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- Mathematics: Cycle 2, Yr 3: Scientific Option
Quebec - Mathematics: Cycle 2, Yr 3: Scientific Option
Progression of Learning | Adopted: 2009
A: : Arithmetic and Algebra
A.C: : Arithmetic and Algebra Concepts
A.C.1: : Arithmetic and algebraic expressions
A.C.1.1: : Real numbers:
A.C.1.1.i: : absolute value, radicals, exponents, logarithms
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
A.C.2: : Relation, function and inverse
A.C.2.1: : Real function:
A.C.2.1.i: : Absolute value function
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
A.C.2.1.ii: : Square root function
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
A.C.2.1.iii: : Rational function
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
A.C.2.1.iv: : Exponential function
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
Greenhouse Effect - Metric
Within this simulated region of land, daytime's rising temperature and the falling temperature at night can be measured, along with heat flow in and out of the system. The amount of greenhouse gases present in the atmosphere can be adjusted through time, and the long-term effects can be investigated. 5 Minute Preview
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
A.C.2.1.v: : Logarithmic function
Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
A.C.2.1.vi: : Sinusoidal function
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
Uniform Circular Motion
Measure the position, velocity, and acceleration (both components and magnitude) of an object undergoing circular motion. The radius and velocity of the object can be controlled, along with the mass of the object. The forces acting on the object also can be recorded. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
A.C.2.1.vii: : Tangent function
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
A.C.2.2: : Operations on functions
A.C.3: : System
A.C.3.1: : System of first-degree inequalities in two variables
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
A.P: : Arithmetic and Algebra Processes
A.P.2: : Analyzing situations
A.P.2.1: : Observing, interpreting and describing different situations
A.P.2.1.i: : Modelling situations and drawing a scatter plot
A.P.2.1.i.a: : Determining the type of dependency relationship, interpolating and extrapolating using the line of best fit, with or without the help of technology
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
A.P.2.2: : Representing a situation involving a real function: verbally, algebraically, graphically and using a table of values
A.P.2.2.i: : Finding the rule of a function or its inverse, depending on the context
Pendulum Clock
Find the effect of length, mass, and angle on the period of a pendulum. The pendulum is attached to a clock that can be adjusted to tell time accurately. The clock can be located on Earth or Jupiter to determine the effect of gravity. 5 Minute Preview
Period of a Pendulum
Practice measuring the period of a pendulum. Perform experiments to determine how mass, length, gravitational acceleration, and angle affect the period of a pendulum. 5 Minute Preview
A.P.3: : Optimizing a situation, taking into account different constraints
A.P.3.1: : Representing a situation, using a system of equations or inequalities
Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
A.P.3.2: : Solving a system of equations or inequalities: algebraically or graphically
A.P.3.2.i: : Representing and interpreting the solution set
Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
A.P.3.3: : Choosing one or more optimal solutions
Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
A.P.3.4: : Analyzing and interpreting the solution(s), depending on the context
Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
G: : Geometry
G.C: : Geometry Concepts
G.C.1: : Analytic geometry
G.C.1.1: : Standard unit circle
G.C.1.1.i: : Trigonometric identity
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
G.C.1.1.ii: : Vector
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
G.C.1.1.iii: : Conics (centred at the origin)
G.C.1.1.iii.a: : Parabola
Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
G.C.1.1.iii.b: : Circle
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
G.C.1.1.iii.c: : Ellipse
Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview
G.C.1.1.iii.d: : Hyperbola
Hyperbolas
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview
Correlation last revised: 2/26/2010
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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