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Quadratics

The theory of quadratics allows us to solve maximisation/minimisation problems . 

Inquiry Questions

How can we use quadratic functions to maximize profits or minimize cost?
How can we model the trajectory of objects moving around us (like a ball being thrown)?

Resource

Desmos

Desmos is an interactive graphing calculator that allows teachers to set engaging instruction, exploration and practice tasks. With many existing resources, and capacity to create your own, there are applications for all year levels and topics. 

A collection of activities, each used by South Australian teachers in the past, that can be used to engage students in learning activities of between 10 and 40 minutes, to support students in their understanding of Quadratic equations. 

Consider using the activity builder to assign questions that will allow you to gauge student understanding. 

Link: Activity Collection

 

 

Khan Academy

A learning sequence that begins from describing parabolas through to factoring quadratic equations. Individual videos can be used to provide direct instruction or support, while the related questions can be set as practice as they have aligned support and feedback. 

Link: Khan Academy Quadratics

GeoGebra

GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. 

Although Desmos does quadratics well, the need to engage with a full activity means there is still place for GeoGebra. This activity is a single page with some guiding questions that allow students to work through understanding the form of a quadratic equation. In particular, the “trace vertex” feature provides a visual clue to the impact of changing coefficients. 

Link: GeoGebra

 

TES – Quadratic Area Puzzles

TES is an English resource website that is one of the largest resource sites available with most resources made by teachers and reviewed for use. 

Link: TES

This resource can be used as a set of practice activities, and a unique puzzle can be given to each student as a form of quiz to check for progress through the topic. The puzzle links areas of rectangles with the factorisation of quadratic polynomials designed to develop fluency and problem-solving skills. 

reSolve

The reSolve teaching resources provide exemplary materials from Years F to 10. They put into practice the elements of the reSolve Protocol and promote fluency, deep understanding, strategic problem solving, and mathematical reasoning. A number of the resources have been made by South Australian teachers, and all are aligned with the Australian Curriculum. 

Link: ReSolve Activity sequence

This three-lesson sequence aims at bringing the real world to Quadratic functions. These lessons reveal the links between the graphs of quadratic functions and the three algebraic forms (turning point form, product, sum of three terms) and the influence of the parameters in the functions. 

Open Middle

While “Open Middle” is an unusual name for a website of mathematics problems, it is a great way of getting students to practice and work within a higher depth of knowledge and conceptual understanding, and encourage critical and creative thinking to approach a problem.  

Link: Open Middle - Quadratics

The problems in this section can be set for practice in a lesson, reducing the number of problems that need to be set. The strategy for the teacher is to “talk-through” the different methods and supporting students to move beyond “guess and check” methods and consider linking their prior knowledge to solve the problems. 

The Improving Mathematics Education in Schools (TIMES) Project

The TIMES project, by the Australian Mathematical Sciences Institute, provides modules that are written for teachers. Each module contains a discussion of a component of the mathematics curriculum from early primary up to the end of Year 10.  

Link: AMSI module

This module is a website that presents similarly to a textbook, and provides explanations, followed by questions and worked examples, along with worked solutions. 

Diagnostic Questions

Diagnostic questions are designed to help identify, and crucially understand students' mistakes and misconceptions in an efficient and accurate manner. In a remote learning environment, these questions are vital for checking on progress. At crucial moments in a lesson, set a diagnostic question or two to quickly ascertain the progress of the class, and importantly, understand misconceptions quickly, which can be hard to achieve in a remote environment. You will need to sign in (for free) to access. 

Link: Diagnostic Questions

This set of questions relates to quadratic graphs. After a period of content delivery or inquiry, one or two diagnostic questions, set to each member of the class via the Learning Management System, collect the results and identify any student or group of students that have misconceptions that you can then address.