Grade Level: Grade 7

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Tabular, symbolic, and graphic representations show relationships among independent and dependent variables to facilitate problem solving.

Skills
Analyze physical phenomena and patterns to identify relationships and make generalizations.
  1.)       Generalize mathematical situations and patterns with algebraic expressions, equations and inequalities.
  2.)       Identify the independent and dependent variables in a given situation.
  3.)      Recognize and explain when a graph should be continuous or a discrete set of points. Describe the affects of characteristics of mathematical relationships on the way the relationship is represented.
  1.)      Use graphs, tables, equations, and verbal descriptions to represent and analyze changes in linear and nonlinear relationships.
  2.)      Recognize that a linear relationship has a constant rate of change.  
Solve problems using a variety of algebraic methods.
  1.)      Solve problems using concrete, verbal, symbolic, graphical and tabular representations. Maintain equivalence in equations to determine solutions.
  1.)      Model and solve one-step and two-step linear equations using a variety of methods.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Numerical quantities can be expressed in multiple equivalent forms.
Mathematical operations and properties simplify quantities and solve problems.

Skills
Represent real-world situations and solutions to problems using the appropriate symbolic form (fractions, decimals, or percents.)
  1.)       Rewrite a rational number in its equivalent fraction, decimal, ratio and percent forms with number patterns and common factors.
  2.)       Identify and classify fractions as terminating or repeating decimals.
  3.)      Estimate and perform computations with fractions, decimals, mixed numbers, improper fractions, ratios, proportions and percents.
  4.)      Multiply and divide mixed numbers and decimals using the distributive property.
  5.)      Use and describe appropriate methods to divide by a fraction or a decimal.
  6.)       Solve practical problems involving rates, scale factors, mixtures and percents with proportions.
  7.)      Estimate to predict outcomes and determine reasonableness of results, and describe whether an estimate is an over- or underestimate.  
Understand the use of scientific notation as related to powers of ten as an efficient method for writing and comparing very large numbers.
  1.)      Use powers of ten and positive exponents to express and compare magnitude of very large numbers and connect to scientific notation.
  2.)      Develop, describe and use a variety of methods to estimate and calculate with very large numbers.   
Use percents to make comparisons between groups of unequal size.
  1.)      Estimate and find percents, including percents greater than 100% and less than 1% using number patterns and the distributive property.
  2.)      Find what percent one amount is of another amount using a variety of strategies.  
Extend the operations of addition, subtraction, multiplication, and division to negative numbers.
  1.)      Solve problems with positive and negative numbers using models and number lines.
  2.)      Use the order of operations to compute and solve a variety of multi-step problems, including those with parentheses and exponents.
  3.)      Explore absolute value while solving problems involving distance.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
The relationship that exists between 2 (nets) and 3 dimensional geometric figures demonstrate how various measurements (surface area) can be used to solve problems.
Geometric shapes can be manipulated to describe transformations of symmetry as the same shapes are viewed from different perspectives.

Skills
Describe and classify polygons according to their transformational properties.
  1.)       Identify which classes of polygons have line and/or rotational symmetry.
  2.)      Use rectangular grids to represent polygons and perform transformations (translations, rotations, reflections, and dilations) on those polygons.
  3.)      Describe the effect of transformations on polygons with line and/or rotational symmetry.  
Understand how three-dimensional objects can be represented in two-dimensions using base plans (footprints), orthogonal views, nets and isometric drawings.
  1.)      Draw and interpret nets, cross-sections, and front, side, top views of various solids.
  2.)      Develop and use strategies to determine the surface area of three-dimensional objects.  
Solve geometric and measurement problems through the use of a variety of tools, techniques and strategies.
  1.)      Use estimation and measurement strategies to solve problems involving the areas of irregular polygons and volumes of irregular solids.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Measures of central tendencies compare, organize, predict, and direct decisions made about data.
Experimental probabilities predict future outcomes based on actual results.
Theoretical probabilities predict future outcomes based on possible results.

Skills
Select the appropriate visual representation of data based on the kind of data collected and the purpose for its use.
  1.)       Formulate questions, design surveys and samplings, organize and analyze gathered data and defend the analysis.
  2.)       Organize and display data using appropriate graphical representations and make and defend predictions based on patterns and trends.  
Understand that measures of central tendency and spread can be used to describe data sets and justify conclusions.
  1.)       Find, use and interpret measures of central tendency and spread including mode, median, mean, range and outliers.
  2.)      Compare two sets of data based on their distributions and measures of central tendency.
Compare and determine experimental and theoretical probabilities.
  1.)      Identify the two ways of obtaining probabilities—by gathering data from experiments (experimental probability) and by analyzing the possible and likely outcomes (theoretical probability).
  2.)      Conduct experiments and compare experimental to theoretical probabilities.
  3.)      Solve problems involving the probability of simple and compound events in familiar contexts.