help me explain this problem

[happycc]

to my kids...

 

There are 8 hippos and crocodiles. There are 2 more crocodiles than hippos. How many hippos are there?

How would you explain this without doing algebra...this is first grade math?

 

I started drawing circles and randomly made a few hippos and a few crocodiles to see if it fits but is there some kind of mathmatical sentence for this?

 

My algebraic mind would rather solve this as h + h=2 = 6 but this is for first grade. This is a singapore math problem through this website I fouund online.

[Maus]

Well, it would be (8 - 2)/2, which they wouldn't know yet.

 

How about: "We have 8 animals total. We can take away the 2 extra crocodiles. Now we have 6 animals. Half of the animals left over here are hippos and half are crocodiles. What would that number be?"

 

A first grader can probably intuitively grasp that half of 6 is 3, even if they don't know division yet.

[EKS]

If this is a Singapore problem, they are probably thinking that you will use a bar diagram to solve it. Make 8 boxes all stuck together. Two of them plus half of the remainder are crocodiles. The other half of the remainder are hippos.

 

You could also use manipulatives. Get 8 objects. Set aside two. Divide the remainder in half. Combine one half with the set aside two. The other half represents the hippos. If you go this route, you might try having your children mess with the manipulatives for a bit first to see if they can figure it out on their own.

[Jen in PA]

If this is a Singapore problem, they are probably thinking that you will use a bar diagram to solve it. Make 8 boxes all stuck together. Two of them plus half of the remainder are crocodiles. The other half of the remainder are hippos.

 

You could also use manipulatives. Get 8 objects. Set aside two. Divide the remainder in half. Combine one half with the set aside two. The other half represents the hippos. If you go this route, you might try having your children mess with the manipulatives for a bit first to see if they can figure it out on their own.

 

:iagree:

[lakerks]

I've had no experience w/Singapore, so take this with a grain of salt.

 

For first grade, maybe it's just a matter of trial and error. In other words, what possible combinations could we have that would add up to a total of eight animals? 6 and 2? No, that wouldn't be a difference of 2. How about 7 and 1? No, not a difference of 2. How about 5 and 3? Yes, that would work.

[boscopup]

You might try getting an actual Singapore book that teaches the bar models. The Challenging Word Problems workbook is inexpensive and gives examples of this type of problem, taking you step by step through example problems.

[onaclairadeluna]

Like other people have said, I'd do trial and error first.

 

I would take 8 pennies and tell my child that these are all animals. We know we have this 8 total. We also know that we have two more crocodiles than hippos. Now we have to figure out how many we have of each.

 

Then I would take two pieces of colored paper and say lets put the hippos on the gray one and the crocodiles on the green one. Could we have 7 hippos and 1 crocodile? Why not? Let's try something else? What should we try? And just do it this way trial and error until the child figures out the answer.

 

I would do this before I did the singapore bar diagrams. The reason I'd do it this way is it gives you a good idea of what your child knows already. It also gives them a chance to figure out the method on their own. If they do this they will have a better understanding of the bar diagrams which can help them solve increasingly abstract problems.

[happycc]

Yes ideally it would be better to get the singapore book but alas no money YET-not until we get our money from the charter school so it is just the free stuff online until then or whatever I have at home already...found this on the net...

 

http://www.teach-kids-math-by-model-method.com/index.html

 

helps explain some of the methods a bit....

 

so if you can solve these problems this way...have you noticed kids being able to solve problems in other textbooks using the same method?

[EKS]

 

so if you can solve these problems this way...have you noticed kids being able to solve problems in other textbooks using the same method?

 

Yes. It is an extremely powerful method.

[boscopup]

Yes ideally it would be better to get the singapore book but alas no money YET-not until we get our money from the charter school so it is just the free stuff online until then or whatever I have at home already.

 

Ok, gotcha. :) If you do a google search on this forum (put "site:welltrainedmind.com" next to your search terms) for "bar model", you'll probably find some threads where good examples are used, sometimes with drawn images thrown in! The method really is pretty neat.

[veggiegal]

Hmmm...I'd approach it by using clay, and having the kids build 8 "generic animal shapes" (head, body, legs, etc. but not too much detail because we don't know what type of animal they are). I'd then ask them to start making the animals into hippos and crocodiles--say, one of each--and then ask if we have "two more crocodiles than hippos". If they understand, no, we don't, we have an equivalent number of each, I'd ask them to change some animals to make "two more crocodiles than hippos". Ideally the kids would change 2 animals into crocs, leaving 3 crocs, 1 hippo, and 4 generic animals. (If they started getting confused by the extra generic animals, temporarily take them away--let's solve this problem for a smaller and easier number). Once you've got 2 more crocs than hippos, ask the kids what animals we need to make with the 4 remaining generic animals--they might see an equal number (2) of each is needed; if not, walk them through building 1 more hippo and 1 more croc. At 4 crocs, 2, hippos, do we still have "two more crocs than hippos?" Yes. So when we added an equivalent number of each animal (built one of each), it didn't change the "2 more crocs than hippos" being true. So we need to do the same with the 2 remaining generic animals--make 1 of each: 1 croc, 1 hippo.

