When you find an activity we will post it according to coded expectation in one of the three strands for the course.

Strand: A: Characteristics of Functions

Expectation

Description

Files/Web Link

A1.1

This lesson allows students to freely vary the input to a process (represented by a “machine” diagram) and observe the resulting output. Students will investigate and understand the symbolic language in the notation of functions used in mathematics.

A function associates exactly one output value y with each possible input value x. If more than one output value y is associated with a single input value x, that process does not describe a function. In this lesson, students are presented with graphs and tables and asked to determine which represent functions and which do not.

Students will graphically explore a variety of different functions and their inverses. By grabbing and dragging a point along a graph, students will be able to visualize the relationship between an ordered pair on a function and the related ordered pair on the inverse of that function.

This lesson involves investigating vertical and horizontal translations of a function. Students will recognize how transformations of the form
y = f(x) +c and y = f(x-h) change the graph of y = f(x). Questions #1 – 3 address vertical translations and horizontal translations are used in questions # 4 – 7.

This lesson involves investigating vertical stretches or compressions and reflections through the x-axis of a function. Students will learn to recognize how transformations of the form y = a f(x) change the graph of y = f(x).

This lesson merges graphical and algebraic representations of a quadratic function and its linear factors. Students will manipulate the parameters of the linear functions and will observe the resulting changes in the quadratic function. Students will find the zeros of the quadratic function by finding the zeros of its linear factors. As a result, students will solve quadratic equations by factoring and will be able to explain why this process is valid.

This lesson involves investigating how the graph of an exponential function changes when 0 < b <1, b = 1, or b >1. As a result, students will graph an exponential function and describe the domain, range, and y-intercept.

Students will use the Lists and Spreadsheet application along with the Data and Statistics application to compare a linear and an exponential relationship.

Students will run two experiments that involve simulating pouring out coins from a bag. They will collect the data and graph it, using different methods to find equations to model the data. Then students will find the inverse of the data and corresponding equation to model it.

In this activity, students will explore applications involving bacteria growth and decay, where exponential functions are used to represent the data. They will also explore the domain and range of the exponential functions in the context of the applications.

Students explore a geometric sequence that models the spread of the 2004 Mydoom virus. After finding a rule for the sequence, they apply it recursively to extend it and graph the resulting data as a scatter plot. They then derive, evaluate, and graph an exponential function to model the data. The activity concludes by discussing the meaning of the parameters a and b in the exponential function f(x) = abx.

Students will explore geometric series. They will consider the effect of the value for the common ratio and first term using sliders. Students will graphically and numerically analyze geometric series using graphs and spreadsheets. They will also consider the derivation of the sum of a finite geometric series and use it to solve several problems while comparing their answer to those found using sigma notation.

In this activity, students begin by finding common ratios of geometric sequences on a spreadsheet and then create scatter plots of the sequences to see how each curve is related to the value of the common ratio and/or the sign of the first term of the sequence. Students then generate sequences and develop a general explicit formula for the sequence. This is followed by discovering the geometric mean of two numbers and finding the sum of a geometric series.

This lesson involves manipulating a special right triangle that is half of an equilateral triangle (the 30°-60°-90° triangle) and a special right triangle that is half of a square (the 45°-45°-90° triangle). As a result students will:

Determine the relationships among the lengths of the sides of a 30°-60°-90° triangle and a 45°-45°-90° triangle.

Students systematically explore the effect of the coefficients on the graph of sine or cosine functions. Terminology describing the graph—amplitude, period, frequency, phase shift, baseline, and vertical offset—is introduced and then reinforced as the student calculates these values directly from the graph using the handheld's geometry and measurement tools. File title is Getting Triggy With It.

Students will look at sinusoidal data related to a ferris wheel and fit curves to that data. They will use their knowledge of transformations of sinusoidal functions to make adjustments to the function definitions based on changes in real-world situations.

Nspire Resources for MCR3U (Grade 11 University Mathematics)Introduction to the new Nspire CAS Handheld

Version 1.7 of Nspire CAS Operating System

This page contains resources aligned with the curriculum expectations for this course

Ministry expectations:

## Activity Search Starting Points:

(Click on Standards Search on Right)

When you find an activity we will post it according to coded expectation in one of the three strands for the course.

## Strand: A: Characteristics of Functions

ExpectationDescriptionFiles/Web LinkA.1.7

y = f(x) +c and y = f(x-h) change the graph of y = f(x). Questions #1 – 3 address vertical translations and horizontal translations are used in questions # 4 – 7.

## Strand: B: Exponential Functions

ExpectationDescriptionFiles/Web Link## Strand: C: Discrete Functions

ExpectationDescriptionFiles/Web LinkIn this activity, students will explore the link between Pascal’s Triangle and the expansion of

binomials in the development of the Binomial Theorem.

C2.3

C2.3

## Strand: D: Trigonometric Functions

ExpectationDescriptionFiles/Web LinkStudents systematically explore the effect of the coefficients on the graph of sine or cosine functions. Terminology describing the graph—amplitude, period, frequency, phase shift, baseline, and vertical offset—is introduced and then reinforced as the student calculates these values directly from the graph using the handheld's geometry and measurement tools. File title is Getting Triggy With It.Page last updated on May 26, 2010