Special Cases in Addition


Note: To find out if the child memorized not only the process of calculating in addition, but also the concept, the teacher organizes special combinations, starting with the combination that is familiar to the child.

…addition combination booklet
…large sheet of paper or chart,
…red and black pens
…special combination cards

Taking any one page of the booklet, the teacher asks, ‘When you work on this page, in this case 1+1, what are you looking for? the sum. In the work you have been doing up till now, you have been calculating the sum. On the chart the teacher writes the title, gives an example, and reads the example to the child.

0 – Calculating the Sum
1 + 2 = ? (One added to two gives you what number?)
The child fills in all the sums for that page.

1 – Calculating the Second Addend
1 + ? = 3 (One added to what number gives you three?)
Let’s cover the column of second addends with a strip of paper. Note, this is the first time the child considers a problem of this type. What must we solve here? the second addend.

2 – Calculating the First Addend
? + 2 = 3 (what number added to 2 will give you 3?)
On the model page with totals, the column of first addends is covered. The child sees that in order to complete this combination, the first addend must be found.

3 – Inverse of Case Zero; Calculating the Sum
? = 1 + 2 (what number is obtained by adding one and two?)
The same column of combinations is written on another sheet, without their sums this time, and with the addends to the right of the equal sign. The child sees that the sum must be calculated, as in the first case. The difference is that the problem is set up in reverse order.

4 – Inverse of 1st Case, Calculating the Second Addend
3 = 1 + ? (3 is equal to one plus what number?)
The sums are written in this inverted model, and the column of second addends is covered. The child sees that he must find the second addend.

5 – Inverse of 2d Case, Calculating the First Addend
3 = ? + 2 (three is equal to what number plus 2?)
The column of first addends is covered.

6 – Calculating the First and Second Addends
3 = ? + ? (three was obtained by adding the first number to the second number. What were these numbers?)
In this last case, both columns of addends are covered with strips of paper, leaving only the sum.

Collective Activity:
The teacher passes out the combination cards. In turn the child reads the problem, states what must be found, and finds the case on the chart.

Individual Work:
When the child has understood all of the cases as presented, he may work with these special combination cards. He fishes for one, reads it and writes the equation in his notebook, substituting the red question mark for the right number written in red

Direct Aims: to memorize addition combinations
to make the child realize what must be calculated

Indirect Aim: to prepare first degree equations in algebra, i.e. ( 4 + x = 6).

Notes: On the chart, #0 is not a special case since this is what is familiar to the child. In cases #1, #2, #4, #5, and #6, subtraction is indirectly involved. For this reason fewer activities for memorization of subtraction are necessary.

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