Number Patterns

[Aubrey]

Dd7 has always had trouble with these, & I can't understand why or what to do for her. When they go backward, she has an especially hard time.

 

She's doing Singapore 2A now, & she has no trouble multiplying, dividing, etc.

 

The problem that sent my blood-pressure through the roof today was:

 

36, 33, ___, ____, 24

 

Her first response (always) is to look at the numbers in isolation: 1s digit, 10s digit, w/out regard for the whole. I remind her *a lot* to look. at. the. whole. Try counting by *something.* But she just sits there until I've pretty much done it for her, so I've been backing off more & more.

 

Her 2nd response to this one was 36 + 33 = 69 - 45 = 24. I thought that was a good try, but I told her to try again.

 

She put 39, 21 in the blanks. Why? "Because it's counting by 3s." Ok, so she's figured out the hard part.

 

"Is 33 more or less than 36?" I ask her. "More," she replies.

 

After long, sullen stares, etc., she says she thought I was talking about 39. She'll do that, too--say she thought I was talking about some number in isolation rather than, "I thought you were asking if 39 was more or less than 36." Single words that have no meaning like that make me want to peel my skin off.

 

We finally talk though it, & she understands (on some level!) that it's counting backwards by 3s. Now when I ask, "So what's 3 less than 33?" she answers, "27."

 

Y'all are going to say, well, she clearly doesn't know her facts well enough. Can you believe that that's not the problem? She learned her facts faster & better than ds, just to show him up. :lol: Somehow, she's not hearing "33-3" but something MYSTERIOUS. And then she's guessing. Her next guess was 29.

 

While I got up to take deep breaths, she changed it to 30 & exclaimed that she had the answer:

 

36, 33, 30, 21, 24. :banghead:

 

So if you can believe that the adding/multiplying/counting by 3s is *itself* not the problem, but the mental gymnastics of number patterns, what do I do? Sometimes it feels like riding in the passenger seat while someone drives off a cliff slowly. She's screaming, crying, "I don't know what to do!" And I'm screaming, "Hit the brakes!" And when she tries, she hits the accelerator, but mostly, she just holds her feet up in the air, screaming & closing her eyes. :svengo:

[Guest]

...have her show it with her manipulatives or a diagram. Then ask her to use the rule to determine the next number in the sequence.

 

This is along the lines of what I was thinking as I read your post. Perhaps the number sequence is just too abstract for her, in and of itself. Pick a simpler backwards sequence and lay it out with candies, legos, blocks, or something similar, and ask her to put down the number of items that would follow that pattern. With dd I'd make up stories that made the arithmetical operation (in this case, subtraction) apparent -- what happened between the first and second element in the series? The dog snuck away three candies (or something along those lines).

 

At any rate, I'd make it more concrete, then put the numbers beneath the items.

[Guest]

...have her show it with her manipulatives or a diagram. Then ask her to use the rule to determine the next number in the sequence.

 

This is along the lines of what I was thinking as I read your post. Perhaps the number sequence is just too abstract for her, in and of itself. Pick a simpler backwards sequence and lay it out with candies, legos, blocks, or something similar, and ask her to put down the number of items that would follow that pattern. With dd I'd make up stories that made the arithmetical operation (in this case, subtraction) apparent -- what happened between the first and second element in the series? The dog snuck away three candies (or something along those lines). Or if you have a good long flight of stairs near you, you could enact going up and down stairs by threes and relate it to the sequences.

 

At any rate, I'd make it more concrete, then put the numbers beneath the items.

[Aubrey]

She seems to be attempting to solve by recognizing a particular pattern she's seen before, but can't arrange it mentally to get the sequence in order on paper.

 

Yes, she seems to get very stuck in one mode of thought. For the LONGEST time, she couldn't handle any kind of change in vocabulary--for ex, she could add just fine, but if she was asked to find the sum or the total, she'd end up in tears. I don't know how to classify that, but it's...as if...well, it's almost like a blind spot in her brain. If I hold her hand, turn her to the left, then she can see the path. But there's no peripheral vision.

 

You might want to ask her how the first number relates to the second, i.e. determine the rule,

 

I do this all the time.

 

and have her show it with her manipulatives or a diagram.Then ask her to use the rule to determine the next number in the sequence.

 

I finally did this yesterday w/ cuisenaire rods. She was aggravated at me at first because she said, "I already know how to count by 3s." I encouraged her to just trust me, & we built patterns increasing by 3 by using several different combinations of blocks. Eventually she had the AHA! moment & saw the pattern. Then we built the pattern from her worksheet & filled in the answers she had written, & she laughed, seeing that they were clearly wrong. She was able to then find the correct answer & extend the pattern further.

 

If you want to lead her to figuring out that a rule is necessary to determine, you could start with sequences made of shapes or pattern blocks or sounds and have her make up sequences for you to figure out. Bead necklaces are usually popular w/small fry in starting this 'game'.

 

Yes, we have all of those & have used them, but she has a problem jumping from blocks to numbers. I would say it's the problem of going from the concrete to the abstract, but this seems different. Because numbers have *value* & relational value...well, it's as if she's OVER thinking that. Like she can't see the forest for the trees? It's hard because it's SO different from how my older child approached the same thing, so I guess it continues to surprise me, lol.

