Mathematics: 7^th Grade

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Content Overview: By the end of seventh grade, the student will explain the relationships among rational numbers; identify equivalencies among fractions, decimals, ratios, and percents; and express numbers in standard and exponential form. The student will identify properties of rational numbers and apply them when predicting the sum, difference, product, and quotient of whole numbers, decimals, fractions, and mixed numbers. The student will determine when estimation is sufficient. The student will use ratios and proportions to measure indirectly and justify choice of methods when obtaining reasonable approximations rather than exact measures. The student will solve problems using rates and make conversions within the U.S. Customary or Metric systems. The student will describe and construct congruent, symmetric, and similar geometric figures as well as simple geometric transformations using a compass, straightedge, and/or computer software. The student will calculate the probability that an event will occur and can compare experimental and theoretical results. The student will justify conclusions based on having organized data using stem-and-leaf plots or other appropriate forms. The student will represent number patterns using graphs, evaluate simple expressions, solve simple equations and inequalities containing one variable, and solve problems after translating the information into algebraic expressions.

Process Overview: By the end of seventh grade, the student will use and explain a variety of strategies. The student will recognize the need to modify or abandon an unproductive approach, and design and conduct simple open-ended investigations. The student will validate thinking using patterns, relationships, and counterexamples, and reflect on and evaluate procedures and results in new problem situations. The student will be comfortable with available technology and use it to retrieve information helpful to understanding mathematics. The student will express mathematical understanding in both everyday and mathematical language, and recognize the extensive use of mathematics outside the classroom.

1.1 Number Sense

• 1.1.1 adds, subtracts, multiplies, and divides non-negative whole numbers, decimals, fractions, and mixed numbers using order of operations
• 1.1.2 shows understanding of non-negative fractions, decimals, percents, and place value using models (such as fraction circles, base-10 blocks, etc.)
• 1.1.3 uses symbols to demonstrate properties of the rational number system (properties of addition: commutative, associative, zero; properties of multiplication: commutative, associative, identity, zero; distributive property of multiplication and addition)
• 1.1.4 converts and identifies fraction, decimal, ratio, and percent equivalencies
• 1.1.5 compares and numerically orders whole numbers, fractions, and decimals
• 1.1.6 represents prime and composite numbers, factors and multiples, and divisibility of numbers
• 1.1.7 expresses numbers in factored form including all factor pairs
• 1.1.8 explains the use of mental arithmetic, paper and pencil, calculator or computer as appropriate for a given situation involving non-negative rational numbers
• 1.1.9 identifies situations involving non-negative rational numbers in which estimation is sufficient and computation is not required
• 1.1.10 determines and justifies the reasonableness of answers by estimating results prior to actual computation with non-negative rational numbers (using rounding, compatible numbers, etc.)

1.2 Measurement

• 1.2.1 measures using formulas for perimeter, area, and volume
• 1.2.2 selects and uses tools with calibrations that provide appropriate degree of precision
• 1.2.3 understands relationship among perimeter, area, and volume
• 1.2.4 solves problems using rates and determines the appropriate units
• 1.2.5 describes and justifies methods used to obtain approximations when given no exact measures
• 1.2.6 makes conversions within U.S. Customary and Metric systems

1.3 Geometric Sense

• 1.3.1 identifies shapes by number of sides and describes shapes using geometric language (such as type of angle, parallel sides, perpendicular, etc.)
• 1.3.2 identifies and plots x-coordinate, y-coordinate, slope, x-intercept, and y-intercept
• 1.3.3 constructs and describes symmetric, congruent, and similar geometric figures
• 1.3.4 describes and constructs simple transformations using combinations of translations, reflections, and rotations

1.4 Probability and Statistics

• 1.4.1 calculates the probability that an event will occur in experimental and theoretical situations
• 1.4.2 compares experimental and theoretical results
• 1.4.3 implements an investigation in which a random sample of data representing a described population is collected
• 1.4.4 collects, organizes, and displays data using appropriate form
• 1.4.5 calculates and demonstrates the appropriate use of mean, median, mode, and range
• 1.4.6 predicts outcomes of experiments and simulations, and compares the predictions to experimental results
• 1.4.7 makes and justifies inferences based on experimental results

1.5 Algebraic Sense

• 1.5.1 recognizes, extends, creates, and represents numbers using tables, graphs, and function rules
• 1.5.2 translates a given problem situation into a simple mathematical equation and finds the solution
• 1.5.3 evaluates simple expressions and formulas
• 1.5.4 solves simple equations and inequalities containing one variable
• 1.5.5 represents equalities and inequalities using =,<, and >

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

2.1 searches systematically for patterns in simple situations

2.2 develops and uses a variety of strategies and approaches (such as guess/check/revise, work backwards, etc.)

• 2.2a identifies missing or extraneous information
• 2.2b uses formulas, strategies, algebraic properties, and order of operations to solve problems
• 2.2c shows all steps when solving a problem
• 2.2d recognizes the need to modify or abandon an unproductive approach

3. The student uses mathematical reasoning.

3.1 makes, tests, and justifies conjectures and inferences

3.2 validates thinking and mathematical ideas using patterns and relationships

3.3 checks results for reasonableness and accuracy

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

4.1 organizes and clarifies mathematical information by reflecting, verbalizing, discussing, or writing

4.2 uses reading, listening, and observation skills to access and extract mathematical information

4.3 clearly and effectively expresses or presents ideas and situations using both everyday and mathematical language (such as models, tables, charts, written reflections, or algebraic notation)

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

5.1 connects conceptual and procedural understandings among different mathematical content areas

5.2 identifies mathematical patterns and relationships in other disciplines

5.3 uses mathematical thinking and modeling in other disciplines

5.4 explains the extensive use of mathematics in everyday situations, and occupational/career areas

5.5 uses available technology to browse, select, and retrieve mathematical information