Shared Gizmo List: MCF3M Grade 11 University-College Math

The mixed grade 11 uc mathematics course.
11th Grade Math

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Shared by a high school math teacher in Ontario.

Getting Started - What I know and what I remember

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   Lesson Info
Modeling and Solving Two-Step Equations Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps.
  5 Minute Preview   Lesson Info
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 (x, y) point to be a solution of one equation, or of a system of two equations.
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Addition of Polynomials Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes.
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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.
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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.
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Functions and Polynomial Functions

Introduction to Functions Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.
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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.
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Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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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.
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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.
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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   Lesson Info
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.
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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.
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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.
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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.
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Roots of a Quadratic Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
  5 Minute Preview   Lesson Info

Trigonometry

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.
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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.
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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.
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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.
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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.
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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.
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Exponential Functions

Introduction to Exponential Functions Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph.
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Multiplying Exponential Expressions Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
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Compound Interest Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance.
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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.
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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.
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