 

Function Machine is a good mental math game to play to develop this kind of number sense.

This fellow has some fun ideas: http://www.philtulga.com/resources.html

 

Thanks. I'll look at that. I also requested several math story books from the library. I don't know how much that will help, but I do know that she tends to learn things better when they're set in the context of a conversation or a relationship.

 

Last night, I worked out a "spy code" for her (she & ds love to play spy & try to write codes) based on number patterns & (for the sake of conversation/relationship), I let them work it out together this morning. They both LOVED that.

 

But jeepers. I can't do that every day! :lol:

[Aubrey]

This is along the lines of what I was thinking as I read your post. Perhaps the number sequence is just too abstract for her, in and of itself. Pick a simpler backwards sequence and lay it out with candies, legos, blocks, or something similar, and ask her to put down the number of items that would follow that pattern. With dd I'd make up stories that made the arithmetical operation (in this case, subtraction) apparent -- what happened between the first and second element in the series? The dog snuck away three candies (or something along those lines).

 

At any rate, I'd make it more concrete, then put the numbers beneath the items.

 

Singapore also does a crossword puzzle type thing where there are different number patterns, intersecting at numbers they share. She has trouble even w/ counting by 1s when it's presented as a pattern like this. It's like her brain just freezes, & if she writes anything at all, it's completely bizarre.

 

Otoh, if I can make her slow down & calm down & say the numbers out loud with me (ie pay attention to the WHOLE number, not just its digits, or the maze of the puzzle), she does better. But it's an awful lot of hand-holding, & in the end, I'm left wondering whether or not she really understands or if I just did a lot of talking.

[Aubrey]

Ah, her comment is telling. She is relying on memory instead of solving this particular group of numbers for the rule used. She'll likely need some more guided practice with finding and making up rules before she solos.

 

This is helpful! I'm going to have to think about it for a while. "Rule" vs "memory." Hmmm.

 

Sometimes the reach exceeds the grasp. It will be helpful if she goes concrete to pictorial, then uses pictorial for a while before going to abstract, if drawing doesn't bother her (if it does, stick with the manipulatives). One way to do this without getting her upset is to introduce the concept of 'proof'...i.e. mathematicians show their solutions, not just give their answers. Once you get her in the habit, it'll save a lot of headbanging down the road.

 

Math always seems like reach & grasp to me, lol. Both of my bigs have always gotten extremely frustrated w/ math that's too easy & weepy w/ math that's too hard. *sigh*

 

"Proof" is a good idea. I loved that part of geometry. As it is, I'll ask my kids "why" they have a particular answer (whether it's right or wrong), but they generally think I'm just being difficult & don't really engage the question. Maybe I can work on that. :001_smile:

 

Thanks for your thoughts!

[nmoira]

Have you tried using a number line? I find them particularly useful when kids are drawing a blank on arithmetic sequences. I'd also be inclined to stick a "39" in front of the 36, so she can see three consecutive terms in the pattern. Patterns that start out with only two terms drive me nuts because I can almost always see other alternatives.

 

39, 36, 33, ___, ____, 24

 

ETA: Yes, I tend to overthink things. :tongue_smilie:

Edited January 21, 2011 by nmoira

[Aubrey]

We did a similar-ish problem together tonight. A cup, a bowl, & a plate weight 650g. The cup & the plate weigh 500g. The cup & the bowl weigh 330g. How much does the cup weigh?

 

Her thoughts on the problem were really random at first, but I used a bookmark to get her to focus on small parts of it at a time. Since it was evening, well, there was actually more going on, but a different kind of thing, so...I don't know. The point at which I'd normally get exasperated, my mom called, so my attention was split.

 

That split attention slowed me down enough that she had a chance--w/ a few hints--to figure it out. Getting the weight of the plate did not immediately tell her how to figure the weight of the bowl. Getting the weight of the bowl next made her laugh w/ delight, but *still* she didn't immediately know how to get the weight of the cup.

 

I think...I forget how hard it is. I've often thought how much better of a parent (I feel like) I am as they get older. I think dd is on that threshold, & I still forget. 7 is small. It's ok if she doesn't get it right away. It's ok if I help. If I skip math altogether, she'll be better off than if I scare her to pieces w/ getting too annoyed. :001_huh:

[Aubrey]

Consider:

 

0,3,6,9,_,_

 

and

 

1,4,7,10,_._

 

Both are count up by threes.

 

The first will be recognized by a child who is using memory of 'count by threes' or 'multiples of three'. The second won't be recognized, b/c most people don't teach count by threes that way. The second sequence forces many children to learn to find the rule.

 

Oooh, good thought. Thank you!

[elise1mds]

Ohhhhh I feel your pain. I had my son doing a page of something similar a week or two ago and you'd have thought I was trying to murder him. "BUT, MOM!!! I CAN'T DO THIS!!! IT STARTS AT THE WRONG END!!!!"

 

:glare:

 

I love the links. I'll be checking those out.