Inverse operations refer to two mathematical operations that undo each other. When you apply an operation to a number and then apply its inverse operation, you will return to the original number. For example, addition and subtraction are
inverse operations because adding a number and then subtracting the same number will bring you back to the starting point. Similarly, multiplication and division are
inverse operations because multiplying a number and then dividing it by the same number will also return you to the original number.
Full definition
The lesson gets children to use knowledge
of inverse operations and algebra rules to calculate a number represented by a letter.
Includes Bronze, Silver and Gold learning objectives: Bronze: I can calculate the output of a function machine Silver: I can calculate the input of a function machine using
inverse operations Gold: I can use a function machine to solve equations Includes answers
Check that a calculation gives an answer of the correct size by using simple approximations and
inverse operations if needed.
The repeated reasoning that results from fact families is
about inverse operations, addition and subtraction, multiplication and division.
Other students will have learned about reciprocals and that multiplication and division are
inverse operations.
The second and third questions use
inverse operations, and the third in particular gives pupils something a lot more interesting to think about.
Slides to formalise the idea of
an inverse operation, followed by a set of questions to check pupils can correctly correctly identify the inverse of a given operation and a worksheet of straight - forward fill the blank questions (albeit with decimals, to force pupils to use inverse operations).
Objectives covered: Add and subtract numbers mentally, including: a three - digit number and 1s; a three - digit number and 10s; a three - digit number and 100s Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction Estimate the answer to a calculation and use
inverse operations to check answers Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
They must find as many combinations as possible and check their answers using
the inverse operation.
It explores other mathematical concepts such as greater than and less than;
inverse operations; word problems and number sequences.
Examples and a set of questions on using
inverse operations to reverse a flowchart and solve its corresponding equation.
Plenary: A prompt to discuss an example of an equation that can't be solved using
inverse operations.
A complete lesson on solving one step equations using
inverse operations.
- NA2.1 simplify numerical expressions involving integers and rational numbers, with and without the use of technology - NA2.3 relate their understanding of
inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations - NA2.7 solve first - degree equations, including equations with fractional coefficients, using a variety of tools and strategies.
A complete lesson on solving two step equations using
inverse operations.
Walmsley's lesson was on the idea that multiplication and division are
inverse operations: that 8x2 = 16 and 16 ÷ 2 = 8.
For students that are struggling with changing the subject and
inverse operations, these functions machines might help make the topic clearer.
In this course, students begin with the fundamentals of algebra, where they compare, order, and perform operations on rational and irrational numbers, use
inverse operations to solve for a variable in one - and two - step equations, write and solve two - step equations from contextual situations, and analyze properties of functions, focusing on linear functions.
Even the most talented algebra teacher can not teach both her subject area and make up ground for students who are enrolled in her classroom and still do not have a basic number sense (for example, the understanding that multiplication and division are
inverse operations).
This multi-tasking proved troublesome for pupils, particularly question 17 from paper two, where pupils had to halve, use
inverse operations and work with decimals.
In the main part they learn how to use the method and
inverse operations to solve a two - step equation.