St. Rose School
Mathematics Curriculum Standards
June 2003

Grade 8

By the end of grade eight, students have mastered the four arithmetic operations with positive and negative integers. Students are adept at manipulating numbers and two-step equations and understand the general principles at work. They know the Pythagorean Theorem and solve problems in which they compute the length of an unknown side. Through the introduction to the study of algebra students develop an understanding of the symbolic language of mathematics. In addition, algebraic skills and concepts are introduced and used in a limited variety of problem solving situations.

Number Sense

• Students compare and order positive and negative fractions, decimals and mixed numbers. Students know the properties of whole numbers, fractions, decimals and positive and negative integers. They solve problems involving ratios, proportions and percentages:
  
  
  • Compare and order positive and negative fractions, decimals and mixed numbers and place them on a number line
    
    
  • Use proportions to solve problems such as finding the length of a side of a polygon similar to a known polygon
    
    
  • Solve problems that involve discounts, markups, commissions and profit and compute simple and compound interest
    
    
• Students use exponents, powers, and roots and use exponents in working with fractions:
  
  
  • Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why
    
    
  • Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers
    
    

Algebra and Functions

• Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs:
  
  
  • Use algebraic terminology (e.g. variable, equation, term, coefficient, inequality, expression) correctly
    
    
  • Students identify and use the arithmetic properties of integers and rational and real numbers, including the closure properties for the four basic arithmetic operations, where applicable
    
    
• Students understand and use such operations as taking the opposite, finding the reciprocal, and taking a root.
  
  
• Students solve equations and inequalities involving absolute value.
  
  
• Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x©5) + 4(x©2) = 12.
  
  
• Students solve a limited quantity of multi-step problems, including word problems, involving linear equations and linear inequalities in one variable.
  
  
• Students graph a linear equation. They are also able to sketch the region defined by a linear inequality.

Measurement and Geometry

• Students know the Pythagorean, Theorem, and deepen their understanding of plane geometry by constructing figures that meet given conditions and by identifying attributes of figures:
  
  
  • Identify and construct basic elements of geometric figures (e.g. altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; radii, diameters, and chords of a circle) by using a compass and straightedge
    
    
  • Understand and use coordinate graphs to plot simple figures and determine their image under translation and reflections
    
    
  • Know the Pythagorean Theorem and its converse and use it to find the missing side of a right triangle and the lengths of other line segments and in some situations, empirically verify the Pythagorean Theorem by direct measurement
    
    
  • Demonstrate an understanding of conditions that indicate two geometrical figures measurement. That are congruent and what congruence means about the sides and angles of the two figures

Statistics, Data Analysis and Probability

• Students continue to collect, organize and represent data sets that have one or more variables and identify relationships among variables within a data set:
  
  
  • Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and any apparent relationship that exists between
    
    
  • Understand the meaning of, and be able to compute the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set

Mathematical Reasoning

• Students continue to make decisions about how to approach a problem.
  
  
• Students continue to use strategies, skills and concepts in finding solutions.
  
  
• Students continue to determine if a solution is complete and move beyond a particular problem by generalizing to other situations.
  
  

* See Grade Seven Standards for St. Rose School for more definite objectives and also Grade Eight Standard, Algebra, 5.0.