St. Rose School
Mathematics Curriculum Standards
June 2003

Grade 7

By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerator and denominators and properties of exponents. Students know how to compute the surface area and volume of basic three-dimensional objects. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percent) and are proficient at changing from one to another. They increase their facility with ratio and proportion; compute percentages of increase and decrease, and simple compound interest.

Number Sense

• Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
  
  • Read, write, and compare rational numbers in scientific notation (positive powers of 10) with approximate numbers using scientific notation
    
    
  • Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers
    
  • Convert fractions to decimals and percents and use these representations in estimation, computation, and applications
    
    
  • Differentiate between rational and irrational numbers
    
    
  • Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions
    
    
  • Calculate given percentages of quantities and solve problems involving discount and interest
    
    
• Students use exponents, powers, and roots and use exponents in working with fractions:
  
  
  • Multiply and divide expressions involving exponents with a common base
    
    
  • Add and subtract fractions by using factoring to find common denominators
    
    
  • Multiply, divide, and simplify rational numbers by using exponent rules

Algebra and Functions

• Students express quantitative relationships using algebraic terminology:
  
  
  • Use variables and appropriate operations to write an expression, an equation, or an inequality, that represents a verbal description (e.g., three less than a number, half as large as area A)
    
    
  • Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2
    
    
  • Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used
    
    
  • Use algebraic terminology (e.g., variable, equation, term) correctly
    
    
  • Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph
    
    
• Students interpret and evaluate expressions involving integer powers and simple roots:
  
  
  • Interpret positive whole-number powers as repeated multiplication and negative whole-numbers powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents

Measurement and Geometry

• Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
  
  
  • Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters)
    
    
  • Read drawings and models made to scale
    
    
  • Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer
    
    
• Students compute the perimeter, area and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
  
  
  • Use formulas routinely for finding the perimeter and areas of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and circular cylinders
    
    
  • Estimate and compute the area of more complex or irregular two and three-dimensional figures by breaking the figures down into more basic geometric objects
    
    
  • Compute the length of the perimeter, the surface area of the faces and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplies by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplies by the cube of the scale factor
    
    
  • Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3])

Statistics, Data Analysis, and Probability

• Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
  
  
  • Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data
    
    
  • Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and how any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level)

Mathematical Reasoning

• Students make decisions about how to approach problems:
  
  
  • Analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns
    
    
  • Formulate and justify mathematical conjectures based upon 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 and algebraic 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 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 determine a solution is complete and 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 to new problem situations