Hi, I am a student currently interning in a 3rd grade classroom in a state that has just adopted the Common Core Standards. I have to teach a lesson that has these kinds of problems:

"Miguel is thinking of a 5-digit odd number between 48960 and 49058. the ones digit is 3 more than the tens digit. What number could Miguel be thinking of?"

I have gone over what digits are, and reviewed odd and even numbers. The students are having trouble putting all of the clues in the problem together to solve it though. I have absolutely no idea how to teach them how to do this.

Before CCS, some teachers in my school have been hand holding and "helping" students complete their work- students in this class have very poorly developed critical thinking and problem solving skills.

Does anyone have any ideas or strategies I can use to teach the kinds of problems mentioned above?

I have no idea who to teach it, but if I had to do it (without math teaching background) I would just take the problem apart and use logic and elimination.
1. Look at the problem and pick out the cues:
it has be an odd number. So whatever number he's thinking of will have to end in 3, 5, 7 or 9
2. the numbers are between 48960 and 49058 so they have to fall into this range.
3 tell students that there are lots of good answers, not just one.
4. test an answer starting from the beginning: 48960 + 3= 48963, could that be it? no, because 3 is not 3 more than 6.
5. what is 6 + 3? = 9, so could it be 48969? yes, why? it is odd. the ones digit is 3 more than the tens. It falls within the range.

Then you'd probably have to do a lot of these types of problems for them to really get it.

I'm probably way off on how to teach it, and I don't know if there is a sytematic way to do it, but it is thinking critically and it's solving a problem.
I could never be a math teacher, because I always do things this way, even if I had a formula to follow.

Start with even and odd, which it sounds like you've done. After that, the kids need to be able to pick out numbers between two numbers. Number lines might help with that. Show them the two numbers on a number line, and get examples of numbers in between the two. The last clue just requires them to have some basic idea of place value. Show them a number like 25... "Why doesn't 25 work?" and then have them help you find a number using 25 that would meet the clues.

Just out of curiosity, what is the goal of teaching kids something like this? It sounds like a fun little logic exercise, but is there a practical aspect to it?

Make a t-chart to record the possible combinations. In this problem, the possibilities for tens and ones are : 03,14, 25, 36, 47, 58, 69. So, now they have done one part of the problem.

Next, they write the complete numbers out between 48960 and 49058 that include the above endings.

48969 is the only possibility for the 48000 numbers.
49003, 49014, 49025, 49036, 49047, 49058.

The 'secret' of these problems is to break them into manageable parts and use charts to record either guesses or possibilities, depending on the problem. This would be a challenging problem for 5th, but not impossible. It would require the use of organization and good practice at place value positions and logic.

Start with even and odd, which it sounds like you've done. After that, the kids need to be able to pick out numbers between two numbers. Number lines might help with that. Show them the two numbers on a number line, and get examples of numbers in between the two. The last clue just requires them to have some basic idea of place value. Show them a number like 25... "Why doesn't 25 work?" and then have them help you find a number using 25 that would meet the clues.

Just out of curiosity, what is the goal of teaching kids something like this? It sounds like a fun little logic exercise, but is there a practical aspect to it?

Thank you! None that I can see. My cooperating teacher asked me to make a lesson based on these problems because they are going to show up on a district math test the students are required to take in which they are supposed to add and subtract within one million.

Make a t-chart to record the possible combinations. In this problem, the possibilities for tens and ones are : 03,14, 25, 36, 47, 58, 69. So, now they have done one part of the problem.

Next, they write the complete numbers out between 48960 and 49058 that include the above endings.

48969 is the only possibility for the 48000 numbers.
49003, 49014, 49025, 49036, 49047, 49058.

The 'secret' of these problems is to break them into manageable parts and use charts to record either guesses or possibilities, depending on the problem. This would be a challenging problem for 5th, but not impossible. It would require the use of organization and good practice at place value positions and logic.

I have no idea who to teach it, but if I had to do it (without math teaching background) I would just take the problem apart and use logic and elimination.
1. Look at the problem and pick out the cues:
it has be an odd number. So whatever number he's thinking of will have to end in 3, 5, 7 or 9
2. the numbers are between 48960 and 49058 so they have to fall into this range.
3 tell students that there are lots of good answers, not just one.
4. test an answer starting from the beginning: 48960 + 3= 48963, could that be it? no, because 3 is not 3 more than 6.
5. what is 6 + 3? = 9, so could it be 48969? yes, why? it is odd. the ones digit is 3 more than the tens. It falls within the range.

Then you'd probably have to do a lot of these types of problems for them to really get it.

I'm probably way off on how to teach it, and I don't know if there is a sytematic way to do it, but it is thinking critically and it's solving a problem.
I could never be a math teacher, because I always do things this way, even if I had a formula to follow.