Grade Level: Grade 8

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools, and technology.

Skills
Analyze physical phenomena, functions and patterns to identify relationships and make generalizations.
  1.)       Write recursive and explicit functions to generalize patterns.
  2.)       Identify relationships that are linear and nonlinear and compare and contrast their properties using tables, graphs, equations and verbal descriptions.
  3.)       Recognize and solve problems of direct variation.  
Describe the affects of characteristics of linear relationships on the way the relationship is represented verbally and in tables, graphs and equations.
  1.)       Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.
  2.)       Compare and contrast the graphs of lines with the same slope versus those with different slopes.
  3.)       Interpret slope and y-intercepts from contextual situations, graphs, and linear equations.
  4.)       Given two linear relationships in context, recognize that they may have a common solution. 
Solve problems using various algebraic methods and properties.
  1.)       Solve multi-step equations using algebraic properties.
  2.)       Use tables, graphs and equations to represent mathematical relationships and solve real-world problems.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technology.

Skills
Compare and order integers, powers, and roots using number lines and grids.
  1.)       Compare, locate, label and order rational numbers on number lines, scales, coordinate grids and measurement tools.
  2.)       Identify another rational number between any two rational numbers.
  3.)       Solve a variety of problems involving integers, powers, roots, and scientific notation.
Extend the understanding of scientific notation to very small numbers.
  1.)       Use powers of ten and negative exponents to write decimal fractions.
  2.)       Use powers of ten and positive and negative exponents to express and compare magnitude of very large and very small numbers and connect to scientific notation.
  3.)       Find the results of multiplication and division with powers of ten using patterns in operating with exponents.
  4.)       Develop, describe and use a variety of methods to operate with very large and very small numbers.  
Solve problems involving fractions, decimals, ratios and percents.
  1.)       Estimate and solve problems involving percent increase and decrease.  
Make generalizations about operations with very large and very small numbers.
  1.)       Use the rules for exponents to multiply and divide with powers of ten, including negative exponents.
  2.)       Develop, describe and use a variety of methods to estimate and calculate mentally with very large and very small numbers.  
Connect the exponential growth and decay models to repeated multiplication by the same factor.
  1.)        Solve problems that involve repetitive patterns and iterations, such as compound interest, using tables, spreadsheets and calculators.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools, and technology.

Skills
Explore the relationships among sides, angles, perimeters, areas, surface areas and volumes of congruent and similar polygons and solids.
  1.)       Explore the effect of scale factors on the length, area, and volume ratios of similar polygons, circles and solids.
  2.)       Make and test conjectures about the relationships among angles, sides, perimeters, and areas of congruent and similar polygons including the Pythagorean Theorem.  
Model geometric relationships in a variety of ways.
  1.)       Use coordinate geometry to explore and test geometric relationships of parallel and perpendicular lines and polygons and their transformations.  
Use a variety of concrete methods including displacement to find volumes of solids.
  1.)       Develop measurement strategies to find the surface area and volume of pyramids, cones, spheres and irregular solids.
  2.)       Use estimation and measurement strategies to solve problems involving the volumes of solids.
Solve problems involving measurement through the use of appropriate tools, techniques and strategies.
  1.)       Use the Pythagorean Theorem to solve indirect measurement problems.
  2.)       Describe the accuracy of estimates and measures and the precision of measurement tools.
  3.)       Solve dimensional analysis problems.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Data can be analyzed to make informed decisions using a variety of strategies, tools, and technology.

Skills
Construct appropriate representations of data based on the size and kind of data set and the purpose for its use.
  1.)       Collect, organize, display, compare, and analyze large data sets.
  2.)       Construct a variety of data displays, including box-and-whisker plots, and identify where measures of central tendency and dispersion are found in graphical displays.   
Make and evaluate statistical claims and justify conclusions with evidence.
  1.)       Make predictions from scatter plots using or estimating a line-of-best-fit.
  2.)       Make inferences and evaluate reasonable hypotheses based on experimental data.
  3.)       Analyze and interpret data using descriptive statistics including range, mode, median, quartiles, outliers and mean.
  4.)       Determine the accuracy of statistical claims.
  5.)       Describe the role of random sampling, random number generation and the effects of sample size in statistical claims.  
Determine possible outcomes using a variety of counting techniques.
  1.)       Distinguish between combinations and permutations as ways to predict possible outcomes in certain situations.
  2.)       Use combinations and permutations, trees, networks (counting strategies) in a variety of contexts, and identify when order is irrelevant in determining a solution.