TI-Nspire Activities & Ideas 28 activities so far!!!

The following are activities that I have developed for TI-Nspire and TI-Nspire CAS. There is a brief explanation of the file(s), the Nspire files to download, and any accompanying files (like pdf’s) for the student or teacher. Feel free to pass them along and please contact me with any suggestions.

Completing the Square Parabolas Algebra 1, Algebra 2, Precalculus

This document is designed to either introduce or review how to use "completing the square" to rewrite an equation of a parabola from standard form into vertex form. Four different examples will be illustrated, step-by-step. The graphs validate the work.

TI-Nspire File(s): Parabola_Graphing_Comp_the_Square.tns Accompanying file(s): NONE

Complex Numbers – An Introduction to i, Adding, Subtracting, Multiplying, and Powers of i

Algebra 2, Precalculus

This document assists the student in learning about the Imaginary Numbers for the first time. Explanations are supplied and 15 examples/exercises are illustrated for the student to do along with the document. I used this with great success in Algebra 2.

TI-Nspire File(s): Complex_Numbers_Intro.tns Accompanying file(s): NONE

Given the Roots of a Quadratic Equation, Find the Equation in Both Forms

Algebra 2

The student is given the solutions (roots, zeros) to a quadratic equation and is asked to find the quadratic equation that has those solutions. The equation must be stated in both forms: Standard Form and Vertex Form. Three examples are illustrated completely followed by four exercises to be completed by the student.

TI-Nspire File(s): Given_Roots_Find_Quad_Equation.tns Accompanying file(s): NONE

Hero’s Formula (aka Heron’s Formula)

Trigonometry, Precalculus

This formula is used to calculate the area of any triangle if given the lengths of the 3 sides. This very short document presents both parts of the formula and illustrates how to use it with an example. Each step is shown clearly. A great introduction to this topic.

TI-Nspire File(s): Heros_Formula.tns Accompanying file(s): NONE

The Law Of Cosines

Trigonometry, Precalculus

This document has 4 examples that clearly illustrate how to use the Law of Cosines to solve triangles with different sets of data supplied. Each step is clearly shown and a fifth example is supplied for the student to test his/her understanding. A great first day assignment. In fact, I used this in place of teaching the Law of Cosines this year! Two pdf documents are included as accompanying files.

TI-Nspire File(s): Law_of_Cos.tns Accompanying file(s): Law_of_Cosines_GIFT.pdf Page39AdvancedMathBook.pdf

The Law Of Sines & Find the Area of a Triangle Using the Sine Ratio

Trigonometry, Precalculus

This document contains two examples. The first example illustrates how to use the sine function to calculate the area of a triangle given certain dimensions. The second example illustrates how to use the Law of Sines to solve a triangle given certain dimensions.

TI-Nspire File(s): Area_Law_of_Sines.tns Accompanying file(s): NONE

Maximize the Area of A Rectangle Inscribed Under a Parabola

Calculus, Precalculus

This activity asks the student to find the rectangle with maximum area under a given parabola. To assist the student in generating the correct equation, there is an interactive graph that illustrates the many possible rectangles. And the student can check to see if his/her equation is correct by graphing on top of the data that is generated.

TI-Nspire File(s): Max_Area_of_Inscribed_Rectangle_in_Parabola.tns Accompanying file(s): NONE

MANUFACTURING A GALLON CAN -- A MINIMIZATION PROBLEM Desk Top Demonstration

Calculus, Precalculus

A metal can in the shape of a rectangular solid with a square base (top and bottom) is to be manufactured at a minimum cost for materials. Your responsibility is to find the dimensions of the can (to the nearest hundredth of an inch) that minimizes the cost (to the nearest tenth of a penny). This has an interactive graph/picture that shows all possible configurations for the can and its costs.

TI-Nspire File(s): One_Gallon_Can_DeskTop.tns Accompanying file(s): NONE

LRAM_RRAM_MRAM -- A Graphical Investigation

Calculus

This interactive activity is designed for the student to investigate how area bounded by a curve and the x-axis can be approximated with areas of rectangles using LRAM, RRAM, and MRAM. The student can change the function definition and see the resulting change in areas. The student can change the x-coordinate of the either endpoint of the interval. This uses only 4 rectangles.

