Students work in pairs. They use two identical boards and only one kind of variable
counter, for example, a green square counter named s. The teacher shows students two
configurations of counters, one for each board.
Task
Put these configurations on your boards and find the value of the variable token for which
both boards have the same value.
Example
Add -7 to each board.
| 2s + 6 + 1 - 6 - 1 |
5 + 6 + 3 + 1 - 6 - 1 |
Regroup 7 - 7 = 0 on both boards.
Regroup 5 + 3 = 2 + 2 + 2 + 2 on rightmost board.
Halve the value of both boards.
So, s = 4.
Remark
In choosing a task the teacher should pay attention to the range of numbers represented on
the boards, in order not to give a task that is impossible.
The Method of Solving These Problems
Regroup the tokens on each board. Remote at the sane time two tokens, one from
each board, if they have the same value. Continue until all variable counters remain on
one board and all other counters are on the other board. Also on these boards, you can
sometimes halve both values or divide them by 3,5, 6, or 10.
Example
So, s = 13/7.
Example 2
Regroup 3 + 3 + 2 + 2 = 10 on the rightmost board.
Divide by 5 on both boards.
So, s = 2.
The teacher should explain this method to students. But the students need to find how to
use it efficiently. So such tasks should be given several times until they become routine.
Examples
| 6s + 5 + 5 |
10 + 10 + 10 + 3 + 1 |
Add -10 to each board.
| 6s + 5 + 5 - 10 |
10 + 10 + 10 + 3 + 1 - 10 |
Regroup 10 - 10 = 0 on both boards.
Regroup 10 + 10 + 3 + 1 = 6 + 6 + 6 + 6 on rightmost board.
Divide by 6 on both boards.
So, s = 4.
Webpage Maintained by Owen Ramsey
Number Board index
|
