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? Thank you!:help:

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.

I had to edit my first answer because I didn't read the question correctly. Hahaha, even teachers .......

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.

In answer to let me wax philosophical, beginning with a quote from Upsadaisy, and expand on some points that she and Linguist have made. The question in hand shows, first, that a kid is sufficiently master of a range of number-sense skills to be able to juggle more than one of them at once. It tests several number-sense concepts at once: greater than/less than, odd vs. even, and place value come to mind, and there are doubtless others that aren't coming to mind simply because they're so much a part of my mental furniture that I don't always notice myself using them. These are concepts that your kids should know, and if each concept were presented in its own question, your kids would probably do fine. But it's really hard to write a question that's challenging for fifth graders that focuses solely on place value or solely on odd vs. even. Secondly, the question can be cracked only by taking it apart into its components. This is a crucial skill not merely for state math tests but also for reading-comprehension tests, and not merely for tests but for both critical thinking and ANY subject matter, from agriculture to world languages. The kid who can notice how some part of the question or content is similar to things the kid already knows or can do is the kid who's (a) going to be able to do very much what Linguist did with the question (for the record, I bet Linguist would teach this question very well), and (b) going to be able to parse the words into concepts, and (c) the kid who may have already figured out how the skills they teach in language arts really do help one in science and vice versa (for science is about noticing and doing something with causes and effects), and how the skills they teach in history really do help one in math and vice versa (for history and math are about kinds of relationships), and so on.

Yes, all the component skills are important. Yes, problem solving is important. So... why not find a way to integrate these skills and problem-solving in a way that's actually meaningful, instead of giving them something that third graders will instantly recognize as "never going to use this" type of work? There are plenty of meaningful examples of multi-step problems, open-ended problems, etc., that have real-world applications. Using something like this seems like it's a completely artificial skill, and the kids will recognize it as such. To me, this question would be a great morning work question, or a question to extend thinking for students who have already demonstrated mastery of component skills.

I think there are lot of things in math the kids would view as something they would never use in real life. And a lot of it is true. When I was in school I viewed these applications (the example the OP posted) as something challenging to figure out, therefore fun. I remember one math problem we had, that I particularly liked (and remember because I was the 1st one to solve it) that went like this: we had the dimensions of the bath tub, the amount of water that flows from the faucet / minutes and had to figure out by what time the tub would overflow. So we had to figure out the volume of the tub and how much time it would take. It had some other complications, like it's now halfway full, by what time do I turn off the water for it to be 3/4 full, or full but not overflow, things like that. It was fun, therefore challenging. Did I ever use that formula in real life? No. I don't think you can make everything relevant to life, and it's ok.

Teacher aides "helping" students is a major problem in our school as well. It's like they believe the success of the student is their success (that sounded wrong). I want the aide to simply give lower students a fair shot at solving the problem, guiding them and giving them problem solving techniques, but you're right, they typically just tell them "yes" or "no" until the student lands on the correct answer... As far as your problem, my kids have trouble deciphering the whole "x is y more than z"... and for early 3rd grade, that's a bit tricky to do 4 digit numbers. I'd start with 2 digit numbers and work my way up. ex: what number is 2 MORE THAN 10? and so on

Let me note that I quoted you because I thought you'd said something worth thinking about. I'm always open for discussing the formats of test questions and even disputing them: few things make me crankier faster than tests written badly. I would like to see considerably fewer formal assessments to determine readiness for the formal assessments to determine readiness for the formal assessments to determine readiness for the state test, and I think one route there is to be more intentional about transferability of skills - which, yes, includes transfer of skills not only from more artificial situations to more authentic ones but also transfer of skills the other way around. What I've found in writing multiple-choice math questions is that there's a delicate balance between authenticity and swamping the test taker: a question that's framed authentically enough to be engaging pretty much has to have a question stem big enough that some test takers automatically find it disengaging and shut down.