Equal Additions

Prior knowledge

Addition basic facts

Background

These exercises start with students solving subtraction problems by turning the subtrahend (second number) into a tidy number, usually a decade and adjusting the first number accordingly, e.g. 72 - 39 = 73 - 40. Exercise 1 stays with whole numbers less than 100 while Exercise 2 extends the range to three and four digit numbers, and Exercise 3 introduces the same strategy to decimal subtraction. This will require a sound understanding of place value.
In later exercises the focus shifts from the computational answer and back to the relationship between the two subtraction statements in each answer. By writing down their thinking, students are being prepared to look at this relationship while still computing the answer.

Equality
The purpose of Exercises 4 and 5 is to draw student’s attention to the concept of equality. Students will see that the equation remains in balance if the same change ismade to both sides of the equation.  For example 56 - 38 = 58 - 40, bother numbers on both side have increased by two and in 74 - 44 = 68 - 40 both numbers on both sides have decreased by 4. This highlights that both equal additions and equal subtraction are valid strategies.

Algebra
Algebraic symbols appear in Exercise 6. The numerical examples of the previous exercises have prepared the students to think and view the structure of the problems in a particular fashion. This thinking doesn’t now change, it is simply the symbolism of algebra that is introduced.
Exercises 7 and 8 explore the effect of subtracting a bracketed quantity. Students are encouraged now to look beyond the equal compensation strategy itself and uncover a simple approach to handling such subtractions.

Comments on the Exercises

Exercise 1
Asks students to use the equal additions strategy with two digit numbers.

Exercise 2
Asks students to use the equal additions strategy with three digit numbers.

Exercise 3
Asks students to use the equal additions strategy with decimal numbers.

Exercise 4
Asks students to decide if equations are true or false by working out if the equation sides are balanced, e.g. True or false 56 - 38 = 58 - 40/

Exercise 5
Asks students to complete an equation by providing a number to balance the equation.

Exercises 6, 7, 8
Asks students to generalise the equal additions strategy by using symbols and numbers in equations e.g. n - 38 = (.......) - 40.