# Equal Additions

Teacher’s Notes

These exercises and activities are for students to use independently of the teacher to practice number properties

### Number Framework domain and stage:

Addition and Subtraction. Advanced additive to advanced multiplicative

### Curriculum reference:

Number, levels 4-5

### Numeracy Project book reference

These activities can be used to follow the teaching episodes based on **Equal Additions - Book 5 , page 38** and are for those students who are able to use the associated number properties.

### Prior knowledge. Students should be able to:

- Instantly recall the addition of single-digit numbers up to a total of 20
- Know the related subtraction facts
- Add and subtract on decimals with tenths and hundredths

### During these activities, students will meet:

- Subtraction problems that can be solved by equal additions
- Subtraction problems that can be solved by equal subtractions
- Algebraic expressions derived from equal additions problems.

### Background

These exercises start with students solving subtraction problems by turning the subtrahend (second number) into a tidy number, usually a decade. 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 completely shift the student’s attention to the two subtraction statements formed by the computational strategy of ‘equal addition’. Exercise 4, Question 3 is critical to further understanding of this exercise, and hinges on the student’s willingness to ‘read the equality backwards’, and so 88-60 is a simpler and equivalent computation to 84-56. This example also brings to light the relationship that while equal additions retains equality, so does equal subtractions. This is further explored in the rest of the exercise. By the end of the exercises the relationships are not necessarily those used in an efficient computation of the problem. The purpose now is to highlight the principle of equal compensation applying to any set of numbers of this form.

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.