 

By modelling the problem this way, you've given them a concrete intro to the idea of a variable (generic animal), and also demonstrated the "solve a simpler version of the problem via guess and check" method, when you got to 3 crocs, 1 hippo. I think both ideas--variables can have various values, and one helpful strategy when stumped is to change a harder problem a simpler one--are worth demonstrating early.

[happycc]

and that didn't work for her. She still got it wrong...

argh...in addition she is not understand the questions that go like this;

 

there were 6 crocodiles. there were three more apes than crocodiles. how many animals all together?

 

or

 

lizardman swallowed 5 flies, Iguana man swalled 3 more flies than lizardman. How many flies did Iguanaman swallow?

 

I went over the word problems with her and we answered them together on the whiteboard and then I gave her the word problem paper to solve on her own she still got them wrong.

 

WHAT IS SHE NOT GETTING?

[happycc]

I might give this a whirl. But honestly am I going to have to make playdough models each time for every problem with this child?

[Dana]

I might give this a whirl. But honestly am I going to have to make playdough models each time for every problem with this child?

 

When you're getting started, maybe.

 

Moving to the bar models is an abstraction.

In the CWP 1 I have (old version), there aren't bar models until what would be 1B of the text. It's all pictures at first. You move from the concrete (models, counters, pictures) to the abstract.

 

They also start in the text with pictures, then tell stories about them. Then have students do the problems like you mentioned. Maybe do something similar... start with a situation, tell a story that's a word problem... see if that helps with the leaps.

[FairProspects]

Ok, gotcha. :) If you do a google search on this forum (put "site:welltrainedmind.com" next to your search terms) for "bar model", you'll probably find some threads where good examples are used, sometimes with drawn images thrown in! The method really is pretty neat.

 

Does MM use this bar method too? If so, which level introduces the concept?

[texasmama]

If this is a Singapore problem, they are probably thinking that you will use a bar diagram to solve it. Make 8 boxes all stuck together. Two of them plus half of the remainder are crocodiles. The other half of the remainder are hippos.

 

This is where my brain went after three years of teaching Singapore math to my kids. I had to learn to think in bar diagrams rather than algebraically.

[texasmama]

and that didn't work for her. She still got it wrong...

argh...in addition she is not understand the questions that go like this;

 

there were 6 crocodiles. there were three more apes than crocodiles. how many animals all together?

 

or

 

lizardman swallowed 5 flies, Iguana man swalled 3 more flies than lizardman. How many flies did Iguanaman swallow?

 

I went over the word problems with her and we answered them together on the whiteboard and then I gave her the word problem paper to solve on her own she still got them wrong.

 

WHAT IS SHE NOT GETTING?

 

These are two step word problems, which are very complex for kids at the beginning stages of learning. I work alongside my kids and when we come to a problem which is a two step word problem, I ask them if the problem is a one step or two step.

 

In your shoes, I would make up several of these types of problems, have her watch you figure them out yourself using manipulatives, a white board, etc. so she understands that she must do the first part of the problem first before attempting the final tally. Stress the two part process of figuring the final answer. Lather, rinse, repeat, expect a lot of reinforcement to be needed.

[veggiegal]

I might give this a whirl. But honestly am I going to have to make playdough models each time for every problem with this child?

 

No, but by moving from concrete to abstract you can help nail down where the problems lie. Is it a question of translation? Can your child show you "two more red blocks than blue blocks?" (or coins, or beans, or socks, or whatever manipulative you have handy)--play around with "3 more red socks than blue socks", "one fewer penny than dime", etc. Once your child understands that bit of translation between English words and math language (math representation, concretely), you can ask about how many the "two more than" group (red blocks) and the other group (blue blocks) make "all together". Is she understanding the connection between this and the phrase "all together" from the original question? You can build on this foundation, showing her how the clay (or other concrete representations) can be made more abstractly, via a drawing of crocs and hippos, or tally marks, to circles and eventually--way down the road--x's and y's.

[EKS]

Just use some counters. Beans or something. And lead her through the problem.

 

How many crocodiles?

Six.

Put six beans in a line. Those are the crocodiles. [it would help if the counters were two different colors]

She does this.

How many apes does it say there are?

Three more than crocodiles. [if she can't answer this, help her, even if it means answering for her]

How can we show that with the beans?

[if she can't figure this out, do it for her, lining up six ape beans and then three more ape beans right underneath the crocodile beans to show the correspondence]

How many beans?

Fifteen.

How many animals?

Fifteen.

 

Then make up another problem exactly like this one using the same animals and slightly different numbers and lead her through in the same way. Hopefully, she will be able to do more herself the second time around. Once she is comfortable with this, have her do variations the same way. Eventually you can go from counters to bar diagrams, but keep in mind that Singapore doesn't stress bar diagrams until the third grade.