TI-Nspire File(s): LRAM_RRAM_MRAM.tns Accompanying file(s): NONE

LRAM_RRAM_MRAM -- Program

Calculus

This program approximates the area bounded by a curve and the x-axis over a closed interval using LRAM, RRAM, MRAM. The student can decide the function, the left endpoint, the right endpoint, and the number of subintervals.

TI-Nspire File(s): LRMRAM_Program.tns Accompanying file(s): NONE

Investigating the Graphs of Parabolas

Algebra 2, Precalculus

A graph of a quadratic equation will be shown. Also shown is the equation of the parabola in vertex form: y = a*(x - h)^(2) + v. The user is able to change any/all of the 3 parameters: a, h, v, and the graph will automatically change to reflect those changes in parameters.

TI-Nspire File(s): Investigating_the_Graphs_of_Quadratic_Equations.tns Accompanying file(s): NONE

The Quadratic Formula – Two Examples to Illustrate How to Use It

Algebra 1, Algebra 2, Precalculus

The student is slowly taken through how to solve a quadratic equation using the Quadratic Equation. Each step is shown and clearly explained. This is good to use as an introduction or to use as a review.

TI-Nspire File(s): Quadratic_Formula.tns Accompanying file(s): NONE

Study Cards: Parabola Equations

Algebra 2, Precalculus

A graph of a parabola will be shown. You are asked to find the equation of the parabola in vertex form: y = a*(x - h)^(2) + v. Press enter on the double up arrow in the Ans section to see the answer. There are 19 different graphs. Great practice to learn about translations.

TI-Nspire File(s): Study_Cards_Parabola_Equations.tns Accompanying file(s): NONE

The Great Applied Problem

Geometry, Trigomometry, Precalculus, Calculus

This is the Nspire version of my all time favorite applied problem that can be used in Geometry, Trigonometry, or Calculus. I have 3 different versions of this: Student (handheld), Teacher (handheld), and a Dynamic Extension that is best used on a desktop.

TI-Nspire File(s): The_Great_Applied_Problem_STUDENT.tns The_Great _Applied_Problem_TEACHER.tns The_Great_Applied_Problem_DYNAMIC_Extension.tns Accompanying file(s): NONE

Fractional Exponents Exploration

Algebra 2, Precalculus

Interactive activity is designed for students to 'discover' what a fractional exponent means by using the Calculator APP to explore expressions like 25 to the one-half power, or 64 to the one-third power.

TI-Nspire File(s): Fractional_Exponents_Exploration.tns Accompanying file(s): NONE

Factoring Modules 1, 2, 3, 4, 5, 6, 7, 8

Algebra 1, Algebra 2, Precalculus

Students are shown how to factor expressions using several different techniques, each module shows a different technique. Module 1: GCF; Module 2: Sum and Difference of 2 Squares; Module 3: Trinomials by Trial ‘n Success with leading coefficient 1; Module 4: Trinomials by Trial ‘n Success with leading coefficient not 1; Module 5: Sum of 2 Cubes; Module 6: Difference of 2 Cubes; Module 7: By Grouping (4 terms); Module 8: Summary of previous 7 modules. Exercises are given and the correct answers are supplied using the Q & A feature of Nspire.

TI-Nspire File(s): Factoring_1.tns Factoring_2.tns Factoring_3.tns Factoring_4.tns Factoring_5.tns Factoring_6.tns Factoring_7.tns Factoring_8.tns Accompanying file(s): Factoring_Gift_54_Problems.pdf

Maximize the Area of a Basketball Key

Calculus

This acitivity is designed for calculus students. Problem: you are given 100 feet of fence and you are to enclose a figure that looks like a basketball key: consisting of a rectangle with a semicircle attached to the top of the rectangle. Find the dimensions of this shape that uses 100 feet of fence to enclose it and also has the maximum area. Find that maximum area.

TI-Nspire File(s): Maximize_the_Area_of_a_Basketball_Key.tns ANS_KEY_Basketball_Key.tns Accompanying file(s): Maximize_the_Area_of_a_Basketball_Key.pdf

Distance from a Point to a Line Activity (CAS)

Geometry, Algebra 2, Precalculus, Calculus

This activity is designed for students to investigate how to calculate the distance from a point to a line. Multiple representations are used: pencil and graph paper, graphing calculator, CAS. Eventually the student will generate (derive) the Distance From a Point to a Line formulas using CAS.

