Problem
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?

What is this problem about?
This problem practices the addition of 2-digit numbers. As the curriculum document states that children need to develop "accuracy, efficiency, and confidence in calculating – mentally, on paper, and with a calculator" this problem can be used to practice any or all of these skills. Encourage the children to share the methods that they use to solve the problem. For example some children may mentally count on while others will find it easier to use a rounding method.
91 + 19   
counting on: 91 + 10 + 9
rounding: 91 + 20 – 1

This problem also offers the opportunity for children to "play" with numbers. As well as practising addition the children are encouraged to look for patterns in their answers. This play encourages children to increase their understanding of numbers and how they relate to one another.  It also helps develop problem solving skill and creativity.

Achievement Objectives
Number (Level 2)
- write and solve story problems which involve whole numbers using addition, subtraction, multiplication or division

Mathematical Processes
-devise and use problem solving strategies (look for patterns)

Resources required
calculator (depending on addition method being practised)
hundred's board
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- add 2-digit numbers with and without renaming

 Teaching Sequence

1. Introduce the problem – you could do this by writing 2 reversed 2-digit numbers eg 14 and 41. Ask the children what they can tell you about the 2 numbers. If they identify that they are reversed numbers then introduce the problem.
2. It is important that they are clear about how to reverse numbers and that they understand the difference between 2 and 3-digit numbers.
3. You may decide to do an example with the class.
4. Discuss with the children the strategies that they could use to add 2-digit numbers.
5. Let the children work on the problem individually before putting them in small groups. Some children are quicker than others when computing and it is important that all children have the opportunity to "play" with the problem before getting them to share their findings. If all children  have some work to bring to the group they are more likely to be involved in the solution.
6. As you circulate, encourage the children to explain how they are getting the answers.
7. Ask the children how they could organise their reversed numbers so that they could look for patterns in the answers. A good starting point would be to sort the 2 and 3-digit answers into lists or they may decide to identify the reversed numbers that give a 2-digit answer on the hundred's board.
8. Share patterns.

Extension problem
Is there a pattern in the numbers that give 3-digit sums?

Solution
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.

For the development band students, you might notice that the sum in every case above is a multiple of 11.