The Mathematics Curriculum in Primary and Lower Secondary Grades

The current mathematics curriculum for fourth grade was implemented in 2012,9 and the curriculum for eighth grade was implemented in 2013;10 TIMSS 2015 was administered in Chile in 2014. Exhibits 1 and 2 present the content areas and fundamental objectives of the mathematics curriculum for Grades 4 and 8.

Exhibit 1: Mathematics Curriculum, Grade 4

Content Area Fundamental Objectives
Numbers and Operations
  • Represent and describe numbers from 0 to 10,000
  • Describe and apply mental arithmetic strategies
  • Demonstrate understanding of addition and subtraction up to 1,000
  • Apply the properties of 0 and 1 for multiplication and the property of 1 for division
  • Demonstrate understanding of the multiplication of three-digit numbers by one-digit numbers
  • Demonstrate understanding of division with double-digit dividends and single-digit divisors
  • Solve routine and non-routine problems in everyday contexts that involve money, selecting and using the proper operations
  • Demonstrate understanding of fractions with denominators 100, 12, 10, 8, 6, 5, 4, 3, and 2
  • Add and subtract fractions with the same denominator (100, 12, 10, 8, 6, 5, 4, 3, and 2) in concrete and pictorial ways in a problem solving context
  • Identify, describe, and represent proper fractions and mixed numbers up to 5 in concrete, pictorial, and symbolic ways, in a problem solving context
  • Describe and represent decimals (tenths and hundredths)
  • Add and subtract decimals (with place value to the hundredth) in a problem solving context
Algebra and Patterns
  • Identify and describe number patterns in tables that involve an operation, manually and/or using educational software
  • Solve equations and inequalities for values from 0 to 100 in one step, using addition and subtraction, checking the results in a pictorial and symbolic manner,  and applying the inverse operation (addition or subtraction)
Geometry
  • Describe the absolute location of an object on a simple map with informal coordinates (e.g., with letters and numbers) and the relative location in relation to other objects
  • Determine the views of three-dimensional figures from the front, the side, and above
  • Demonstrate understanding of line of symmetry
  • Move, rotate, and mirror two-dimensional figures
  • Construct angles using a protractor and compare them
Measuring
  • Read and record various time measurements on analog and digital clocks, using the concepts of a.m., p.m., and 24 hours
  • Convert among units of time in the context of problem solving (i.e., the number of seconds in a minute, the number of minutes in an hour, the number of days in a month, and the number of months in a year)
  • Measure length in standardized units (m, cm) and convert between units (e.g., from m to cm and vice versa) in the context of problem solving
  • Demonstrate understanding of the concept of area of rectangles and squares
  • Demonstrate understanding of the concept of volume
Data and Probabilities
  • Conduct surveys, analyze the data, and compare with the results of random tests, using charts and graphs
  • Perform randomized experiments, tabulate the results, and represent them in graphs constructed manually and/or using educational software
  • Read and interpret pictographs and simple bar graphs with scale, and report findings

Exhibit 2: Mathematics Curriculum, Grade 8

Content Area Fundamental Objectives
Numbers
  • Demonstrate understanding of multiplication and division of integers
    • Represent them in concrete, pictorial, and symbolic ways
    • Apply procedures used in multiplication and division of natural numbers
    • Apply the rule of order of operations
    • Solve routine and nonroutine problems
  • Use multiplication and division of rational numbers in the context of problem solving
    • Represent them on the number line
    • Use different number sets (fractions, decimals, and integers)
  • Explain multiplication, division, and the process of forming powers of numbers with natural number bases and  exponents up to 3, in concrete, pictorial, and symbolic ways
  • Demonstrate understanding of the square roots of natural numbers
    • Estimate them intuitively
    • Represent them in concrete, pictorial, and symbolic ways
    • Apply them in geometrical situations and in daily life
  • Solve problems involving percent changes in different contexts, using pictorial representations and recording the process symbolically (e.g., annual savings interest)
Algebra and Functions
  • Demonstrate understanding of operations and algebraic expressions
    • Represent them in pictorial and symbolic ways
    • Relate them to the area of squares and rectangles and the volume of parallelepipeds
    • Determine factored forms
  • Demonstrate understanding of the concept of function in terms of linear change
    • Use tables
    • Use machine metaphors
    • Establish rules for x and y
    • Graph them manually and/or by using educational software (e.g., Cartesian plane, Venn diagrams)
  • Model situations in everyday life and in other academic subjects, using linear equations of the form ax = b ;x/a = b ;a ≠ 0;ax + b = c ;x/a + b = c ;x = b + cx ; a(x + b) = c ;ax + b = cx + d (a, b, c, d, e)
  • Solve linear inequalities with rational coefficients in the context of problem solving, using graphic representations and symbolic representations, generated manually and/or by using educational software
  • Demonstrate understanding of affine functions:
    • Generalize as the sum of a constant with a linear function
    • Move linear functions in the Cartesian plane
    • Determine the constant change from one interval to another, graphically and symbolically, manually and/or by using educational software
    • Link them to simple interest
    • Use them to solve everyday life problems and in other academic subjects
Geometry
  • Develop formulas for finding the surface area and volume of prisms with different bases and cylinders
    • Estimate surface area and volume
    • Use nets to find the surface area of prisms
    • Apply the formula for volume of a cube (base height) to different prisms and cylinders
    • Apply these formulas to geometric problems and problem solving in daily life
  • Explain in concrete, pictorial, and symbolic ways the validity of the Pythagorean theorem, and apply the theorem to geometric problems and solving problems in daily life, manually and/or by using educational software
  • Describe the position and transformations (i.e., translations, rotations, and reflections) of two-dimensional figures in a coordinate plane, manually and/or by using educational software, involving:
    • Vectors used in translations
    • The axes of the Cartesian plane (e.g., lines of reflection)
    • Points in a plane of rotation
  • Perform rotations, translations, and reflections in the Cartesian plane and in space, manually and/or by using educational software; apply these transformations to the lines of symmetry of polygons and polyhedra, and in geometric problems related to art
Probability and Statistics
  • Demonstrate an understanding of statistical measures of position (i.e., percentiles and quartiles)
    • Identify the population above or below the percentile
    • Represent them in diagrams, manually and/or by using educational software
    • Use them to compare populations
  • Evaluate the way data is presented
    • Compare information from the same data set displayed in different types of graphs to determine the strengths and weaknesses of each
    • Justify the choice of graph for a given situation and its corresponding data set
    • Detect manipulation of graphics to represent data
  • Explain the multiplication principle of probability
    • In specific situations
    • Represent it in regular tables and trees, generated manually and/or by using educational software
    • Use it to calculate the probability of compound events