Content Standards
 Performance Indicators
 Instructional Practice
 Assessment Tools
 Reporting Tools

A. NUMBER: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems. 
WHOLE NUMBER





No performance indicator. It is expected that students continue to use prior concepts and skills in new and familiar contexts. 




RATIONAL NUMBER





A.1. Students express or interpret numbers using scientific notation from reallife contexts.
 a. Use positive and negative integer exponents for powers of ten.
 (Connected Mathematics ProjectGrowing, Growing, Growing) Express very large and very small numbers using scientific notation.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Convert between standard and scientific notation forms and compare the relative size of numbers including the interpretation of numbers as displayed on calculators and computers.
 (GGG) Convert between scientific and standard notation both on paper and with a calculator.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

REAL NUMBERS 




A.2. Students understand the set of real numbers as containing the rational numbers and the irrational numbers.
 a. Know that there are real numbers that are not rational numbers.
 (Connected Mathematics ProjectLooking for Pythagoras) Express square roots in radical form and as "approximately equal to" a rounded decimal form.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Know some common examples of irrational numbers including pi or those arising from square roots.
 (LFP) Give examples of familiar irrational numbers.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Use square roots.
 (LFP) Determine lengths of diagonal line segments and perimeters of irregular figures using square roots.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 d. Be able to estimate the value of the square roots of whole numbers and place them on the number line.
 (LFP) Express lengths of squares in radical form and also in rounded decimal form. Locate square roots on a number line.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:
 understand that most measurements are approximations and that taking repeated measurements reveals this variability;
 understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
 understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

MEASUREMENT AND APPROXIMATION


 

B.1. Students understand and use derived measures (measurements expressed as rates).
 a. Calculate measures using multiple attributes including speed (distance per time).
 (Moving Straight Ahead) Calculate walking rates by measuring distance and time. Calculate distance given speed and time.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Solve for an unknown component of a measure including finding time given average speed and distance.
 (MSA) Calculate time given speed and distance.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

B.2. Students convert across measurement systems and within a system for different units in derived measures.
 a. Approximate metric and customary equivalents given a conversion factor.
 (Algebra) Convert ratios to equivalent ratios using unit analysis
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Convert derived measures, including feet per second to miles per hour.
 (MSA) Convert between units in motion problems.
(Algebra) Convert ratios to equivalent ratios using unit analysis.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

DATA ANALYSIS


 

B.3. Students use the mean, median, mode, range, and quartiles to solve problems involving raw data and information from data displays.

 (Comp sheets) Calculate mean, median mode and range.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

PROBABILITY


 

B.4. Students understand and apply concepts of probability.
 a. Use appropriate terminology to describe complementary and mutually exclusive events.
 (What Do You Expect?) Describe complementary and mutually exclusive events.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Use an understanding of relative frequency to make and test conjectures about results of experiments and simulation.
 (WDYE) Predict results and test predictions about number of occurrences of a color on a spinner, heads or tails, or outcomes on a die.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Compute probabilities for compound events, using such methods as organized lists, tree diagrams, and area models.
 (WDYE) Utilize tree diagrams and area models for more complex probability situations.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct twodimensional and threedimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results. 
GEOMETRIC FIGURES


 

C.1. Students know and use properties of polygons.
 a. Apply the triangle inequality.
 (LFP) Calculate if three random lengths can form a triangle.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Find the sum of the measures of the interior angles of a polygon. 
 

 c. Apply the property that the sum of the measures of the exterior angles of a polygon is 360 degrees. 
 

C.2. Students know and use angle properties of parallel lines to solve problems and determine geometric relationships.  a. Know and use properties of angles created when parallel lines are cut by a transversal. 
 

 b. Use angle properties to determine whether lines are parallel.   

 c. Know and use properties of angles created by parallel lines and transversals to determine the angle properties of trapezoids and parallelograms, and apply these properties in problem situations. 
 

C.3. Students know and use the Pythagorean Theorem.

 (LFP) Determine if a triangle is a right triangle using the Pythagorean Theorem. Determine missing values in right triangles using the Pythagorean Theorem.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

GEOMETRIC MEASUREMENT


 

C.4. Students find the volume and surface area of prisms, pyramids, cylinders, and other figures composed of these solids.  a. Apply the understanding that the volume of prisms and cylinders can be found by multiplying the area of a base by the height of the solid. 
 

 b. Apply the understanding that the volume of pyramids can be found by multiplying the area of a base by 1/3 the height of the solid. 
 

 c. Apply the understanding that the surface area of a figure is the sum of the areas of its faces and find the surface areas of cylinders. 
 

TRANSFORMATIONS


 

No performance indicator. Although no performance indicators are stated, students are expected to continue to use prior concepts and skills in new and familiar contexts. 

 

D. ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations. 
SYMBOLS AND EXPRESSIONS





D.1. Students create, evaluate and manipulate expressions.
 a. Create and evaluate expressions using real numbers.
 (MSA, Comp sheets) Evaluate expressions with real numbers. Write variable expressions given a situation.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Add and subtract linear expressions.
 (MSA) Add and subtract linear expressions.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Apply the properties of the real number system, including distributive and associative laws, to create equivalent expressions.
 (MSA, Comp sheets) Use distributive, associative and commutative properties to create equivalent expressions and solve equations.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

EQUATIONS AND INEQUALITIES


 

D.2. Students understand and solve problems involving linear equations.
 a. Solve any linear equation including linear equations of the form ax + b = cx + d.
 (MSA) Use property of equality (golden rule of math) to solve linear equations.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Recognize that, in general, linear equations have just one solutionbut know also that some linear equations can have no solution and those linear equations that are identities have every value of x as a solution.
 (MSA) Solve linear equations and recognize when there is no solution or an infinite number of solutions.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Use graphs to estimate solutions to equations and systems of equations, check algebraic approaches, provide alternative solution paths, and communicate the solution to a problem.
 (MSA) Use graphs to estimate solutions to problems. Use algebraic methods when an exact solution isn't a realistic expectation on a graph.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

D.3. Students understand and solve linear inequalities in one unknown.
 a. Represent problem situations as inequalities.
 (Thinking with Math Models) Students will write inequalities to represent situations. (Algebra) Write inequalities from a word problem.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Solve linear inequalities.
 (TWMM) Students will solve linear inequalities through symbolic method, using graphs or tables. (Algebra) Solve and graph linear inequalities.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Interpret the solutions to linear inequalities.
 (TWMM) Students will explain what their solutions mean to inequalities. (Algebra) Find and interpret solutions to linear inequalities.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

FUNCTIONS AND RELATIONS


 

D.4. Students understand and use the basic properties of linear relationships, y = kx + b.
 a. Understand that a linear relationships are characterized by a constant rate of change.
 (MSA) Identify a linear set of data by looking for a constant rate of change in a table or a straight line on a graph.
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 b. Understand that the graph of a linear relationship y = kx + b is a line where the slope is k and b is the y coordinate of the point where the graph crosses the y axis (i.e., value of y when x = 0).
 (MSA) Define slope and yintercept. Write equations given a graph by finding the slope (rate of change) and yin homework
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays

 c. Translate common linear phenomena into symbolic statements and graphs, and interpret the slope and y intercept of the graph of y = kx + b in terms of the original situation.
 (MSA) Write linear equations given computation sheets, homework
  classroom tests
 classroom quizzes
 projects
 common assessments
 performances/displays/presentations
 teacher checklists
 teacher rubrics
 large scale assessments: NWEA, MEA
  report cards
 progress reports
 student/parent conferences
 teacher websites
 email communication
 power school
 community performances/displays
