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Math problem solving for 6th grade


fourisenough
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Hi, all. My youngest DD, age 11, is about halfway through CLE 6th grade math. Her arithmetic skills are solid and we’ve been consistent, if not, enthusiastic math learners from the beginning.

What I’m finding that she now needs is gentle, step-by-step, explicit instruction and practice with problem solving. She even has difficulty with the few, very straightforward word problems in CLE. I think in the past, it would have been recommended that we try the Fan Math Process Skills books. I looked them up and found they’re out of print; the one used copy I found on Amazon was $47,000!
 

Any other ideas? I’m open to a printed book I could help her work through; a tutor (any takers?); or an online class. Thanks in advance!

Edited by fourisenough
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In my experience, word problems ARE math. As a silly example, if you can do 3 + 5 but can't tell me what you get if you have 3 apples and 5 apples, then we have a serious problem. 

What I would do is spend a lot of time talking to her about the word problems. Make sure that they are connected to her experiences in a reasonable way. Make sure she feels able to experiment and tries things. Make sure that her understanding of the operations ties into her understanding of the world. 

Can you give me an example of a word problem she's struggling with and also how she would approach it? In my experience, you need to lean into her own logic, however incomplete and rudimentary it is. Teaching key words and rote approaches tends to backfire and not lead to longterm retention. 

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@SusanC Great idea! I’d love to support Farrar’s work and I remember discussing the original book years ago. I’ll check it out. 
 

@Not_a_Number Thanks for weighing in. As an example, she just had this problem in her CLE book 605, Lesson 4:

“It is about 4,000 miles across the Atlantic from Norfolk, VA to Lisbon, Portugal. Traveling west along a straight line from Lisbon to Norfolk, you would first reach the Azores, a group of small islands about 1,200 miles from Lisbon. How far are the Azores from Norfolk? Draw a diagram to help you find the solution.” 

I had her read the problem, then I read it to her again. She looked at me and asked, “So, what am I supposed to do?” I told her she needed to figure out how to solve it. She looked at me with a blank stare. I asked her what mathematical operation she thought she would need to perform. She had no idea. She couldn’t even figure out what to draw. (Incidentally, this is a kid who tests 90th percentile or better on all verbal/reading/writing exams. She also draws a fairly accurate map of the world once per week, so she shouldn’t have been stumped with the geographic info in the problem.) I helped her/showed her what to draw and when I placed the X where the Azores were located relative to the two other points, she blurted out, “Oh, it’s 2,800 miles!” Her mental math is quite strong. She is a bit of a perfectionist who doesn’t like to make mistakes, so I think she’s just very hesitant to play around, talk through, or experiment at all. Any thoughts for helping a student like this?

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38 minutes ago, fourisenough said:

I had her read the problem, then I read it to her again. She looked at me and asked, “So, what am I supposed to do?” I told her she needed to figure out how to solve it. She looked at me with a blank stare. I asked her what mathematical operation she thought she would need to perform.

I wouldn't ask her a mathematical operation at this step. I'd probably try to gently to get her to engage with the problem AT ALL. Draw the picture, make a map, anything to get her started.

 

38 minutes ago, fourisenough said:

She is a bit of a perfectionist who doesn’t like to make mistakes, so I think she’s just very hesitant to play around, talk through, or experiment at all. Any thoughts for helping a student like this?

Ooh, tricky! It does sound like you're right. 

I'd do lots of word problems with her, and I'd be VERY encouraging of anything she tries, as long as it's not totally ridiculous. I remember getting annoyed at DD8 when she was little and wanted to see how much to add up instead of subtracting (like, you know, you have 8 apples, together we have 10 apples, how many do I have types of questions), and I freely admit I was wrong. Things went better for us when we stopped thinking in terms of "operations" and started thinking about "mental models and visualization." Same thing with adding instead of multiplying... no, you don't want them to add 5 + 5 + 5 + 5  every time they are asked about 4 people with 5 apples each, but it's RIGHT and needs to be encouraged. Later, once that kind of problem is easy, you can remind them that we have a NAME for repeated addition and that this would help 😉 . 

