Mathematics, Secondary 1

Unit 1: Arithmetic

The PDA Arithmetic branch, Secondary 1.

• Meanings of a fraction: part of a whole, division, ratio, operator, measure
• Choosing an operation to model a situation
• Recognizing ratios and rates

• Reading and writing numbers in fractional and decimal notation
• Translating a situation into a sequence of operations
• Representing numbers in fractional or decimal notation
• Translating a situation with a ratio or a rate

• Approximating numbers: estimating, rounding, truncating
• Anticipating the result of an operation
• Operating on decimals using the rules of signs
• Operating on positive fractions
• Recognizing a proportional situation

• The concept of absolute value

• Squares and square roots
• Powers with integral exponents
• Sequences of operations in the correct order

• Order of magnitude with scientific notation

• Ordering and comparing fractions and decimals
• Comparing numbers across notations

• Finding equivalent expressions
• Approximating the result of a calculation
• Comparing ratios and rates qualitatively
• Comparing ratios and rates quantitatively

• Interpreting the result of an operation in context
• Computing sequences of operations in writing
• Representing a proportional situation

• Divisibility rules for 2, 3, 4, 5 and 10
• Effect of changing a term in a ratio or rate

• Using a calculator for ordered operations
• Solving proportional situations with strategies

• Finding a percentage of a number
• Finding the whole from a percentage

• Interpreting ratios and rates

Unit 2: Algebra

The PDA Algebra branch, Secondary 1.

• The idea of an unknown
• Variables and constants
• The idea of a parameter
• Vocabulary of algebraic expressions
• Distinguishing an unknown from a variable

• Building an algebraic expression
• Representing an equation another way

• Interpreting an algebraic expression in context

• Equivalent algebraic expressions
• Transforming equalities to keep them balanced

• Transforming equalities and equations

• Evaluating an algebraic expression
• Describing a pattern with an equation

• Operating on algebraic expressions
• Describing relations or formulas
• Analyzing a situation across representations

• Factoring out a common factor
• Manipulating and rearranging formulas
• Representing a situation with a graph

• Solving first-degree equations ax + b = cx + d

• Validating a solution by substitution

• Interpreting solutions and making decisions

Unit 3: Geometry

The PDA Geometry branch, Secondary 1.

• Recognizing and naming regular convex polygons
• Recognizing a dilatation
• Angles in a triangle
• Central angles and arcs
• Segments and lengths in a plane figure

• Decomposing plane figures
• Right prisms, cylinders and pyramids
• Constructing the image under a dilatation
• Justifying statements about lengths
• Area of circles and sectors
• Area of composite figures
• Lateral and total area of prisms, cylinders, pyramids
• Surface area of decomposable solids
• Area under an isometry

• Describing circles and sectors
• Justifying statements about area

• Lines and segments in figures
• Justifying with congruence, similarity, equivalence
• Justifying with angle properties

• Properties of plane figures via transformations

• Justifying with properties of plane figures and solids

• Nets of a solid
• Properties and invariants of transformations
• Recognizing congruent or similar figures

• Naming the solid from a net
• Identifying congruence via transformations
• Recognizing the transformation between a figure and its image
• Types of angles formed by lines
• SI units of length
• Relationships between SI units of area

• Altitude, apothem and lateral face
• Constructing the image under a transformation
• Properties and invariants of congruent or similar figures
• Duration versus position in time
• Finding angle measures using angle properties
• Perimeter and circumference relations
• Constructing area relations

• Metric relations in plane figures

Unit 4: Analytic Geometry

The PDA Analytic Geometry branch, Secondary 1.

• Locating numbers on an axis

• Locating points in the Cartesian plane

Unit 5: Statistics

The PDA Statistics branch, Secondary 1.

• Stratified and cluster sampling
• Choosing a representative sample

• Recognizing sources of bias

• Types of statistical variables

• Frequency tables and circle graphs

• Comparing one-variable distributions

• The concept of the arithmetic mean

• Calculating and interpreting the mean

• Range and interquartile range
• Percentiles

• Choosing the appropriate statistical measure

Unit 6: Probability

The PDA Probability branch, Secondary 1.

• Multi-step random experiments

• Networks, tables and Venn diagrams
• Odds versus probability

• Types of events

• Mutually exclusive and independent events

• Theoretical versus experimental probability

• Calculating the probability of an event