St. Rose School
Mathematics Curriculum Standards
June 2003

Grade 6

• Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages:
  
  
  • Compare and order positive fractions, decimals, and mixed numbers and place them on a number line
    
    
  • Interpret and use ratios in different contexts to show the relative sixes of two quantities, using appropriate notations (a/b, a to b, a:b)
    
    
• Students calculate and solve problems involving addition, subtraction, multiplication, and division:
  
  
  • Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation
    
    
  • Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 divided 15/16 = 5/8 x 16/15 = 2/3)
    
    
  • Determine the least common multiple and greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction)

• Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions:
  
  
  • Write and solve one-step linear equations in one variable
    
    
  • Write and evaluate an algebraic expression for a given situation
    
    
  • Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process
    
    
  • Solve problems manually by using correct order of operations or by using a scientific calculator
    
    
• Students analyze and use tables, graphs and rules to solve problems involving rates and proportions:
  
  
  • Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches)
    
    
  • Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity
    
    
  • Solve problems involving rates, average speed, distance, and time
    
    
• Students investigate geometric patterns and describe them algebraically:
  
  
  • Use variables in expressions describing geometric quantities(e.g., P = 2w + 2l, A = ½ bh, C = ?d—the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively)
    
    
  • Express in symbolic form simple relationships arising from geometry

• Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
  
  
  • Understand the concept of a constant such as ?; know the formulas for the circumference and area of a circle
    
    
  • Know common estimates of ? (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements
    
    
• Students identify and describe the properties of two-dimensional figures:
  
  
  • Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms
    
    
  • Use the properties of complimentary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle
    
    
  • Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle)
    
    

• Students compute and analyze statistical measurement for data sets:
  
  
  • Compute the range, mean, median, and mode of data sets
    
    
  • Understand how additional data added to data sets may affect these computations of measures of central tendency
    
    
  • Understand how the inclusion or exclusion of outliers affects measures of central tendency
    
    
  • Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given content

Mathematical Reasoning

• Students make decisions about how to approach problems:
  
  
  • Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns
    
    
  • Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed
    
    
  • Determine when and how to break a problem into simpler parts
    
    
• Students use strategies, skills and concepts in finding solutions:
  
  
  • Use estimation to verify the reasonableness of calculated results
    
    
  • Apply strategies and results from simpler problems to more complex problems
    
    
  • Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic techniques
    
    
  • Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning
    
    
  • Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work
    
    
  • Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy
    
    
  • Make precise calculations and check the validity of the results from the context of the problem
    
    
• Students move beyond a particular problem by generalizing to other situations:
  
  
  • Evaluate the reasonableness of the solution in the context of the original situation
    
    
  • Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems
    
    
  • Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.