Grade Level: Grade 6

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Patterns and functional relationships can be analyzed to make predictions and interpret real world situations.
Patterns and functional relationships can be represented graphically, numerically, symbolically, and verbally.

Skills
Identify relationships and make generalizations through the use of patterns.
  1.)       Describe, analyze, and extend numeric, geometric and statistical patterns and use them to identify trends and justify predictions.  
Represent and analyze mathematical relationships with the help of tables, graphs, equations, and inequalities.
  1.)       Determine the nature of changes in linear relationships using graphs, tables and equations.
  2.)       Represent numerical and contextual situations with algebraic expressions, equations and inequalities.   
Solve real-world problems using algebraic methods.
  1.)       Use variables as placeholders, to denote a pattern, to write a formula and to represent a function or relation.
  2.)       Evaluate algebraic expressions and formulas using substitution.  
Demonstrate how to maintain equivalence in equations.
  1.)       Model and solve one-step linear equations by maintaining equivalence.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Quantitative relationships can be represented interchangeably using fractions, decimals, and percents.

Skills
Relate whole numbers, fractions, decimals and integers to number lines, scales, the coordinate plane and problem solving situations.
  1.)       Locate, order and compare whole numbers, fractions, decimals and integers on number lines, scales and the coordinate grid.
  2.)       Explain orally and in writing when a situation requires an exact answer and when an estimate is sufficient.   
Express place value patterns using exponents to write powers of ten.
  1.)       Recognize place value patterns when multiplying and dividing decimals by powers of 10.
  2.)       Compare large numbers using expanded forms and powers of ten.
  3.)       Develop, describe and use a variety of ways to estimate and calculate with large numbers and connect the strategies to powers of ten.  
Interpret and connect fraction notation to division.
  1.)       Use models and common factors to identify equivalent fractions and their decimal representations.
  2.)       Determine the decimal equivalents of fractions.
  3.)       Recognize that multiplication by a unit fraction is equivalent to dividing by the fraction’s denominator.   
Compare quantities and solve problems using ratios, rates, and percents.
  1.)       Estimate and find percents using benchmarks and number patterns.
  2.)       Convert between rates using ratios and proportions.
  3.)       Solve problems involving ratios, proportions, and percents.  
Solve problems using a variety of computational strategies including the use of calculators.
  1.)       Estimate and predict reasonable answers and recognize and explain when an estimate will be more or less than an exact answer.
  2.)       Use a variety of computational strategies (mental computation, paper-and-pencil, and calculator) to add, subtract, multiply and divide multi-digit numbers in the context of multi-step word and practical problems.
  3.)       Apply the order of operations and algebraic properties (associative, commutative, distributive, inverse operations and additive and multiplicative identities) to estimate and solve multi-step problems.
  4.)       Use factors of composite numbers, powers of 10 and divisibility rules to find products and missing factors.
  5.)       Add, subtract and multiply fractions and decimals using a variety of computational strategies.
  6.)        Create and solve a variety of problems involving fractions, decimals, mixed numbers, money and simple percents.  
Describe when products of quotients with fractions and decimals can yield a larger or smaller result than either factor.
  1.)       Determine the fractional part of a set using procedures connected to models.
  2.)       Represent division with decimals, fractions and mixed numbers as related to models and context.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Relationships among the attributes of geometric figures (perimeter, areas, volume, and surface area) may change or remain constant as angles and lengths change.
Customary and metric systems use specific standards of measurement to quantify and solve problems.

Skills
Classify polygons according to their properties.
  1.)       Use the relationships of sides and angles to classify sets and subsets of polygons.
  2.)       Make and test conjectures about side and angle relationships and congruence.  
Examine the relationships between the measures of area of 2-dimensional objects and volumes of 3-dimensional objects.
  1.)       Use the rectangle as a basic shape to model and develop formulas for the area of triangles, parallelograms, trapezoids and circles.
  2.)       Recognize the relationships among radius, diameter, circumference and area of circles.
  3.)       Develop and use strategies to determine the volume of rectangular solids and cylinders.  
Construct similar polygons on coordinate grids.
  1.)       Explore similarity of polygons as a result of dilations (a reduction or enlargement) and their effects on their measures.   
Solve problems involving measurement through the use of a variety of tools, techniques and strategies.
  1.)       Estimate and determine length, area, volume, mass and angle measures.
  2.)       Select and use appropriate units, strategies and tools to measure and solve problems involving length, perimeter, area, volume, capacity, weight, mass, temperature, and angles.  
Use specific ratios to convert between measures of length, area, volume, mass and capacity in the customary and metric systems.
  1.)       Use different ratios to convert between units of length, area, and volume in the customary and metric system.
  2.)       Recognize and use powers of ten as conversion ratios in the metric system.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Differences in experimental variables change the accuracy and the relationship between experimental and theoretical probabilities.
Methods of data collection and representation determine the validity of the interpretation.

Skills
Display and compare sets of data using various systematic or graphical representations.
  1.)       Compare sets of data graphically using histograms, double bar graphs, back-to-back stem and leaf plots and scatter plots.
  2.)       Construct circle graphs and recognize that they represent data proportionally.
  3.)       Use systematic listing and counting strategies to solve problems.  
Describe the shape of data sets using the measures of spread and central tendency.
  1.)       Describe the shape of data sets using measures of spread (range and outliers) and central tendency (mode, median and mean).
  2.)       Recognize that changes in a data set can affect the mode, median, mean and range. Understand that probabilities are more reliable to use as predictors when there is a large number of trials.
  1.)       Explore the relationship between the number of trials in an experiment and the predicted outcomes.
  2.)       Design and conduct probability experiments and make predictions about outcomes that are equally likely or not equally likely.  
Express probability using various numerical representations.
  1.)       Express probabilities as fractions, ratios, decimals and percents.