TI-Nspire File(s): Student_Distance_Point_to_a_Line.tns Teacher_Distance_Point_to_a_Line.tns Accompanying file(s): Distance_Point_to_a_Line_ActivityCAS.pdf

Radical Expression Investigation Modules 1 to 4 (CAS)

Algebra 1, Algebra 2, Precalculus

This activity is designed to assist students in learning how to simplify radical expressions, add, subtract, multiply, divide. Students will need the accompanying pdf.

TI-Nspire File(s): Radical_Investigation_Module_1.tns Radical_Investigation_Module_2.tns Radical_Investigation_Module_3.tns Radical_Investigation_Module_4.tns Accompanying file(s): Radical_Investigation_Gift.pdf

Study Cards – Trigonometry Unit Circle Values in Degrees and Radians

Trigonometry

This activity uses the Notes Q & A feature to simulate electronic flash cards. Right now there are the trig unit circle values in both radian and degree modes, either from 0 to 2 pi or 0 to 360 degrees. More will be added later.

TI-Nspire File(s): Degree_Study_Cards_Unit_Circle_sin_cos_tan.tns Radian_Study_Cards_Unit_Circle_sin_cos_tan.tns Radian_Study_Cards_Solve_Trig_Equations_sin_cos_tan.tns Accompanying file(s): NONE

Study Cards – Basic Graphs Given the graph, state the equation BG 1

Algebra 2, Precalculus

This activity uses the Notes Q & A feature to simulate electronic flash cards. There are 18 Basic Graphs, each on its own “card”. Students will be asked to state the equation that is graphed.

TI-Nspire File(s): Study_Cards_BG_1_Basic_Graphs_Equations.tns Accompanying file(s): NONE

Study Cards – Basic Graphs Given the graph, state the equationBG 2

Algebra 2, Precalculus

This activity uses the Notes Q & A feature to simulate electronic flash cards. This is very similar to BG_1 except that the graphs have been translated. There are 17 Basic Graphs, each on its own “card”. Students will be asked to state the equation that is graphed.

TI-Nspire File(s): Study_Cards_BG_2_Basic_Graphs_Equations.tns Accompanying file(s): NONE

Synthetic Substitution Examples

Algebra 2, Precalculus

This activity shows students how to evaluate functions using synthetic substitution (by hand) and then check the answer by using Nspire.

TI-Nspire File(s): Synthetic_Subst_examples.tns Accompanying file(s): NONE

Evaluate functions at variable expressions

Algebra 2, Precalculus

This activity shows students how to evaluate a quadratic function at expressions like (x + 3) and at (– x).

TI-Nspire File(s): Evaluate_functions_at_variable_expressions.tns Accompanying file(s): NONE

Minimization Application Problem by Graphing on Nspire

Precalculus

This activity supplies a cost equation and the student is asked to find its minimum value graphically and interpret the solution in words.

TI-Nspire File(s): Minimization_application_problem_by_graphing.tns Accompanying file(s): NONE

Calculus Review of s(t), v(t), and a(t)

AP Calculus

This activity asks students to review the relationships among a position function, s(t), its velocity function, v(t), and its acceleration function, a(t). Graphically and analytically.

TI-Nspire File(s): Calculus_review_of_s(t)_v(t)_a(t).tns Accompanying file(s): NONE

Arithmetic Progression: find the missing terms

Precalculus

This activity provides two terms of an arithmetic progression (sequence) and asks the student to find the 4 other terms.

TI-Nspire File(s): Arith_Prog_find_the_missing_terms.tns Accompanying file(s): NONE

Geometric Progressions and Arithmetic Progressions 9 examples and application problems

Precalculus

This activity contains 9 examples and applied problems with the solutions explained using the Geometric and Arithmetic Progression formulas.

TI-Nspire File(s): Geom_Prog_Arith_Prog_9_ex_and_apps.tns Accompanying file(s): NONE

More Activities Will Be Continually Added As They Are Developed. Come back soon.