving multi-step computations with rational numbers, including whole number powers, and square and cube roots.

·         Use estimation to determine the reasonableness of answers in situations involving multi-step computations with rational numbers, including whole number powers, and square and cube roots.

1.2 Understand and apply concepts and procedures from measurement.

Grade 9/10

Grade 11

Grade 12

Attributes, Units and Systems

1.2.1

Understand how changes in one or two dimensions of an object can affect perimeter, area, surface area, and volume. W

·          Describe and compare the impact that a change in one or more dimensions has on objects (e.g., doubling the edge of a cube affects the surface area). [CU, MC]

·          Describe how changes in the dimensions of objects affect perimeter, area, and volume in real world situations (e.g., how does the change in the diameter of an oil drum affect the area and volume). [CU, MC]

1.2.2

· 

1.2 Understand and apply concepts and procedures from measurement.

Grade 9/10

Grade 11

Grade 12

Attributes, Units and Systems

1.2.3

Understand how to convert within systems (U.S. or metric).

·         Understand how to convert within U.S. or within metric systems to achieve an appropriate level of precision.

Procedures and Estimation

1.2.4

· 

1.2 Understand and apply concepts and procedures from measurement.

Grade 9/10

Grade 11

Grade 12

Attributes, Units and Systems

1.2.5

Apply formulas to calculate measurements of right prisms or right circular cylinders. W

·          Explain how to use a formula for finding the volume of a prism or cylinder. [CU]

·          Use a formula to find the volume of a prism or cylinder. [SP, RL]

1.2.6

Understand and apply strategies to obtain reasonable measurement at an appropriate level of precision. W

·          Identify situations in which approximate measurements are sufficient; use estimation to obtain reasonable measurement at an appropriate level of precision.

·          Estimate quantities using derived units of measure (e.g., distance or time using mph, cost using unit cost). [SP, RL]

·          Estimate derived units of measure (e.g., mph, people/year, g/cc). [MC]

·          Apply a process that can be used to find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones. [SP, RL, CU]

1.3 Understand and apply concepts and procedures from geometric sense.

Grade 9/10

Grade 11

Grade 12

Properties and Relationships

1.3.1

Understand and apply the properties and relationships among the characteristics of 1-dimensional, 2-dimensional, and 3-dimensional figures W

·          Describe 2- and 3-dimensional geometric figures and figures using geometric properties

·          Compare 2-dimensional, and 3-dimensional shapes according to characteristics, including faces, edges, and vertices, using actual and virtual modeling. [CU]

·          Describe or classify various shapes based on their characteristics.

·          Make and test conjectures about 2-dimensional and 3-dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given 3-dimensional shape). [SP, RL, CU, MC]

1.3.2

Understand and apply geometric properties and relationships. W

·          Use geometric properties and relationships to describe, compare, and draw 2-dimensional and 3-dimensional shapes and figures.

·          Construct geometric figures using a variety of tools and technologies (e.g., angle bisectors, perpendicular bisectors, triangles given specific characteristics). [MC]

·          Given a set of characteristics, draw a plane shape and justify the answer. [SP, RL, CU]

·          Use the properties of 2-dimensional and 3-dimensional shapes to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles). [SP, RL, CU, MC]

1.3 Understand and apply concepts and procedures from geometric sense.

Grade 9/10

Grade 11

Grade 12

Locations and Transformations

1.3.3

Apply understanding of geometric properties and location of points to answer questions. W

·          Use geometric properties to describe or identify the location of points on coordinate grids.

·          Describe the location of points that satisfy given conditions (e.g., the set of points equidistant from a given point, a point equidistant from a given set of points). [CU]

·          Represent situations on a coordinate grid or describe the location of points that satisfy given conditions (e.g., locate a gas station to be equidistant from given cities; locate a staking point to maximize the grazing area of a tethered goat). [MC, SP, RL]

·          Use tools and technology to draw points that satisfy given conditions.

·          Identify, interpret, and use the meaning of slope of a line as a rate of change using physical, symbolic, and technological models. [SP, RL, MC]

1.3.4

Apply understanding of multiple transformations to answer questions. W

·          Apply multiple transformations to create congruent and similar figures in any or all of the four quadrants.

