Singapore Questions (2A)

[Guest]

We finished our math up for the year and decided to finish up with some Singapore. I wanted to give it another try and see if it is something we might do next year as our main math. I was bummed that I needed to back up to 2A with my son, although I am reading that Singapore is ahead and well, so be it.

 

He actually is fine with everything (I have heard a couple times, "I already know this") but the area that is most unknown are the word problems. I've looked a little online, and it seems that the kids are supposed to distinguish if they are giving you 2 parts and you are figuring out the whole (+) or 1 part and the whole (-). So, when we do the word problem, we are trying to distinguish if they have given us parts or a whole/part and he can't always see that. I also searched and found this idea of the bar graph, and so I have tried a couple times to draw the bars to help him see what part is missing. This is a real challenge for me to teach and a real challenge for him to grasp.

 

The kinds of problems we are having trouble with are: Sam is 23 years old. He is 24 years younger than his father. how old is his father?*** OR John has 23 stamps and Bob has 50 stamps. How many fewer stamps does John have than Bob? These are just examples I thought up off the top of my head to illustrate where we are coming from.

 

I would be so grateful if I could get some teaching tips for teaching these kinds of problems. (Speak PLAINLY, please! :D)

 

Also, we are coming from a very spiral program, and from my understanding, Singapore is mastery. So does this mean that he needs to have a concept DOWN before moving on to a new one?

 

Running out for the afternoon - be back later!

 

***Edited to make my word problem make sense. :p

[Tanikit]

I am teaching my DD to do these types of bar problems. Sometimes I get her to draw the entire problem as it is written - so for the stamp problem she would actually draw all the stamps and label them John and Bob - using counters speeds this process up and makes it even easier to see. Then she needs to understand what is being asked: How many fewer stamps does John have than Bob - this takes a few steps in a younger child, though an older one should see it more easily.

 

1. With the counters out ask: Who has more stamps? Who has less/fewer stamps? - this is to check vocabulary

2. Then set the counters out in rows just as if they were the bar drawings that Singapore expects - using Maths blocks that fit together makes it even easier as you then break off the part that is more than the other (this is similar to using c-rods)

3. when they can do it with the blocks/counters then draw the bar diagrams and show how that works.

 

Your Sam question I do not think you phrased correctly as if Sam's Dad is 24 years older than Sam then naturally Sam must be 24 years younger than his Dad.

If however they were asking how old is Sam's Dad (23 + 24) then I would probably first show a child how to do this with very small numbers - it must make sense to them. ie Your baby brother is 2 years old and you are 5 years older than him - how old are you? What did you do to get that answer? Ok now do the same for Sam and his Dad...

 

I am using both a spiral and mastery program with my DD so I can't answer your other question - I find if my DD does not have it down after Singapore she will pick it up again in the spiral and vice versa.

[Guest]

Thank you for your response. Hm, we kind of did everything you said, so I guess it will just take a bit more time. And yes, I did phrase the father/son question wrong and it was indeed what you had said. :o That's what I get for writing as I'm running out the door, lol. I like your idea of using smaller numbers. (Somehow whenever I involve cookies or candy, the questions suddenly become much more doable, too!)

 

I am curious if he is supposed to have this mastered right.this.second. I am not even good at these kinds of problems, so I hope not...

[Dahliarw]

While Singapore doesn't spiral like other programs, topics are revisisted from year to year and book to book (even between 2a and 2b). Yes, you want your child to have a decent understanding, but the topic will come up again, at a higher level. So for example, 2a teaching mutiplication by 2 and 3. 2b teaches multiplication by higher numbers. There are also review sections within the books that go back to earlier material as a way of helping the children remember it. And if you buy the tests there are culmulative tests as well that cover multiple units.

 

As for word problems, drawing them out or using maipulatives helped my ds. Also teaching key phrases (like "more than" usually means subtraction, "total" or "all together" usually means addition, etc).

