This problem solving activity has a number focus.
Here’s a subtraction problem.
The numbers a and b stand for digits.
If the two subtraction sums give the same answer, what digits do a and b stand for?
This problem requires a sound knowledge of place value. It is essential for students to understand the grouping and place value basis of our number system. They must be able to:
Here’s a subtraction problem. The numbers a and b stand for digits. If the two subtraction sums give the same answer, what digits do a and b stand for?
This problem can be adjusted in many ways.
For example:
Change the number 5. Replace it in all the subtraction sums by 2 or 8 or ? What happens to a and b? Is there a pattern?
Pose these problems:
5000 | 5abc |
-abc5 | -5000 |
Or
50000 | 5abcd |
-abcd5 | -50000 |
Several strategies can be used to solve this problem, including guess and check. One way is to just observe that in the left subtraction, there must be 5 ones. In the right subtraction there are b ones. Therefore, b has to be 5 because the two answers are the same.
Consider the tens. Since we now know that b = 5, the number that is to be found in the units column of the answer of the left subtraction is 4. In the right subtraction we see that
a = 4. Just check that there is nothing wrong with a = 4 and b = 5.
Changing 5 to 2 will give a = 1 and b = 8; changing 5 to 8 will give a = 7 and b = 2. Perhaps you see that pattern: (5 x 9 = 45; 2 x 9 = 18; …)
5000 problem is very interesting. It doesn’t work! There are no values of a, b, c that will make the two subtractions equal. Posing your students a problem that doesn't work is a worthwhile and legitimate challenge.
The surprising thing is that the 50000 problem works again! And the pattern here looks a lot like the 500 problem!
This problem might make a good investigation. There’s a lot in it and students find it fun to do.
Printed from https://nzmaths.co.nz/resource/500-problem at 7:34pm on the 19th April 2024