L2 Use Inverse Operations to Check Answers

Description

This Year 3 maths lesson on inverse operations helps pupils understand how addition and subtraction are connected and how the inverse can be used to check the accuracy of calculations. Through discussion, reasoning activities and a teacher-style checking task, children develop a deeper understanding of number relationships and mathematical reasoning.

The lesson begins with a starter activity revising previous Year 3 learning on addition, subtraction, place value and multiplication. Pupils solve several calculations on whiteboards using either mental strategies or formal written methods. The answers are then linked to fact families, helping children recognise the inverse relationship between addition and subtraction. Pupils discuss why knowing fact families can make checking calculations quicker and more reliable.

During the main teaching input, pupils learn how to use the inverse to check answers. They examine a worked example where a pupil checks the subtraction calculation 496 – 123 = 473. By performing the inverse addition 123 + 473, children discover that the total should equal the original number (496) if the subtraction is correct. As the result is 596, they identify the mistake and discuss how the inverse operation helped reveal the error.

Children then work through a table of calculations together, using inverse operations to decide whether answers are correct or incorrect. They are encouraged to reason about whether using the inverse is the most useful checking strategy in each case, or whether other approaches, such as place value understanding or estimation, might be more efficient.

In the independent activity, pupils take on the role of the teacher. They are given a sheet of completed calculations and must select at least four to check. Children cut and stick the problems into their maths books, write the inverse calculations to test the answers, and explain whether the original calculation is correct. They are also encouraged to reflect on when using the inverse method is particularly helpful.

The plenary introduces missing number problems, demonstrating how using inverse operations can help solve them more easily. Pupils practise rewriting calculations so the unknown number appears after the equals sign, helping them understand how inverse relationships support problem solving.

The lesson also addresses common misconceptions, such as repeating the same calculation instead of using the inverse, misunderstanding the meaning of “inverse”, or failing to estimate whether an answer is reasonable. This helps pupils build stronger reasoning skills and a deeper understanding of mathematical relationships.

This resource is ideal for Year 3 maths lessons on inverse operations, fact families, checking calculations, and reasoning about number relationships, supporting pupils in becoming more confident and accurate mathematicians.