·          Use multiple transformations (combinations of translations, reflections, or rotations) to draw an image. [SP, RL]

·          Use dilation (expansion or contraction) of a given shape to form a similar shape. [SP, RL]

·          Determine the final coordinates of a point after a series of transformations. [SP, RL, CU]

·          Examine figures to determine rotational symmetry about the center of the shape. [SP, RL]

·          Given two similar shapes, define a set of transformations that would map one onto the other.

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 9/10

Grade 11

Grade 12

Probability

1.4.1

Understand and apply the concept of conditional probability. W

·          Understand, use, and compare the probabilities of dependent and independent events.

·          Determine and justify whether the outcome of a first event affects the probability of a later event (e.g., drawing cards from a deck with or without replacement). [CU]

·          Explain the difference between dependent and independent events. [CU]

1.4.2

Apply understanding of counting procedures and probabilities of dependent and independent events. W

·          Determine probabilities of dependent and independent events

·          Generate the outcomes and probability of multiple independent and dependent events using a model or procedure (e.g., tree diagram, area model, counting procedures.). [SP, RL]

·          Generate the outcomes and probability of events using a counting procedure (e.g., the number of license plates that can be made with three letters and three numbers; winning the lottery). [SP, RL]

·          Explain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology. [CU]

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 9/10

Grade 11

Grade 12

Statistics

1.4.3

Apply appropriate methods and technology to collect data for a given research question. W

·         Evaluate methods and technology used to investigate a research question.

·         Collect data using appropriate methods. [SP, RL]

·         Use technology appropriately to collect data. [SP, RL]

·          Given a situation, identify inappropriate data collection methods that might impact the accuracy of the results. [SP, RL]

1.4.4

Understand and apply techniques to find the equation for a reasonable linear model. W

·          Determine the equation for a reasonable line to describe bivariate set of bivariate data.

·          Determine the equation of a line that fits the data displayed on a scatter plot. [SP, RL]

·          Use technology to determine the line of best fit for a set of data. [MC]

1.4 Understand and apply concepts and procedures from probability and statistics.

Grade 9/10

Grade 11

Grade 12

Statistics

1.4.5

Analyze a linear model to judge its appropriateness for a data set. W

·          Determine whether a straight line is an appropriate way to describe the trend in a set of bivariate data

·          Determine whether the underlying model for a set of data is linear. [SP, RL, MC]

·          Decide and explain whether it is appropriate to extend a given data set following a line of best fit. [SP, RL, MC]

1.4.6

Apply understanding of statistics to make or evaluate a statistical argument.  W

·          Identify trends in a set of data in order to make a prediction based on the information. [CU, MC]

·          Justify a prediction or an inference based on a set of data. [CU, MC]

·          State possible factors that may influence a trend but not be reflected in the data (e.g., population growth of deer vs. availability of natural resources or hunting permits). [MC, CU, SP, RL]

·          Use statistics to support different points of view. [SP, RL]

·          Given a point of view and a set of statistics, develop an argument to support the point of view. [SP, RL, CI, MC]

·          Analyze a set of statistics to develop a logical point of view. [SP, RL]

·          Justify or refute claims and supporting arguments based on data.

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 9/10

Grade 11

Grade 12

Patterns, functions and other relations

1.5.1

1.        Understand characteristics of processes that can be defined as repeated addition (linear) or repeated multiplication (exponential). W

·          Recognize, extend or create a pattern or sequence between sets of numbers and/or linear patterns.

·          Find the equation of a line in a variety of ways (e.g., from a table, graph, slope-intercept, point-slope, two points). [SP, RL, MC]

·          Generate and use rules for a pattern to make predictions about future events (e.g., population growth, future sales, growth of corn stalks, future value of savings account). [SP, RL, MC]

·          Identify, extend, or create a geometric or arithmetic sequence or pattern. [SP, RL]

1.5.2

Analyze a pattern, table, graph, or model involving repeated addition (linear) or repeated multiplication (exponential) model to write an equation or rule. W

·          Identify or write an equation or rule to describe a pattern, sequence, and/or a linear function.

