Equations of 3 variables can be visualised in three dimensions. In this activity students are provided with 5 sets of three equations. Supporting the understanding and development is a 3D graph for each equation set. Students can see how pairs of graphs interact or all three. An estimate for the point of intersection is gained from the 3D graph. Students are then provided with a scaffolded learning environment and resources where they progressively eliminate a variable. What does it mean graphically when a variable is removed?




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What happens when you square an imaginary number? Does it get bigger or smaller? How can you tell if the number will get bigger or smaller? This seems straight forward enough, but a really surprising result occurs if you add something after you square, then repeat, square and add, square and add. While the activity involves only adding, squaring and graphing complex numbers, the results are truly amazing.



 TINspire™ CX
 TINspire™ CX CAS

1


Students collect data for a bouncing ball using a CBR connected to their calculator. Consecutive ball bounces are modelled using combinations of translational, intercept and standard form of a quadratic equation. Each student has their own data so each student’s working and answers will be unique making it the ideal assessment task!



 TINspire™ CX CAS
 TINspire™ CX

5


This task provides a creative way to reinforce linear function algebra with Years 9–10 students land to learn about transformations of sets of such functions. The focus is on the students discovering what effect each parameter in the function (e.g. gradient & yintercept) might have on the shape and location of the set of graphs.




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What is the difference between simple and compound interest? Visually we can see that simple interest is linear and compound is nonlinear. These visuals can be used to improve student understanding of what a significant difference this can make over time. Dynamic representations illustrate how increasing the number of compounding periods and interest rates dramatically effect the contribution compounding interest has to the overall balance. Recursive techniques, including spreadsheets and formulas help reinforce the concepts numerically. See how you can retire with a million dollars on just $60.00 per week.



 TINspire™ CX CAS
 TINspire™ CX

26


How and why are transformations of exponential function different from polynomials? What is a dilation away from the x or y axis? This activity provides a series of questions, explorations and dynamic visuals that will help students understand transformations of exponential functions, including a selection of homomorphic representations.



 TINspire™ CX CAS
 TINspire™ CX

30


A collection of data from bouncing balls to pendulum swings and discharging capacitors are included in this activity for students to model. In each example the original function is presented and students determine the appropriate transformations to f(x) so that it models the collected data.




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A collection of data from bouncing balls to pendulum swings, discharging capacitors and Olympic rings are included in this activity for students to model. In each example the original function is presented and students determine the appropriate transformations of f(x) so that it models the data (or rings).



 TINspire™ CX CAS
 TINspire™ CX

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Watch Activity Tutorial
Vectors can be used to solve quite complex problems, in this activity students use position vectors in component form to describe points on the Cartesian plane. Students then explore these points, located on the function y = 1/x forming a triangle with some very interesting properties.




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Vectors can be used to solve quite complex problems. In this activity students use position vectors to describe points on the Cartesian plane. Students explore three points located on the function y = 1/x forming a triangle with interesting properties.




5


Vectors can be used to solve quite complex problems, in this activity students use position vectors to describe points on the Cartesian plane. Students explore three points located on the function y = 1/x forming a triangle with interesting properties.




31


Pascal's Triangle goes way beyond coefficients of binominal expansions and combinatorics. In this activity students are introduced to the basics but go on to explore other relationships and patterns such as the triangular and tetrahedral numbers, Fibonacci sequence and even Euler's number. There are so many hidden gems in this amazing triangle.




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The Golden Ratio and its association with the Fibonacci sequence is well know, but there is much more to explore. Variants of the Fibonacci sequence of the form t(n+2)=t(n)+a.t(n+1) also generate specific ratios. For a = 2 the ratio is referred to as the Silver Ratio, for a = 3, the Bronze Ratio. Collectively these are called the metallic ratios where a = 1 is the specific case and equals the Golden Ratio.




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Pascal’s Triangle goes way beyond coefficients of binomial expansions and combinatorics. In this activity students are introduced to these basics but go on to explore other relationships and patterns such as the triangular and tetrahedral numbers, the Fibonacci sequence and even Euler’s number. There are so many hidden gems in this amazing triangle.




5


Pascal’s Triangle goes way beyond coefficients of binomial expansions and combinatorics. In this activity students are introduced to these basics but go on to explore other relationships and patterns such as the triangular and tetrahedral numbers, the Fibonacci sequence and even Euler’s number. There are so many hidden gems in this amazing triangle.




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