Teaching mathematics
Teaching mathematics

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Teaching mathematics

2.3 Adding and subtracting fractions

Learners are often told that the denominator in the fraction denotes what kind of a fraction it is (halves, thirds, etc.) and that it is only possible to add or subtract the same types of fraction, i.e. the denominator has to be the same number. This is where the difficulty lies as learners struggle to find out which number should be the common denominator and what needs to be done to change each fraction so that they do have the same denominator. Several rules and procedures exist to help learners to add and subtract fractions but, since the conceptual basis is poorly understood, learners typically do not remember the rules and procedures. This often leads to fractions being taught again and again with little success.

It is worth looking at other methods which build on and develop learners’ conceptual understanding of fractions. The next section gives an approach to teaching the adding of fractions which is based on learners’ prior knowledge of finding fractions of a quantity.

Activity 6 Shading a grid

Timing: Allow 10 minutes

Try the following activity.

Draw a 6 by 4 grid. Next shade the grid according to this schedule (with no shading overlapping):

Shade one divided by two in red

Shade one divided by four in blue

Shade one divided by eight in green

Shade one divided by 24 in yellow

Shade one divided by 12 in grey

The whole rectangles should have been shaded once the activity is completed.

Discussion

Did your grid look like this, or at least have the same number of parts per colour?

Figure 3 shading fractions of a rectangle

Activity 7 Use the grid to add fractions

Timing: Allow 5 minutes

I hope it is clear that each box in the rectangle is one divided by 24 since the grid has been split into 24 equal parts. This should help you (and your students) to calculate the following additions of fractions based on the shaded grid.

multiline equation row 1 one divided by two plus one divided by eight equals row 2 sum with, 3 , summands one divided by four plus one divided by six plus one divided by 12 equals row 3 one divided by eight plus one divided by 24 equals

Discussion

Did you get these answers?

multiline equation row 1 one divided by two plus one divided by eight equation left hand side equals right hand side five divided by eight row 2 sum with, 3 , summands one divided by four plus one divided by six plus one divided by 12 equation sequence 12 divided by 24 equals one divided by two row 3 one divided by eight plus one divided by 24 equation sequence four divided by 24 equals one divided by six

With some experience of adding fractions using this grid shading methods students should begin to see that they are looking for a common denominator which would have been the number of parts in the grid. Subtraction can be carried out in a similar way by thinking about shading parts on the grid and then rubbing some of them out.

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