School Improvement 154 Mathematics MATHEMATICS CONTENT STANDARDS Grade 6 The following concepts and skills should be mastered by all students upon completion of sixth grade. The Major Concepts should be taught in depth using a variety of methods, applications, and connections to other concepts when possible so that all students have accessibility to and an understanding of these concepts. MAJOR CONCEPTS
Develop an understanding of and fluency with multiplication and division of fractions and decimals. Write, interpret, use, simplify, and solve mathematical expressions and equations. Develop a basic understanding of integer operations. Standard 1: Algebraic Reasoning: Patterns and Relationships – The student will use algebraic methods to describe patterns, simplify and write algebraic expressions and equations, and solve simple equations in a variety of contexts.
1. Generalize and extend patterns and functions using tables, graphs, and number properties (e.g., number sequences, prime and composite numbers, recursive patters like the Fibonacci numbers).
2. Write algebraic expressions and simple equations that correspond to a given situation.
3. Use substitution to simplify and evaluate algebraic expressions (e.g., if x = 5 evaluate 3 - 5x).
4. Write and solve one-step equations with one variable using number sense, the properties of operations, and the properties of equality (e.g., 1/3x = 9).
Standard 2: Number Sense and Operation – The student will use numbers and number relationships to solve a variety of problems. The student will estimate and compute with integers, fractions, and decimals.
1. Number Sense: Convert compare, and order decimals, fractions, and percents using a variety of methods.
2. Number Operations
a. Multiply and divide fractions and mixed numbers to solve problems using a variety of methods.
b. Multiply and divide decimals with one- or two-digit multipliers or divisors to solve problems.
c. Estimate and find solutions to single and multi-step problems using whole numbers, decimals, fractions, and percents (e.g., 7/8 + 8/9 is about 2, 3.9 + 5.3 is about 9).
d. Use the basic operations on integers to solve problems.
e. Build and recognize models of multiples to develop the concept of exponents and simplify numerical expressions with exponents and parentheses using order of operations.
Standard 3: Geometry - The student will use geometric properties and relationships to recognize, describe, and analyze shapes and representations in a variety of contexts.
1. Compare and contrast the basic characteristics of three-dimensional figures (pyramids, prisms, cones, and cylinders).
2. Compare and contrast congruent and similar figures.
3. Identify the characteristics of the rectangular coordinate system and use them to locate points and describe shapes drawn in all four quadrants.
Standard 4: Measurement - The student will use measurements within the metric and customary systems to solve problems in a variety of contexts.
1. Use formulas to find the circumference and area of circles in terms of pi.
2. Convert, add, or subtract measurements within the same system to solve problems (e.g., 9' 8" + 3' 6, 150 minutes = __ hours and __ minutes, 6 square inches = __ square feet).
Standard 5: Data Analysis - The student will use data analysis, probability, and statistics to interpret data in a variety of contexts.
1. Data Analysis: Organize, construct displays, and interpret data to solve problems (e.g., data from student experiments, tables, diagrams, charts, graphs).
2. Probability: Use the fundamental counting principle on sets with up to five items to determine the number of possible combinations.
3. Central Tendency: Find the measures of central tendency (mean, median, mode, and range) of a set of data (with and without outliers) and understand why a specific measure provides the most useful information in a given context.