Using equivalence and the compensation property to calculate
Spine 1: Number, Addition and Subtraction – Topic 1.29
Primary
KS2
Year 5
Mastery PD Materials
Introduction
Explore the effect on the sum of changing the value of one or both addends; explore the effect on the difference of changing the value of the minuend, the subtrahend or both. Apply knowledge of compensation properties and inverse operations to calculate and balance equations.
Teaching points
- Teaching point 1: If one addend is increased and the other is decreased by the same amount, the sum stays the same. (same sum)
- Teaching point 2: If one addend is increased (or decreased) and the other is kept the same, the sum increases (or decreases) by the same amount.
- Teaching point 3: If the minuend and subtrahend are changed by the same amount, the difference stays the same. (same difference)
- Teaching point 4: If the minuend is increased (or decreased) and the subtrahend is kept the same, the difference increases (or decreases) by the same amount.
- Teaching point 5: If the minuend is kept the same and the subtrahend is increased (or decreased), the difference decreases (or increases) by the same amount.
- Teaching point 6: The value of the expressions on each side of an equals symbol must be the same; addition and subtraction are inverse operations. We can use this knowledge to balance equations and solve problems.