Mathematics Methods Yr11 by Texas Instruments

Students develop an understanding of concepts, build techniques and solve applied problems involving functions, calculus, probability and statistics. Students use mathematical and statistical reasoning, choose and apply technology appropriately and develop a capacity to communicate in a concise and systematic manner using appropriate mathematical and statistical language.

For more information on the WACE Mathematics Methods course, visit the SCSA website.

WA: Mathematics Methods Yr11 Classroom Activities	Download
Functions and Graphs
Understanding Transformations Watch Activity Tutorial Understanding transformations looks at how points are translated and dilated (towards and away from the axis) and what this means for the equation. The new point tool makes this very intuitive. The extension content naturally blends this approach into matrices and helps students understand rather than blindly applying rules.	Download6
Reflections Watch Activity Tutorial Reflections in the x and y axes, the line y = x and also x = n and y = m, they're all here. The companion video helps students understand reflections and how they can be performed on the calculator. This activity includes a range of extension questions that are more conceptually demanding.	Download1
Building Rules This activity explores three different ways to generate a rule for a particular interactive and dynamic block pattern. Students use symbolic notation to develop algebraic expressions and represent functions, solve systems of simultaneous equations and produce graphs from data. At the end of the activity students are provided with a powerful visual representation of the same problem that helps them produce the same equation simply and easily.	Download21
Number Sums This activity starts with a problem to solve: Determine the number of cans in a stack, 30 rows high. Students use a range of visual and numerical representations of similar, related problems to build an understanding of associated algebraic formulas that can be used to solve this problem. The focus of the activity is on developing algebraic formulas with a fundamental understanding of their structure and therefore a deeper understanding of their meaning.	Download38
Equation of a Circle The aim of this investigation is to develop the equation of a circle of radius, r, centred at the origin, and to explore how the equation changes when the centre is translated parallel to the x and y axes.	Download67
Personal Polynomials Watch Activity Tutorial If A = 1, B = 2 ... your name could be converted into numbers and described as a function, your Personal Polynomial. What does your polynomial look like? Students find their own personal polynomial and then study its properties. They set up and use simultaneous equations to find their polynomial, the bisection method to locate x-axis intercepts and transformations to compare others. Palindromic names create polynomials with an axis of symmetry. Is it possible for two names to generate the same polynomial, Alex(x) compared with Alexander(x)? A guided exploration task that will run over several lessons.	Download80
Trigonometric Functions
Unit Circle Sine Students explore an animated unit circle, looking for patterns. The interactive content allows students to control the level of assistance when answering questions. To understand relationships such as –sin(x)=sin(-x) switch the hint on to see a triangle with its corresponding reflection. The graph of sin(x) is broken into four parts to align with each quadrant of the unit circle and finally, exact angles are reviewed.	Download139
Biorhythms Students use trigonometric functions to model biorhythmic activity. Whilst the psuedo science of biorhythms equates approximately to astrology, the activity content is applicable to graphing simple trigonometric functions involving only transformations. The alignment of days helps students understand the period of the function.	Download1,782
Differential Calculus
Take it to the limit Students explore how a regular polygon can be used to approximate the perimeter and area of a circle. The purpose of the activity is to provide a practical, geometric approach to understanding the concept of a limit.	Download50
Gradient of a function This activity introduces the notion of the gradient of a curve. Initial exploration involves a dynamic tangent where students can use prior knowledge of the gradient of a straight line to determine if the slope is negative, zero or positive. The second stage of the activity goes one step further by quantifying the gradient. The third stage sees the gradient function generated automatically including an opportunity to freely explore the relationship between a parabola and its gradient function. T	Download90
Triangle Areas A triangle circumscribes a rectangle. The triangle is not unique, so what is the minimum area of the triangle that circumscribes the triangle? Students use the dynamic representation on TI-Nspire, data capture and more to explore this problem with some elegant solutions.	Download8
Fill the Vase Students interpret graphs of empirical data with respect to rate of change of the height of water in vases of different shapes that are being filled at a constant rate. Students are provided with a range of graphs and vases. For each graph they must reshape the vase in order to match the volume – height graph. For each vase they must produce a volume – height graph. Practical ideas including data collection and videos are provided in the teacher notes.	Download81
Sequences and Series
Pebbling the Chessboard It’s amazing how often sequences and series pop up in problem solving. In this deceptively challenging problem three discs are placed on a chessboard in a bounded region. The task is to move the pieces out of this region with the only complication being that pieces double when moved. After you’ve struggled to find the solution a geometric sequence comes to the rescue!	Download61

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Understanding Transformations

Reflections

Building Rules

Number Sums

Equation of a Circle

Personal Polynomials

Unit Circle Sine

Biorhythms

Take it to the limit

Gradient of a function

Triangle Areas

Fill the Vase

Pebbling the Chessboard

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