help, how do i teach this? math

[debi21]

I am sure I'm not the first to ask something like this, but please help anyway. :)

 

So I have my 1st grader signed up to take Math Kangaroo next month. We haven't been prepping, and I don't have any expectations, but because I don't want his first ever standardized test to be a complete nightmare (temper tantrum, swearing off math, etc), we are starting to look at a few old problems now, a little less than a month prior. My son is not super gifted, but doing well with Saxon 3 at a charter, occasionally supplemented by me with various things and attendance at a low key math circle. As we go through some problems, I am trying to focus on him not flipping out on tough ones, and secondarily trying to talk strategies - reminding him of possible things he could try - on the ones he finds challenging.

 

Except for the problems that I would solve as a system of linear equations. We've run across three or four. I am at a loss. He is overwhelmed looking at them, and I don't know anything to suggest to help him. He can put together a rudimentary equation or two, but he can't solve. What strategy might a 6/7 year old use to even approach these problems? Would this be something a Singapore bar model could be used for - and if so, what book and what level do I need to look at? Is this covered in the early years (say K-4) in any other curriculum? I don't think I could teach it for this year anyway, but maybe before next. If I find a good resource, maybe I can tell him we'll learn it over the summer and just guess if he sees one like this?

 

(Example problem from 2010 1/2 exam). A dog, a cat, and a monkey together weigh 12 pounds. A cat and 2 monkeys weigh 10 pounds. A dog and three monkeys together weigh 2 pounds more than a cat, a dog, and a monkey. How much does a cat weigh?

 

TIA.

 

 

[hellojwolford]

Here are my two ideas: Fortunately, MK is a multiple choice test. If time allows, he does have the option of trying out each of the choices. Also, many questions seem like complicated "Mind Bender" style problems but they are more easily solved by drawing a picture than a grid.

 

I also recommend having your child practice using scantron sheets. It took my son about five minutes before he had a fit about those :-)

[ikuradesuka]

Wow, I love the plug and play idea.  Good call.  My younger kids struggle with these, too.

 

We have talked about switching animals around on a scale, which can be done with pictures.  Miquon...I want to say the first book of third grade? has some scales with blocks and circles that work this way.

 

d+c+m=12

c+m+m=10

d+m+m+m=14

 

So, if I were trying to keep the scale balanced, I could put a d, c, and m on one side, what do I have to do to the other side?  Well, I could put a cat and two monkeys and a two pound weight (just draw 2 blocks) over there.  Oh, so what if I had a d, c, and m on one side and I wanted to do something with the dog and 3m?  I could add a two lb weight to the d c m side.  

 

Or! What if I started with weights?  I could put a 10 pound weight on that side, and the cat and two monkeys on this side.  I wonder what would happen when I took

the monkeys off?

 

And then after just playing around like that for a while, with no particular place to go, we start wondering things like, if I had 10 pounds, and I took off those two monekys, I guess I'd just have a cat left.  So, does that mean 10 pounds minus 2 monkeys is the same thing as a cat?

 

Huh, then I guess maybe I could switch my scale around like this...d + 10 pounds -2monkeys, plus a monkey = 12 pounds.  

 

So maybe 14 pounds minus 3 monkeys is a dog?  Then I could trade the dog for 14 pounds-3 monkeys plus 10 pounds minus 2 monkeys...plus a monkey.  And by this point we are really laughing.  But then we work through the pile of stuff we've made, and realize that 24 pounds - 4 monkeys is 12 pounds.

 

And I could put less stuff on the scale if I just took 12 pounds off both sides, because that's the same, isn't it?  It's just extra.  

 

And then, it's kind of weird to keep remembering to subtract these silly monkeys, so maybe we should just PUT monkeys on the other side, and then we don't have to think about it.  

 

So these twelve blocks, and those 4 monkeys...if I separated THEM...one monkey gets 3 blocks.

 

And we just keep playing and playing and eventually we know what everything weighs, and who the friends are, and who can sneak off the scale and no one notice, as long as his friends help...

 

Obviously, they don't have the time to play these games while they are taking the test, but I think it really, really helps them get a feel for what equals what and how to get where they need to go.  It becomes a lot faster and a lot more intuitive with time.  

 

Miquon is helpful because they start with just two variables, but by the end of a couple of pages, you are doing three.  

 

 

 

[chocolate-chip chooky]

I plonked this word problem in front of my 9 year old, just to see how she'd attack it .... or if she'd even be willing to, really.

She solved it in ways I haven't officially taught her yet, demonstrating her intuition in maths and reminding me (yet again) that linear learning is not her thing.

 

How do your older kids solve it?

[wintermom]

I plonked this word problem in front of my 9 year old, just to see how she'd attack it .... or if she'd even be willing to, really.

