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- Mathematics: Cycle 2, Yr 2: Scientific Option
Quebec - Mathematics: Cycle 2, Yr 2: Scientific Option
Progression of Learning | Adopted: 2009
A: : Arithmetic and Algebra
A.C: : Arithmetic and Algebra Concepts
A.C.1: : Algebraic expression
A.C.1.1: : Algebraic identity (of the second degree)
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.C.1.2: : Second-degree equation and inequality in one variable
Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region 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: : Real function
A.C.2.2: : Second-degree polynomial function
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
Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
A.C.2.3: : Parameter
Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
A.C.3: : System
A.C.3.1: : System of first-degree equations in two variables
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
A.C.3.2: : System composed of a first-degree equation and a second-degree equation in two variables
Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
A.P: : Arithmetic and Algebra Processes
A.P.1: : Manipulating algebraic expressions
A.P.1.2: : Dividing polynomials (with or without a remainder)
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
A.P.1.3: : Factoring polynomials
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
A.P.1.4: : Expanding, simplifying or substituting expressions, using significant algebraic identities
Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.P.1.5: : Solving first- and second-degree equations and inequalities in one or two variables, depending on the context: algebraically or graphically
A.P.1.5.i: : Validating and interpreting the solution
Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.P.2: : Analyzing situations
A.P.2.1: : Observing, interpreting and describing different situations
Determining a Spring Constant
Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring. 5 Minute Preview
Disease Spread
Observe the spread of disease through a group of people. The methods of transmission can be chosen and include person-to-person, airborne, and foodborne as well as any combination thereof. The probability of each form of transmission and number of people in the group can also be adjusted. 5 Minute Preview
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Drug Dosage
A drug prescription must be carefully planned to maximize benefit while avoiding an overdose. In this Gizmo, you can give a patient one or more pills and monitor the levels of medication in the body through time. Based on the reaction of the patient, determine the ideal levels of medication. Create a dosage schedule so these levels are maintained through time. Four types of pills, each with a different release pattern and target organ, are available for use. 5 Minute Preview
Food Chain
In this ecosystem consisting of hawks, snakes, rabbits and grass, the population of each species can be studied as part of a food chain. Disease can be introduced for any species, and the number of animals can be increased or decreased at any time, just like in the real world. 5 Minute Preview
Greenhouse Effect
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 level of greenhouse gases present in the atmosphere at any given time can be adjusted, allowing the long-term effects to be investigated. 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
Growing Plants
Investigate the growth of three common garden plants: tomatoes, beans, and turnips. You can change the amount of light each plant gets, the amount of water added each day, and the type of soil the seed is planted in. Observe the effect of each variable on plant height, plant mass, leaf color and leaf size. Determine what conditions produce the tallest and healthiest plants. Height and mass data are displayed on tables and graphs. 5 Minute Preview
Half-life
Investigate the decay of a radioactive substance. The half-life and the number of radioactive atoms can be adjusted, and theoretical or random decay can be observed. Data can be interpreted visually using a dynamic graph, a bar chart, and a table. Determine the half-lives of two sample isotopes as well as samples with randomly generated half-lives. 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: : Observing patterns
Disease Spread
Observe the spread of disease through a group of people. The methods of transmission can be chosen and include person-to-person, airborne, and foodborne as well as any combination thereof. The probability of each form of transmission and number of people in the group can also be adjusted. 5 Minute Preview
Drug Dosage
A drug prescription must be carefully planned to maximize benefit while avoiding an overdose. In this Gizmo, you can give a patient one or more pills and monitor the levels of medication in the body through time. Based on the reaction of the patient, determine the ideal levels of medication. Create a dosage schedule so these levels are maintained through time. Four types of pills, each with a different release pattern and target organ, are available for use. 5 Minute Preview
Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Half-life
Investigate the decay of a radioactive substance. The half-life and the number of radioactive atoms can be adjusted, and theoretical or random decay can be observed. Data can be interpreted visually using a dynamic graph, a bar chart, and a table. Determine the half-lives of two sample isotopes as well as samples with randomly generated half-lives. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
A.P.2.2.iv: : Finding the rule of a real function
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
A.P.2.2.v: : Switching from one form to another in writing second-degree polynomial functions: general form, standard form and factored form
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
A.P.2.3: : Interpreting results
Food Chain
In this ecosystem consisting of hawks, snakes, rabbits and grass, the population of each species can be studied as part of a food chain. Disease can be introduced for any species, and the number of animals can be increased or decreased at any time, just like in the real world. 5 Minute Preview
Forest Ecosystem
Observe and manipulate the populations of four creatures (trees, deer, bears, and mushrooms) in a forest. Investigate the feeding relationships (food web) in the forest. Determine which creatures are producers, consumers, and decomposers. Pictographs and line graphs show changes in populations over time. 5 Minute Preview
Plants and Snails
Study the production and use of gases by plants and animals. Measure the oxygen and carbon dioxide levels in a test tube containing snails and elodea (a type of plant) in both light and dark conditions. Learn about the interdependence of plants and animals. 5 Minute Preview
Pond Ecosystem
Measure the temperature and oxygen content of a pond over the course of a day. Then go fishing to see what types of fish live in the pond. Many different ponds can be investigated to determine the influence of time, temperature, and farms on oxygen levels. 5 Minute Preview
Prairie Ecosystem
Observe the populations of grass, prairie dogs, ferrets and foxes in a prairie ecosystem. Investigate feeding relationships and determine the food chain. Bar graphs and line graphs show changes in populations over time. 5 Minute Preview
A.P.2.4: : Comparing situations
A.P.2.4.i: : Solving systems of equations using a table of values, a graph or algebra
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
A.P.2.4.ii: : Interpreting the solution(s), depending on the context
Cat and Mouse (Modeling with Linear Systems) - Metric
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
S: : Statistics
S.C: : Statistics Concepts
S.C.1: : Two-variable distribution
S.C.1.1: : Linear correlation
S.C.1.1.i: : Correlation coefficient
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
S.C.1.1.ii: : Regression line
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
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
S.P: : Statistics Processes
S.P.1: : Organizing and analyzing a two-variable distribution
S.P.1.1: : Drawing a scatter plot
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
S.P.1.2: : Assessing a correlation qualitatively and quantitatively
S.P.1.2.i: : Representing and determining the equation of the regression line
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
S.P.1.2.ii: : Approximating the linear correlation coefficient with or without the use of technology
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
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
S.P.1.2.iii: : Interpreting the linear correlation coefficient
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
G: : Geometry
G.C: : Geometry Concepts
G.C.1: : Equivalent figures
G.C.2: : Analytic geometry
G.C.2.1: : Line and distance between two points
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
G.C.3: : Measurement
G.C.3.1: : Metric and trigonometric relations in triangles: sine, cosine, tangent; sine and cosine laws
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
G.P: : Geometric Processes
G.P.1: : Analyzing situations
G.P.1.1: : Finding unknown measurements, using the concept of distance and the properties of congruent, similar or equivalent figures
G.P.1.1.i: : Angles of triangles or of figures that can be split into triangles
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
G.P.1.1.ii: : Lengths
G.P.1.1.ii.a: : Segments resulting from an isometry or a similarity transformation
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
G.P.1.1.ii.b: : Side of a triangle
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
G.P.1.1.ii.c: : Altitude to the hypotenuse of right triangle and orthogonal projection of the legs on the hypotenuse
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
G.P.1.1.iii: : Areas and volumes of figures
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 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.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
Multiple grade-appropriate versions, or levels, exist for each STEM Case.
Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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Start teaching with 20-40 Free Gizmos. See the full list.
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