This problem solving activity has a number (addition and subtraction) focus.
Take any 2-digit number. Reverse the digits to make another 2-digit number. Add the two numbers together.
How many answers do you get which are still 2-digit numbers?
What do the answers have in common?
This problem provides an opportunity to practise the addition of 2-digit numbers. Encourage students to share the methods they use to solve the problem. For example, when faced with the problem 91 + 19 some students may use place value while others will find it easier to use a rounding method.
This problem also offers the opportunity for students to "play" with numbers. As well as practising addition the students are encouraged to look for patterns in their answers. This encourages students to increase their understanding of numbers and how they relate to one another. It also helps develop problem solving skills and creativity.
As numbers are 'reversed' they swap places. (eg. 41 to 14) It is therefore important to discuss what is happening to the place value of the numbers.
Take any 2-digit number. Reverse the digits to make another 2-digit number. Add the two numbers together.
How many answers do you get which are still 2-digit numbers?
What do the answers have in common?
Is there a pattern in the numbers that give 3-digit sums?
There are many patterns that can be found in this problem. Let's try a few numbers and see what we get:
13 + 31 = 44
26 + 62 = 88
47 + 74 = 121
54 + 45 = 99
68 + 86 = 154
Now we can see that if the sum of the digits in the 2-digit number is less than 10 then the sum of the reversed numbers is less than 100.
27 + 72 = 99
The sum of the digits in the 2-digit number determines the sum of the reversed numbers in the following way:
If the sum is 6 the answer is 66 (24 + 42 = 66; 15 + 51 = 66 etc)
If the sum is 8 then the sum of the reversed numbers is 88.
You might support your students to notice that the sum in every case above is a multiple of 11.
Once again the 3-digit sums are all multiples of 11. To see this, notice that 68 + 86 gives the same answer as 66 + 88. Now both 66 and 88 are multiples of 11, so the sum is too.
Printed from https://nzmaths.co.nz/resource/reversing-numbers at 11:44am on the 26th April 2024