Sixth Grade Learning Expectations

The learning expectations listed below are for sixth grade. Students will be assessed based on their progress toward meeting these grade-level expectations. Promotion will be based on the mastery of the mathematics expectations.

Mathematics Expectations

( PDF Version)

CONTENT STRANDS

1. The student understands and applies the concepts and procedures of mathematics.

1.1 Number Sense

• 1.1.1 uses pictures and symbols to demonstrate understanding of fractions and decimals
• 1.1.2 compares and orders fractions, (denominators of 2, 3, 4, 8, 10, 16, 100), decimals to .001, mixed numbers, and common percents (75%, 50%, 25%)
• 1.1.3 expresses fractions in lowest terms
• 1.1.4 uses concepts of prime and composite numbers
• 1.1.5 uses objects, pictures, and symbols to create and solve equivalent ratios and proportions
• 1.1.6 uses visual and physical models for all operations on fractions and decimals
• 1.1.7 adds, subtracts, multiplies, and divides whole numbers, decimals, fractions, and mixed numbers
• 1.1.8 uses visual and physical models to demonstrate the meaning of division of simple fractions and decimals
• 1.1.9 uses mental arithmetic, paper and pencil, calculator, or computer as appropriate for a given situation involving whole numbers and fractions
• 1.1.10 identifies situations involving whole numbers and fractions in which estimation is sufficient and computation is not required
• 1.1.11 uses estimation prior to actual computation with whole numbers and fractions to determine reasonableness of results

1.2 Measurement

• 1.2.1 applies procedures for determining area of a triangle, circumference of a circle, and volume of a rectangular solid
• 1.2.2 measures a variety of rates (e.g., heartbeat, breath per minute)
• 1.2.3 uses estimation to obtain reasonable approximation of area
• 1.2.4 describes appropriate situations for using standard and nonstandard units of measure
• 1.2.5 demonstrates the relationship among units within the metric and U.S. system
• 1.2.6 selects appropriate measurement tool for a given situation and explains how the selection and use of a particular tool affects precision and accuracy

1.3 Geometric Sense

• 1.3.1 constructs geometric shapes given their properties (e.g., draws a quadrilateral with opposite sides parallel)
• 1.3.2 creates simple scale drawings of plane figures (e.g., doubles the dimensions of a simple polygon)
• 1.3.3 identifies and draws multiple lines of symmetry
• 1.3.4 builds and records similar and congruent figures
• 1.3.5 constructs geometric figures using a variety of tools
• 1.3.6 describes the location of points on a coordinate grid using ordered pairs including negative numbers
• 1.3.7 identifies and draws simple transformations including translations (slides), reflections (flips), and rotations (turns)

1.4 Probability and Statistics

• 1.4.1 uses and describes strategies for determining that the probability of an event is a ratio between 0 and 1
• 1.4.2 displays the sample space of a probability experiment by making a table or using a diagram
• 1.4.3 chooses appropriate strategy for collecting random samples of a representative population
• 1.4.4 organizes and displays data using multiple line graphs and circle graphs; determines which form is most appropriate
• 1.4.5 calculates and demonstrates the appropriate use of mean, median, mode, and range to make inferences and draw conclusions
• 1.4.6 makes predictions, conducts experiments, and compares results with predictions
• 1.4.7 makes inferences and notes trends based on data collected from experiments, multiple line graphs, or circle graphs

1.5 Algebraic Sense

• 1.5.1 creates, analyzes and extends number patterns that involve a combination of one or two operations
• 1.5.2 represents and describes patterns using tables and graphs; supplies missing elements of patterns
• 1.5.3 identifies the correct equation for a given situation
• 1.5.4 sets up and solves one-step single variable equations in a context

PROCESS STRANDS

2. The student uses mathematics to define and solve problems.

2.1 Investigates Situations

• 2.1.1 solves challenging problems that require perseverance
• 2.1.2 solves problems involving integration of topics, such as probability, statistics, geometry and number sense
• 2.1.3 develops and uses a variety of strategies and combination of strategies (e.g. guess-check-revise, work backwards, solve a simple problem and generalize, write an equation, organized list, use proportional reasoning)

2.2 Formulates Questions and Defines the Problem

• 2.2.1 defines problems and identifies irrelevant information in problem situations
• 2.2.2 clarifies the problem and identifies the question being asked
• 2.2.3 distinguishes between relevant and irrelevant information

2.3 Constructs Solutions

• 2.3.1 uses technology (e.g. graphing calculators, spreadsheets) to find and analyze data or represent information
• 2.3.2 solves problems involving multiple steps

3. The student uses mathematical reasoning.

3.1 Analyzes Information

• 3.1.1 validates thinking and mathematical ideas using patterns, relationships, and counter-examples

3.2 Predicts Results

• 3.2.1 develops conjectures based on analysis of new problem situations (e.g. in context of learning divisibility rules, formulates a rule for divisibility by 6 and develops arguments to support the rule)
• 3.2.2 generates and organizes data to test a conjecture

3.3 Draws Conclusions and Verifies Results

• 3.3.1 supports arguments and justifies results using inductive reasoning
• 3.3.2 organizes and clarifies mathematical information by reflecting, writing, and discussing
• 3.3.3 reflects on and evaluates procedures and results through writing and discussion

4. The student communicates knowledge and understanding in both everyday and mathematical language.

4.1 Gathers Information

• 4.1.1 formulates questions and develops a plan for collecting and communicating relevant data
• 4.1.2 uses diagrams, oral narratives, symbolic representations, and written logs to clearly and effectively express ideas
• 4.1.3 uses available technology to browse, select, and retrieve information

4.2 Organizes and Interprets Information

• 4.2.1 organizes and clarifies mathematical information by reflecting and discussing (e.g. during class discussion about probability, presents oral justification for inferences made from experimental data)

4.3 Represents and Shares Information

• 4.3.1 uses both everyday and mathematical language appropriate to the audience

5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

5.1 Relates Concepts and Procedures within Mathematics

• 5.1.1 connects conceptual and procedural understandings among different mathematical content areas (e.g. applies ratios and proportions to indirect measurement tasks)
• 5.1.2 relates and uses different mathematical models and representations for the same situation

5.2 Relates Mathematics to Other Disciplines

• 5.2.1 identifies mathematical patterns and relationships in other disciplines (e.g. shows the relationship between coordinate grids and maps)
• 5.2.2 uses mathematical thinking and modeling in other disciplines
• 5.2.3 understands the contributions to mathematics by different cultures

5.3 Relates Mathematics to Real Life Situations

• 5.3.1 recognizes the use of mathematics outside the classroom and within several occupational/career areas (e.g. banking, engineering)