·          Write an equation for a line given a set of information (e.g., two points, point-slope, etc.). [MC]

·          Write a recursive definition of a geometric pattern (e.g., Start and New = Old * Number)

·          Translate among equivalent numerical, graphical, and algebraic forms of a linear function. [SP, RL]

·          Represent systems of equations and inequalities graphically. [SP, RL, MC]

·          Write a story that represents a given linear equation or expression with more than one variable. [SP, RL, CU, MC]

·          Write an expression, equation, or inequality with two variables representing a linear situation or real-world problem. [SP, RL, MC]

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 9/10

Grade 11

Grade 12

Symbols and representations

1.5.3

1.5.4

Apply understanding of equations, tables, or graphs to represent situations involving relationships that can be written as repeated addition (linear) or repeated multiplication (exponential). W

·             Demonstrate comprehension (read) and represent variable quantities, through expressions, equations, inequalities, graphs, and tables to represent linear situations involving whole number powers, and square and cube roots.

·             Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated addition (e.g., models that are linear in nature).

·             Identify and use variable quantities to read and write expressions and equations to represent situations that can be described using repeated multiplication (e.g., models that are exponential such as savings accounts and early stages of population growth).

·             Recognize and write equations in recursive form for additive models (e.g., starting value, New=Old + some number).

·             Recognize and write equations in recursive form for additive models (e.g., starting value, New=Old × some number).

1.5 Understand and apply concepts and procedures from algebraic sense.

Grade 9/10

Grade 11

Grade 12

Evaluating and solving

1.5.5

Apply procedures to simplify expressions. W

·          Simplify expressions and evaluate formulas involving exponents. [SP, RL]

·         Justify a simplification of an expression involving exponents. [CU]

·          Use multiple mathematical strategies and properties to simplify expressions. [SP, RL]

1.5.6

Apply procedures to solve equations and systems of equations. W

·          Rearrange formulas to solve for a particular variable (e.g., given A = .5 b h, solve for h). [SP, RL]

·          Solve real-world situations involving linear relationships and interpret the solution. [SP, RL, CU]

·          Find the solution to a system of linear equations using tables, graphs and symbols. [CU, MC]

·          Interpret solutions of systems of equations. [CU, MC]

·          Solve multi-step equations. [SP, RL]

·          Use systems of equations to analyze and solve real-life problems. [SP, RL, CU, MC]

2.1 Investigate Situations

Grade 9/10

The following are the times (in seconds) of the Olympics in the given years.  Using this information, is it reasonable to believe that the women will run as fast as the men in this event? Justify your answer using this data/

Grade 11

Grade 12

2.1.1

·          Use strategies (draw pictures, actual and virtual modeling, organized lists) to investigate a network problem (e.g., delivering papers) according to attributes, including regions, edges, and vertices. (1.3.2)

·          Identify missing information in a given situation and make reasonable assumptions as to the possible values for the missing data (e.g., given an average mpg of a car and a question like how far the car can travel on a tank of gas, identify size of the gas tank as missing information and make a reasonable estimate of the size of the tank)(1.2.2).

2.2 Define Problems

Grade 9/10

The following are the times (in seconds) of the Olympics in the given years.  Using this information, is it reasonable to believe that the women will run as fast as the men in this event? Justify your answer using this data/

Grade 11

Grade 12

2.2.1

Understand information to define problems.

·          Use strategies to become informed about the situation (e.g., listing information, examine the table for patterns, create a scatter plot to look for patterns, asking questions).

·          Determine if enough information is given to find a solution (e.g., List what is needed to be found – extend the pattern to see if women’s times will be less).

·          Determine if information is missing or extraneous (e.g., compare the list of known things to the list of needed things to see if there are things that are not needed).

·          Given a situation involving a direct or indirect measurement, identify questions that need to be answered in order to arrive at a solution to the problem. (e.g., If we need to add chemicals to rectangular shaped swimming pool, what do we need to know?)  [1.2.5]

·          Identify a real-life problem situation to match a particular number written in scientific or exponential notation.(1.1.1)

2.3 Construct Solutions

Grade 9/10

The following are the times (in seconds) of the Olympics in the given years.  Using this information, is it reasonable to believe that the women will run as fast as the men in this event? Justify your answer using this data/

Grade 11

Grade 12

2.3.1

Understand how to devise a plan to solve a problem.

·          Organize relevant information from multiple sources (e.g., create a list of known and unknown information, create a scatter plot of men’s and women’s times vs. time on the same coordinate axis to analyze the patterns.).

·          Write a story that represents a given linear equation or expression with more than one variable.

