The Year 3 Inverse Operations 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.
commutative: Calculations which have the same answer no matter what order the numbers are in. Only addition and multiplication are commutative. For example: 2 x 6 = 12 and 6 x 2 = 12 and 5 + 4 = 9 and 4 + 5 = 9.
Varied Fluency
Knowledge Organiser
• Designed to support all children via key information and examples.
Scaffolded Examples
• Finding the whole and the parts in a bar model, then writing its related facts.
Support
• Q1: Write the four related facts from a bar model; the whole is placed in two calculations.
• Q2: Check two additions with the inverse; column subtraction set up in grid.
• Q3: Check a subtraction word problem; column addition set up in grid; no exchanges.
Core
• Q1: Write the four related facts from a bar model.
• Q2: Check two additions with the inverse; blank grid provided.
• Q3: Check a subtraction word problem; blank grid provided; one exchange.
Stretch
• Q1: Find the missing part of a bar model, then write its four related facts.
• Q2: Check two additions with the inverse; two-part exchange in each subtraction; blank grid provided.
• Q3: Check a subtraction word problem; blank grid provided; two exchanges.
Reasoning and Problem Solving
Support
• Q1: Reasoning – explain whether a character has checked an addition correctly; calculations shown using column method.
• Q2: Reasoning – explain whether the related facts have been listed correctly; bar model provided.
• Q3: Problem Solving – find three possible wholes for a given part; the whole is below 500.
Core
• Q1: Reasoning – explain whether a character has checked an addition correctly.
• Q2: Reasoning – explain whether the related facts have been listed correctly.
• Q3: Problem Solving – find three possible wholes for a given part; the whole is between 500 and 900.
Stretch
• Q1: Reasoning – explain which character has checked an addition correctly.
• Q2: Reasoning – explain whether the calculations given can be used to check an answer; includes inverse and estimation.
• Q3: Problem Solving – find three possible wholes for a given part; the other part must be the larger.
Deeper Reasoning
The question in this set focuses on using different representations to match the inverse and fact families to deepen understanding in using inverse operations to check answers.
