Unit 1: Number Sense
Duration
14 Weeks
Learner Profile Attributes
Key Concept
Related Concept(s)
- Approximation
- Quantity
- Representation
- Simplification
Global Context
- Scientific and Technical Innovation
Statement of Inquiry
- Representing numbers in different forms to simplify them can help us to understand human-made systems.
Summative Assessment Criteria
- Criterion A
- Criterion B
- Criterion C
- Criterion D
ATLs (Skills)
- C – Use appropriate forms of writing for different purposes and audiences
- SM – Use appropriate strategies for organizing complex information
- T – Apply skills and knowledge in unfamiliar situations
Curriculum Standards
- SL & EL
– substitute into and evaluate algebraic expressions involving exponents
– describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three
– derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents;
– extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents
– simplify numerical expressions involving integers and rational numbers, with and without the use of technology;*
– solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;*
– relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations;
– add and subtract polynomials with up to two variables , using a variety of tools;
– multiply a polynomial by a monomial involving the same variable, using a variety of tools;
– expand and simplify polynomial expressions involving one variable, using a variety of tools;
– solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies;
– rearrange formulas involving variables in the first degree, with and without substitution;
– solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods.
Logarithms
1. Convert between exponential and logarithmic form: rational bases
2. Evaluate logarithms
3. Change of base formula
4. Identify properties of logarithms
5. Product property of logarithms
6. Quotient property of logarithms
7. Power property of logarithms
Financial Literacy: F2
1. Describe linear and exponential growth and decay
2. Exponential growth and decay: word problems
3. Compound interest: word problems
4. Continuously compounded interest: word problems
Unit 2: Statistics – A Whole Range of Things
Duration
8 Weeks
Learner Profile Attributes
Key Concept
Related Concept(s)
Global Context
- Globalisation and Sustainability
Statement of Inquiry
- How quantities are represented can help to establish underlying relations and trends in the population.
Summative Assessment Criteria
- Criterion A
- Criterion C
- Criterion D
ATLs (Skills)
- S – Practice empathy
- S – Building consensus
- S – Make fair and equitable decisions
- R – Collect, record and verify data
- R – Make connections between various sources of information
Curriculum Standards:
- All Data strands – D Linear Relations
– interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant ;
– pose problems, identify variables, and formulate hypotheses associated with relationships between two variables;
– design and carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology and techniques;
– describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses
– construct tables of values, graphs, and equations, using a variety of tools, to represent linear relations derived from descriptions of realistic situations
– construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools, for linearly related and non-linearly related data collected from a variety of sources;
– identify, through investigation, some properties of linear relations,and apply these properties to determine whether a relation is linear or non-linear;
– compare the properties of direct variation and partial variation in applications, and identify the initial value
– determine the equation of a line of best fit for a scatter plot, using an informal process
– determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation
– describe a situation that would explain the events illustrated by a given graph of a relationship between two variables
– determine other representations of a linear relation, given one representation
– describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied
Unit 3: Geometry and Measurement
Duration
7 Weeks
Learner Profile Attributes
Key Concept:
Related Concept(s)
Global Context
- Orientation in Space and Time
Statement of Inquiry
- Representing transformed objects and studying their form helps enjoy their creativity in space.
Summative Assessment Criteria
ATLs (Skills):
- C – Understand and use mathematical notation
- T – Create novel solutions to complex problems
- T – Apply existing knowledge to generate new ideas, products or processes
Curriculum Standards
- All Geometry and Measurment E
Analytic Geometry
– determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations
– identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b;
– express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0
– determine, through investigation, various formulas for the slope of a line segment or a line, and use the formulas to determine the slope of a line segment or a line;
– identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b;
– determine, through investigation, connections among the representations of a constant rate of change of a linear relation
– identify, through investigation, properties of the slopes of lines and line segments, using graphing technology to facilitate investigations, where appropriate.
– graph lines by hand, using a variety of techniques
– determine the equation of a line from information about the line
– describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation , and describe a situation that could be modelled by a given linear equation
– identify and explain any restrictions on the variables in a linear relation arising from a realistic situation
– determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application
Measurement and Geometry
– determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools, and by examining various values of the area as the side lengths change and the perimeter remains constant
– determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools, and by examining various values of the side lengths and the perimeter as the area stays constant;
– identify, through investigation with a variety of tools, the effect of varying the dimensions on the surface area [or volume] of square-based prisms and cylinders, given a fixed volume [or surface area];
– explain the significance of optimal area, surface area, or volume in various applications;
– pose and solve problems involving maximization and minimization of measurements of geometric shapes and figures
– relate the geometric representation of the Pythagorean theorem and the algebraic representation a2 + b2 = c2;
– solve problems using the Pythagorean theorem, as required in applications;
– solve problems involving the areas and perimeters of composite two-dimensional shapes;
– develop, through investigation, the formulas for the volume of a pyramid, a cone, and a sphere
– determine, through investigation, the relationship for calculating the surface area of a pyramid
– solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures
– determine, through investigation using a variety of tools, and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons
– determine, through investigation using a variety of tools, and describe some properties of polygons, and apply the results in problem solving;
– pose questions about geometric relationships, investigate them, and present their findings, using a variety of mathematical forms
– illustrate a statement about a geometric property by demonstrating the statement with multiple examples, or deny the statement on the basis of a counter-example, with or without the use of dynamic geometry software
Geometry and Measurement: E2
1. Convert between radians and degrees
2. Radians and arc length
3. Quadrants
4. Coterminal and reference angles
5. Find trigonometric ratios using right triangles
6. Find trigonometric ratios using the unit circle
7. Find trigonometric ratios using reference angles
Unit 4: How to Use Algebraic Expressions to Generalise Relationships
Duration
7 Weeks
Learner Profile Attributes
Key Concept
Related Concept(s)
- Equivalence
- Pattern
- Representation
Global Context
- Scientific and Technical Innovation
Statement of Inquiry
- Discovering relationships in patterns and studying equivalence between representations can lead to better models.
Summative Assessment Criteria
ATLs (Skills)
- C – Organize and depict information logically
- T – Gather and organize relevant information to formulate an argument
Curriculum Standards
– substitute into and evaluate algebraic expressions involving exponents.
– describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three.
– derive, through the investigation and exam- ination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents.
– extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents.
– simplify numerical expressions involving integers and rational numbers, with and without the use of technology
– solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion
– relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations.
– add and subtract polynomials with up to two variables
– multiply a polynomial by a monomial involving the same variable
– expand and simplify polynomial expressions involving one variable
– solve first-degree equations, including equations with fractional coefficients, using a variety of tools
– rearrange formulas involving variables in the first degree, with and without substi- tution
– solve problems that can be modelled with first-degree equations, and compare alge- braic methods to other solution methods
Factorization: C5
1. Factor monomials
2. Factor quadratics
3. Factor quadratics using algebra tiles
4. Factor using a quadratic pattern
5. Factor by grouping
6. Factor sums and differences of cubes
7. Factor polynomials
Sequences and Series: C6
1. Find terms of a sequence
2. Find terms of a recursive sequence
3. Identify a sequence as explicit or recursive
4. Find a recursive formula
5. Find recursive and explicit formulas
6. Convert a recursive formula to an explicit formula
7. Convert an explicit formula to a recursive formula
8. Convert between explicit and recursive formulas
9. Introduction to sigma notation
10. Identify arithmetic and geometric series
11. Find the sum of a finite arithmetic or geometric series
12. Introduction to partial sums
13. Partial sums of arithmetic series
14. Partial sums of geometric series
15. Convergent and divergent geometric series
16. Find the value of an infinite geometric series