·          Use technology appropriately to collect and examine data.(1.4.3)

·          Use technology to determine the line of best fit for a set of data.(1.4.4)

·          Use using tools and technology to draw points that satisfy given conditions.(1.3.3)

2.3 Construct Solutions

Grade 9/10

The following are the times (in seconds) of the Olympics in the given years.  Using this information, is it reasonable to believe that the women will run as fast as the men in this event? Justify your answer using this data/

Grade 11

Grade 12

2.3.2

Apply strategies, concepts and procedures to solve a problem.

·          Implement the plan devised to solve the problem (e.g., solve the set of simultaneous equations to arrive at a time where the two times are the same).

·          Use mathematics to solve the problem (e.g., use algebra to write equations for the two linear models, solve the system of equations using either symbols or technology).

·          Check the solution to see if it works (e.g., the solution may be a partial year (i.e., 2003.6). Decide how to deal with this and also if the year is reasonable [ 1925 does not make sense given the context]

·          Explain a method for solving a real world problem involving direct or inverse proportions. (1.1.4)

·          Decide whether it is appropriate to extend data following a line of best fit.(1.4.5)

3.1 Analyze Information

Grade 9/10

Grade 11

Grade 12

3.1.1

Synthesize information from multiple sources in order to answer questions.

·          Use the properties of 2-dimensional and 3-dimensional figures to solve mathematical problems (e.g., find the width of a river based on similar triangles; given a set of parallel lines, a transversal, and an angle, find the other angles).

3.2 Make Predictions, Inferences, and Conjectures

Grade 9/10

Grade 11

Grade 12

3.2.1

Apply skill of conjecturing and analyze conjectures by formulating a proof or constructing a counter example.

·          Make and test conjectures about 2-dimensional and 3-dimensional figures and their individual attributes and relationships using physical, symbolic, and technological models (e.g., diagonal of a rectangle or prism is the longest interior segment; what figures make up cross-sections of a given 3-dimensional shape).(1.3.1)

3.2.2

Analyze information to draw conclusions and support them using inductive and deductive reasoning.

·          Compare and describe the volume of cylinders, cones, and prisms when an attribute is changed (e.g., the area of the base, the height of solid).(1.2.4)

·          Given a set of characteristics, draw a plane shape and justify the answer.(1.3.2)

·          Identify trends in a set of data in order to make a prediction based on the information.(1.4.6)

·          Use statistics to support different points of view.(1.4.6)

3.2.3

Analyze procedures and make needed revisions.

·          Analyze claims and supporting arguments based on data.(1.4.6)

3.3 Draw Conclusions and Verify results

Grade 9/10

Grade 11

Grade 12

3.3.1

Analyze results using inductive and deductive reasoning.

·          Use and analyze properties of 2-dimensional figures and shapes to compare and contrast similar 2-dimensional figures and shapes.(1.3.2)

·          Find a reasonable estimate for the volume of prisms, pyramids, cylinders, and cones.(1.2.6)

3.3.2

Synthesize thinking and mathematical ideas using models, known facts, patterns, relationships, counter examples, or proportional reasoning.

·          Analyze a set of statistics to develop a logical point of view.(1.4.6)

4.1 Gather Information

Grade 9/10

Grade 11

Grade 12

4.1.1

Understand how to develop or apply an efficient system for collecting mathematical information for a given purpose.

·          Efficiently collect data on the outcomes of first events and later events to determine and justify how the first event affects the probability of a later events (e.g. drawing cards from a deck with or without replacement).(1.4.1)

4.1.2

Synthesize mathematical information for a given purpose from multiple, self-selected sources using reading, listening, and observation.

·          State possible factors that may influence a trend but not be reflected in the data. (e.g., population growth of deer vs. availability of natural resources or hunting permits).(1.4.6)

4.2 Organize, Represent, and Share Information

Grade 9/10

Grade 11

Grade 12

4.2.1

Analyze mathematical information to organize, clarify, and refine an argument.

·          Given a point of view and a set of statistics, develop an argument to support the point of view.(1.4.6)

4.2.2

Understand how to express ideas and situations using mathematical language and notation.

·          Explain how division of measurements produces a derived unit of measurement (e.g., miles traveled divided by hours traveled yields the derived unit [miles per hour]).(1.2.2)

·          Describe the location of points that satisfy given conditions (e.g., the set of points equidistant from a given point, a point equidistant from a given set of points).(1.3.3)

·          Describe and compare the impact that a change in one or more dimensions has on objects. (e.g., doubling the edge of a cube affects the surface area).(1.2.1)

·          Explain the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology.(1.4.2)