The Year 6 Inverse Operations (Addition and Subtraction) PowerPoint guides both teachers and children through the lesson, including use of the varied fluency, reasoning and problem solving, deeper reasoning and scaffolded resources. Key learning information about this step:
Key Vocabulary
inverse operations: Used to check working out or to find a starting number by using the opposite operation. Addition is the inverse of subtraction and vice versa. Multiplication is the inverse of division and vice versa.
related facts: Also known as fact families, these are a group of four calculations that are created using the same three numbers, for example 2 + 5 = 7, 5 + 2 = 7, 7 – 2 = 5, 7 – 5 = 2. This can also be used to identify derived facts, for example 20 + 50 = 70.
part-whole model: A representation showing the whole number and the parts it has been split into.
Varied Fluency
Knowledge Organiser
• Designed to support all children via key information and examples.
Scaffolded Examples
• Finding the missing part of a bar model, then writing its related facts.
Support
• Q1: Complete a bar model to find a missing whole or part; write one addition and one subtraction.
• Q2: Finding a missing part in a worded problem; no exchange; calculation grid given.
• Q3: Find missing wholes and parts in one-step calculations; no exchanging.
Core
• Q1: Completing a bar model to find a missing whole or part; all four related facts; bar model given.
• Q2: Complete two worded problems; choose the inverse operation to find either a missing whole or a missing part.
• Q3: Find missing wholes and parts in one-step addition and subtraction calculations; unknown in different positions.
Stretch
• Q1: Completing a bar model; write four related facts; no support.
• Q2: Completing two two-step worded problems; work backwards through two operations in the correct reverse order.
• Q3: Find missing numbers in two-step calculations; undo two operations in reverse order to find missing start number.
Reasoning and Problem Solving
Support
• Q1: Reasoning – explain whether an inverse check is correct.
• Q2: Reasoning – prove claims about addition and subtraction facts using fact families; using structured 4-digit numbers.
• Q3: Problem Solving - find possible starting numbers from a one-step inverse using 4-digit numbers and a given range.
Core
• Q1: Reasoning – explain misconceptions involving whole and parts when checking subtraction.
• Q2: Reasoning - prove claims about both subtraction facts using fact families; within 5-digit fact families.
• Q3: Problem Solving - undo and work backwards through two operations using 5-digit numbers and a given range.
Stretch
• Q1: Reasoning – explain and justify whether an inverse check proves a calculation is correct.
• Q2: Reasoning – deduce and prove related facts from one known 5-digit fact without calculating.
• Q3: Problem Solving – find multiple pairs of values satisfying a two-step inverse relationship with additional constraints.
Deeper Reasoning
The questions in this set focus on problem solving with addition and subtraction to deepen understanding in adding and subtracting whole numbers with more than four digits, including using formal written methods (columnar addition and subtraction), and solving addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
