Embedded Files
Overview
Overview
Compensation
Compensating is a strategy where students change the numbers in a calculation to create one that is easier to solve. Compensation uses ideas of equivalence in addition, and constant difference in subtraction.
Compensation in Addition
When presented with images like these, students will often visualize moving some counters to fill up a 10 frame, or to fill up a row in a hundreds chart.
The equations are annotated to show how many are moving from one addend to the other.
Compensation in Subtraction
The key idea to understand how compensation works in subtraction is called constant difference. This visual (from Bainingcamp’s number line tool) shows that the difference between 10 and 0, 11 and 1 and 12 and 2 always stays equal to 10.
So, 10 - 0 = 10
11 - 1 = 10
12 - 2 = 10
Compensation in Addition
Compensation in Subtraction
Supporting Students with compensation
Supporting Students with compensation
Addition
Understanding compensation in addition can be done with 10 frames and 2 colour counters.
Ask students to help turn over one counter at a time, and tell you the addition equation (sentence) for each one.
10 + 0 = 10
9 + 1 = 10
8 + 2 = 10
7 + 3 = 10
What's the pattern here? How can we change the numbers, without changing the sum?
Subtraction
One way to help students discover how compensation works in subtraction is to ask them to write as many subtractions equations (sentences) that equal a certain number (for example, 20).
This visual shows that to keep the difference (answer) the same, both the minuend and subtrahend (first number and second number) need to go up or down by the same amount.
Games to Promote Compensation
Games to Promote Compensation
Compensation Matching Games
Compensation Matching Games
The cards on the slide deck below could be used in a matching game or “Go Fish” type game to help students become familiar with the different combinations that compose a number.
For example:
Lay out a 3 x 4 array of cards (face up), and deal each player 4 cards each. Players search for a card that goes together with something they have in their hands, and keep the set of 3, with 2 number sentences and a picture.
Students should be encouraged to verbalize their combinations. “ 8 + 6 = 10 + 4”
A more advanced version of the game (in the same card deck below, has 2 cards that make a set, and has no pictures.
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