[Five More Minutes]

The Singapore bar model has been an unfamiliar tool for me. For me, I found that the Singapore text / workbook in levels 1 and 2 didn't spend a lot of time on setting the bar models up for word problems (although it DOES spend a lot of time on parts/whole thinking via number bonds).

 

The CWP for each level spends more time explaining how to set up bar models, which has been helpful, but for us the models really started to click when I picked up the the Fan Math Process Skills books for the younger levels. Those books give baby-step, explicit teaching on how to set up a bar model for each type of word problem. Process Skills books are like the Math Mammoth of Challenging Word Problems: incremental, explicit, with more practice than is necessary in case you have trouble.

 

Looking ahead to Singapore 3A, I see that the text itself is going to be devoting time to teaching the bar model approach. That tells me that in 2A it's considered a skill that is being introduced, rather than something that should be down pat.

 

So if it's only the bar model that is bogging you down in 2A, I really wouldn't worry.

[Dana]

The CWP for each level spends more time explaining how to set up bar models, which has been helpful, but for us the models really started to click when I picked up the the Fan Math Process Skills books for the younger levels. Those books give baby-step, explicit teaching on how to set up a bar model for each type of word problem. Process Skills books are like the Math Mammoth of Challenging Word Problems: incremental, explicit, with more practice than is necessary in case you have trouble.

 

 

Yup, yup, yup.

 

The Process Skills books are here. I used the iExcel books. They have some problems where they're just setting up the bar model for an arithmetic problem. It really helps with set up of problems (and there were some in CWP 5 (old edition) that I couldn't see how to do with a bar model until we did the iExcel setups first!).

 

I also found the text & workbook didn't have enough or difficult enough practice with the word problems. Those came in iExcel, CWP, and IP.

 

For the word problems... doing this example you gave: Sam is 23 years old. He is 24 years younger than his father. how old is his father?

 

One thing I did some was to use Cuisinaire rods to show the part/whole set up. It also made moving to the bar model a bit better. So here, I might start by asking what we know. Here, we can say that Sam is 23. So we can draw a bar (use a rod) to represent Sam and say it's 23.

 

Then I'd ask what else we know.

Well, Sam has a father.

His father is older.

We need another bar... this is a comparison.

Father's bar needs to be longer than Sam's bar.

How much longer?

24 years.

Sometimes the Cuisinaire rods helped... sometimes not :)

Sometimes I'd draw the model...sometimes I'd help my son with it.

 

So now we've got 2 bars... one for Sam that's 23 long and one for his father that's 24 longer than Sam. So his father is the length of Sam + 24... so 23 + 24 = 47 years old.

 

The bar model is really powerful and lets my son solve problems in CWP 4 and 5 that I would use algebra and a system of equations to solve. It's impressive. The key idea is finding a "unit". In this case, Sam is our "unit". (You don't need to talk about this with your child, but I see it all over the place in 5... and it's so cool because it leads so very nicely into algebra!) I'm terribly impressed with how the bar models work out and how powerful they are.

[happypamama]

Sometimes I draw the tree models that Singapore used; that helps my son figure out if he's looking for a part or the whole. I also taught him to look for keywords like "how many more" and such. But for him, using smaller numbers (like his age and his brother's, for instance) really helps him visualize what it is that he wants to find.

[Guest]

Thank you guys so much! I am trying to compare those Process books to the CWP via samples; we may pick up the Process Skills book if it has more hand-holding. I really appreciate the help. Yes, that is the only thing that is a challenge, so I'm glad to know it's just an introduction.

[letsplaymath]

Both of the problems you mention are comparison problems, which are particularly troublesome for young students because there is no movement inherent in the story. Nothing is being "put together" or "taken away" to guide the student's intuition on whether to add or subtract.

 

In such a situation, you may need to rephrase the question slightly to help your student visualize the situation. Instead of asking, "How many fewer stamps does John have than Bob?" you might ask, "How many stamps would we have to give to John so that he would have the same amount as Bob?" for beginners, such a little change in the wording can make a huge difference in understanding, because it lets the student visualize an action: giving stamps to John.