I wouldn't give her specific procedures for word problems, though. That's the kind of shortcut that kids gets to not even try to visualize. "Ah-ha, it says 'overall,' therefore I add!" might get her to do quite a lot of problems correctly, but will lead to problems in the future, because it's skipping a crucial step. 

It's a great thing that her mental math is good! That means that it won't take any working memory for her to do the calculation, which means she can focus on the visualizing/drawing/figuring out/experimenting. 

ETA: oh, start way below her level! Like, literally, start with small numbers of fruit that she can actually draw if she gets stuck. Measurements are HARDER than countable items. They are less easy to visualize. 

Edited by Not_a_Number
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4 hours ago, fourisenough said:


@Not_a_Number Any suggestions for a good source of word problems that would stretch her skills, but not be so hard she checks out and gets overwhelmed?

I am awful with sources, since I always write my own. If it were me, I'd make up my own and start with very easy ones, to get confidence up. 

Edited by Not_a_Number
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You might want to consider the Challenging Word Problems books.  I would get two copies--one for you to work through ahead of your daughter.  I'd start with level 3 (and if that proves to be too challenging, you could back up to level 2).  You are going to need to learn how to use the Singapore Model Method, which is pretty straightforward once you get the hang of it, and then you can teach it to your daughter.  It is a very powerful method and once she masters it, she will probably feel much more confident when approaching word problems.  That said, not all problems need to be approached this way, not even all of the problems in the CWP books.  

(Note that when I was teaching an adult student to do word problems, I used the CWP books and started with level 3.  He did levels 3 and 4 and then was good to take the firefighter exam, which requires 8th grade math ability.  He went from guessing on every problem to confidently solving the problems before looking at the answer choices.  It was amazing.  Anyway, my point here is that there is no shame in starting with level 2 or 3.)

Edited by EKS
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2 hours ago, EKS said:

 Anyway, my point here is that there is no shame in starting with level 2 or 3.)

Gah! I think I’ve just given away some of the CWP books, having written them off for being too difficult for her. I’ll take a look. Thank you for permission to start with lower level books! I always struggle with that. Especially since my DD just ahead of this one is an accelerated learner; It’s so hard not to compare/set unrealistic expectations. 

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45 minutes ago, fourisenough said:

Gah! I think I’ve just given away some of the CWP books, having written them off for being too difficult for her. I’ll take a look. Thank you for permission to start with lower level books! I always struggle with that. Especially since my DD just ahead of this one is an accelerated learner; It’s so hard not to compare/set unrealistic expectations. 

Oh yeah, definitely start on a lower level!! It sounds like this DD has confidence issues as much as anything else. Building up her confidence is Job 1. 

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On 12/14/2020 at 9:29 AM, SusanC said:

That is great that you found what you were looking for! I wanted to also mention fellow boardie Farrar's update of the book Numberless Math Problems. It is a nice way to break down the process of problem solving, talking about the set-up and approach but without getting distracted by the arithmetic.

This looks fun! It's free on Kindle Unlimited and I couldn't resist downloading it right away.  🙂 

 

For the OP, the earlier Zaccaro books may be useful too. I'd start with the Primary Grade Challenge Math. 

I see by your signature this is the youngest? You could try round robin with some problems. Have everyone solve the same problem (with help for youngest if needed), and then have everyone take turns sharing HOW they solved it. Write it out on the whiteboard if needed. You and hub too. There's always more than one way to get there, and seeing all the different methods helps strugglers and entertains the mathy ones. I put Math Olympiad problems (4th-6th grade competition math) on my big white board a couple times a week. My 4th, 7th, and high schoolers do them and we share how we got there. I totally pay correct answers with candy to keep the biggest ones happily participating, but occasionally even the strongest among them gets unseated by not reading carefully. Hub and I jump in too. 

Edited by SilverMoon
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