algebra problems in Sing. 4A

[Gwenny]

How do you teach your children how to do problems like this---I could show them an algebra problem--but they don't know that yet.

3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are in the third pile? TB pg. 41, no. 10

300 children are divided into two groups. There are 50 more children in the first group than in the second group. How many children are there in the second group? TB pg. 40, no. 8

Nicole and Tasha have 2000 stickers altogether. If Nicole has 600 more stickers than Tasha, how many stickers does Nicole have? WB, pg. 64, no. 19

I think I'm missing something.....

[StephanieU]

The first one is hard, but the second and third aren't too bad if you use the bar diagrams (although I haven't used Singapore, so I don't know for sure if this is what they want).


300 children are divided into two groups. There are 50 more children in the first group than in the second group. How many children are there in the second group? TB pg. 40, no. 8
So you have a bar that is 300 units. If you divide it in half, that would be 150 units in each half. But, we want the first part to be 50 more than the second. So, we move the dividing line some. If we move it 10 units to 140/160, they would be 20 apart. If we move it 20 units to 130/170, they would be 40 apart. Hopefully your child can see that how far you move is is half as far apart. So, to get 50 units apart, we need to move it 50/2=25 units. 150-25=125 and 150+25=175. So, the second (smaller) group has 125 children in it.

Nicole and Tasha have 2000 stickers altogether. If Nicole has 600 more stickers than Tasha, how many stickers does Nicole have? WB, pg. 64, no. 19
Again if the stickers are divided evenly, there would be 1000 each. But, since Nicole has 600 more, we need to use 600/2=300 more and 300 less than 1000. So, they have 1300 and 700 stickers. Nicole has 1300 stickers.


3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are in the third pile? TB pg. 41, no. 10

This one is harder because we have twice as many. So, lets make a bar of a unknown length for the third pile because it is the smallest. The second bar for the second bile would be twice as big, so two of those. The first pile would be about the same size as the second pile So, you have about 5 of the bars we started with (one for the third pile and 2 each of the other two piles). So, we know that the third pile is ABOUT 3000/5=600, and the other two piles are ABOUT 1200. So, now for some trial and error. We need the first pile to be 10 more than the second. So, we could do 1205 and 1195. But that won't work because pile three is half as many as pile 2, so they have to be even numbers. So, let's try 1206 and 1196. Half of 1196 is 598. 1206+1196+598=3000!!! The third pile has 598.

[Nealewill]

This is a large picture but this is how I would do the bar graphs. And I would explain it very much like the pp.

[Gwenny]

Okay great! I could get the answers and we did the "let's make a guess to start and move from there" type of way. I never thought of the bar graphs--yes, Singapore uses them a lot but they aren't what I think of. That helps for the next time we get one of those problems. Do they expect the children to come up with that on their own??? Did you have to work that all through with your children? I can see that maybe my next one, who is mathy, MIGHT get that--those seem pretty difficult to sneak in on them. Those kinds of problems are never worked out in the textbook-that I remember anyway. I wonder if they are just seeing how much the kids can pick up? Test their thinking skills?

Thanks so much. I'll remember the bar graphs from now on. I just wanted to show her the algebra problem that takes 1 minute. haha

[mamanlait]

Gwenny,
Do you have the TM (not just the answer book)? That's one of the biggest reasons I have it. The solutions give the bar graphs so you can show your dc how to solve the word problems the Singapore way. My brain immediately goes to solving many of the problems in a traditional algebraic way and I need the handholding of how to show it in that Singaporean way. The Text does a good job of explaining these but then when you hit the Review work, you've got to recall those skills...my kids usually do a better job of it than me!

[Nealewill]

With the first one, I would probably have had to guide my dd how solve. But with the other two, I think she came up with them on her own. I am only in 4B right now so I should remember, but I just can't LOL. I do know that as the year has gone on, she has gotten better and better at doing it alone IMHO. For me, if they don't understand how to draw it - no matter what - I don't sweat it. I just hold their hand a bit and help them along. They gain understanding and usually they can walk through the process fairly well even if I am there to help with a few steps or help them not make a wrong turn, if that makes sense. I am always willing to help as much as they need but only willing to help when they actually need it.

[Nealewill]

I guess I should say I am very mathy and my younger 2 are mathy. My oldest does okay but I would never classify her as "mathy." I love the bar graphs though because they help me teach the kids well. You know you love Singapore when you using all the math tricks you know, multiple ways at times, and drawing things out just for fun to confirm your thoughts

[MomtoJGJE]

If they can't figure it out from the examples we've gone over, then I teach them the algebra. I don't completely understand the bars to be honest, so I just teach them the way I know how to get it.