First of the three ways is, the remainder may be expressed in fractional form, as with
Second, the remainder may be expressed as part of the number sentence associated with the problem, or (4 x 5) + 4 = 24.
Third, the remainder may be dropped. For example, if the child is asked how many cheese boxes (having capacity of eight pieces) will be filled when the shopkeeper has 25 pieces, he can correctly respond "3," rightfully ignoring the remainder.
Fourth, the quotient may be increased by 1. Suppose the child is asked the number of tables required for a party of 15 people if 4 people can be seated at each table, he can correctly respond "4."
You would have realized that the answer should relate to the sense of the problem wherever such is known. When the problem situation is not known and divisions with remainders are being practiced, you and the child may agree on whatever of the given forms you prefer.
One option not recommended is the one presented in the previous article, i.e.
The quotient 4 R 4 is not a number and so is mathematically incorrect.
To help children develop correct visualization of the division some ideas are presented in the article Visualizing the Numbers (Part VI) After children enjoy working out divisions, they should be guided to record their work in the following table.
To the above table add 4 more rows, below the row for division of 8 by 1.
In these rows add the following facts.
- 1st row: 9 divided by 1, 18 divided by 2
- 2nd row: 10 divided by 1, 20 divided by 2
- 3rd row: 11 divided by 1, 22 divided by 2
- 4th row: 12 divided by 1, 24 divided by 2
A stage is reached when the children must learn the division facts so that they know them without having to think. Unless these facts are known perfectly, children are held up when they have to deal with more complicated processes. In many cases where children have difficulty with arithmetic, the trouble can be traced back to a faulty knowledge of the division facts.
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