She solved it in ways I haven't officially taught her yet, demonstrating her intuition in maths and reminding me (yet again) that linear learning is not her thing.

 

How do your older kids solve it?

 

Yes, I've had the same experiences over and over again when I have my dc do math contests at home. I'll do it one way, they'll do it other ways. Sometimes one of the kids figures out the easiest, sometimes me - because I'm getting better now. ;)

 

It's really fun to break away from the traditional math texts and dig into some really interesting problems. I feel like my old math teachers cheated me by never having our classes do any of these things. How many kids are also becoming bored and not working up to their actual potential? 

[Incognito]

Well, if you put the equations by one another, 

 

d+m+c=12

 

d+m+m+m=14

 

c+m+m=10

 

You can see that the first two there are almost the same - that the c=m+m - 2 .  Then you could fill that into the last equation and get an answer for the monkeys, and then you can plug that into the last equation again and get the c, then just hop to the top (or use the middle equation) and get the d.

Edited February 24, 2016 by Incognito

[Miss Tick]

You've got some good talk-through strategies here, so can I just mention, make sure he is clear that there is no

penalty for guessing, so when you are done, make sure you have an answer for all the questions, even the ones you couldn't be sure of. <imagine the non-plussed emoticon here, looking at one of my dc>

[Grover]

OK, logic boy drew this:

circle for dog, square for cat and triangle for monkey.  He says Miquon told him how.

 

Intuitive girl said:

well there are three numbers that add to 12 and one of them plus three of another one adds to 14 so... (head on side)... the dog is 5 and the monkey is 3 so the cat has to be 4.  Does that count as my maths?  Can I watch ponies now? :huh:  oi vey

 

 

[wendyroo]

I'm betting that the main skill they are testing is adding equations together.

 

"A dog, a cat, and a monkey together weigh 12 pounds. A cat and 2 monkeys weigh 10 pounds. A dog and three monkeys together weigh 2 pounds more than a cat, a dog, and a monkey. How much does a cat weigh?"

 

If we add the second equation and the third equation then we will have the same number of dogs and cats as the first equation and we will know that the difference in weigh is all due to the number of monkeys...

 

D + C + M = 12

 

C + 2M = 10

D + 3M = 14

Added together -->  C + D + 5M = 24

 

So, if one cat, one dog and one monkey weigh 12 pounds, and one cat, one dog and five monkeys weigh 24 pounds, then the extra four monkeys must make up the extra 12 pounds.  Each monkey weighs 3 lbs.

 

If one cat and 2 monkeys weigh 10 pounds, and each monkey weighs 3 pounds, then the cat must weigh 4 pounds.

 

If I were showing this to my 6 year old, I would probably not write it out as equations.  I would have him draw the letters C, D and M (multiple times as appropriate) in the correct piles with the weights marked.  Then I would show him how we can combine two piles and compare to the third.

 

Wendy

[MrSmith]

(Example problem from 2010 1/2 exam). A dog, a cat, and a monkey together weigh 12 pounds. A cat and 2 monkeys weigh 10 pounds. A dog and three monkeys together weigh 2 pounds more than a cat, a dog, and a monkey. How much does a cat weigh?

 

TIA.

 

IMO, this (and all similar problems of this sort at the2-3 level) is a logic puzzle.  When my son was younger, we would reason these out, using whatever was available at hand to describe the various scenarios.  Although algebra was never formally discussed, whatever he eventually wrote down was effectively a linear equation.  We did sometimes used bar model for the tougher ones (CWP4+).

 

In this case, I would consider it a success if my student realized that a Dog is 2 pounds more than a Moneky:

 

If D+C+M = 12 AND C+2M = 10, then D = M+2 (because after the dog left and another monkey joined we are still 2 pounds lighter).

 

The rest follows directly, and is more pattern matching than math at that point.

[debi21]

I just wanted to thank everyone for their responses. They were all very helpful to me. The various thought processes and approaches... it was really good to have multiple perspectives. I am not sure my son has the logical ability (or intuition) to do these at this point, but I will expose him to more, certainly. I have a lot more ideas as far as how to scaffold this, which is really what I wanted. And thanks for mentioning Miquon - I am going to look into getting more in the series to do this summer (Have orange and red but we didn't do very well with them - willing to try again!)

 

Also, hellojwolford, thanks for mentioning the scantron sheets. I was planning on introducing those, but it was a great reminder. Can anyone tell me if MK uses the traditional green, rectangle ones... or the pinkish oval ones....or their own? I have just been able to get my hands on a green rectangle one and will review it with my son this week.

 

-Debi

 

[daijobu]

Weirdly, MK posts a copy of their answer cards on their website.  In the past they were the tall rectangular variety with the student's name pre-printed.