When knowing the coordinates of two points, the distance between them, their midpoint, and the equation of the line can be calculated and used to solve problems.
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.
This collection of activities guides students through the language of linear equations, and plotting points. One or more of the activities can be used to help set the scene for the topic, while marbleslides can be a great activity for engaging students in manipulating linear equations.
Practice questions relating to finding the midpoint between two points.
A video that explains how to use the midpoint formula to find the midpoint of a line segment on the coordinate plane or find the endpoint of a line segment given one point and the midpoint.
Which One Doesn't Belong? Is a website that provides thought-provoking puzzles for mathematics teachers, students and families. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong.
The graphs problems can be used as a prompt for a lesson that can be streamed, or alternatively, engaging students in providing their own reasoning through effective communication. If you select graphs that are straight lines to connect with the current learning, it will provide some evidence in the progress of sophisticated language across the topic. In the online environment, posting one of these problems on your Learning Management System, and asking students to vote for their correct answer (but keep this hidden from the students) and write a short response that summarises their reasoning. A follow up can be to review the votes of the poll, and then ask students to write why they think someone would have chosen the other answers. The final step in the sequence is to then reveal a model answer and explain what makes more effective mathematical communication. This can be done once a week to continue to build on the quality of responses over time.
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.
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 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.
The consumer arithmetic unit can be implemented effectively online. This module is a website that presents similarly to a textbook, and provides explanations, followed by questions and worked examples, along with worked solutions.
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
As an inquiry protocol, these mathematics resources do need some structure and group norms to be formed around them, but when used effectively, they can be powerful. This resource can be a good way to engage students with some mathematical activities that can also engage their family, as they are given tools to explain tricks and games.
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.
This set of questions relates to the Algebra of straight line graphs. After a period of content delivery or inquiry, set one or two diagnostic questions, 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.