Algebra - Find a Rule (Two Step) - Presentation

In this engaging algebra lesson, Year 6 students delve deeper into the world of function machines, tackling problems that require a two-step process to find a rule. The lesson prompts students to consider the importance of the order of operations, challenging them with the question of whether the sequence in which functions are solved affects the outcome. For example, students are asked to determine the output when the input is 7, and conversely, to work out the original input if the output is 11. They are also encouraged to think abstractly by considering inputs represented by variables such as 'a' and 'x'. The function machine presented provides a visual aid, showing inputs being transformed by multiplication and addition to produce outputs, which students must calculate using the given operations.

Further activities invite students to explore patterns within function machines, as they complete tables that transform inputs by applying a two-step rule involving multiplication and subtraction. They are tasked with identifying the input that would result in a specific output, using reverse operations to solve the problems. The lesson also includes a challenge where students must simplify a two-step function machine into a single-step operation and verify their answers by testing different values. To deepen their understanding, students examine various algebraic expressions, translating them into the language of function machines. They engage in reasoning tasks, comparing different function machines to determine if they can produce the same outputs and which ones can be represented as a single function. Independent work reinforces these concepts, prompting students to scrutinize function machines, complete tables, and convert two-step functions into one-step functions, fostering a comprehensive grasp of algebraic rules and operations.