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WS04 - Polynomial math art

Mathematics, Year 9

By the end of Year 9, students recognise and use rational and irrational numbers to solve problems. They extend and apply the exponent laws with positive integers to variables. Students expand binomial products, and factorise monic quadratic expressions. They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment. Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions. They graph quadratic functions and solve monic quadratic equations with integer roots algebraically. Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations.

 

They apply formulas to solve problems involving the surface area and volume of right prisms and cylinders. Students solve problems involving ratio, similarity and scale in two-dimensional situations. They determine percentage errors in measurements. Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles. They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings. Students express small and large numbers in scientific notation. They apply the enlargement transformation to images of shapes and objects, and interpret results. Students design, use and test algorithms based on geometric constructions or theorems.

 

They compare and analyse the distributions of multiple numerical data sets, choose representations, describe features of these data sets using summary statistics and the shape of distributions, and consider the effect of outliers. Students explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view. They determine sets of outcomes for compound events and represent these in various ways. Students assign probabilities to the outcomes of compound events. They design and conduct experiments or simulations for combined events using digital tools.

Algebra

AC9M9A02

simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

Algebra

AC9M9A04

identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

Algebra

AC9M9A05

use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings

Algebra

AC9M9A06

experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns

Annotations

 

1. Explains how mathematical functions, specifically quadratics, can be used to construct a model to represent an artwork.

2. Explains how adjustments to the formats of functions are needed to demonstrate the required criteria of the task.

 

3. Identifies different formats for representing quadratic and linear functions within the artwork.

4. Provides a link to a digital graphing tool used to create a piece of digital artwork. See Artefact 2.

 

5. Explains how the 'a' coefficient is varied to achieve a maximum or minimum shape of a quadratic function used to create a section of the artwork.

 

6. Describes how the digital tool is used to experiment, control the variables and cause an effect on the curve.

 

7. Describes how the factored form of a quadratic could be manipulated to create a particular section of the artwork.

8. Describes how to manipulate the algebraic representation of a quadratic function expressed in turning point form and compare the effect on its related graph.

 

9. Expands algebraic expressions, including combinations of binomials.

 

10. Rearranges algebraic terms to set up an equation for solving.

11. Shows how a digital tool can be used to solve algebraic equations.

12. Uses graphing software to demonstrate how a quadratic function has no x-intercepts.

13. Provides an evaluation of the mathematical modelling process used to produce a piece of digital artwork, including consideration of how a more accurate image could be achieved.

Annotations

 

1. Uses the function component of a digital graphing tool to experiment with functions used to model the artwork.

 

2. Recognises the connection between the graphical and algebraic representations of a quadratic function.

 

3. Uses a negative coefficient to draw a quadratic function with a maximum turning point, and a positive coefficient to draw a quadratic function with a minimum turning point.

 

4. Demonstrates how different quadratic and linear functions are used to show symmetry within the artwork.

 

5. Uses the format for entering a linear function within a digital graphing tool.

 

6. Uses the slider functionality of a digital graphing tool to identify a point of intersection between function graphs.