# Stumped on Singapore Math problem..Help!

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Singapore 3A in my teachers guide/ standards edition page 70.

Enrichment problem

Ann and Amy have \$42 altogether. Ann has \$12 less than Amy. If Amy gives \$3 to Ann, how much more money does Amy have than Ann?

Now here is the part that stumps me:

They say " A straightforward way to solve this is to find the amount each has, (2 units = 42-12=30; one unit =15.; Ann has 15, Amy has 15+12 =27

Where are these units they are talking about....

I get the pictures.....but the whole units part is stumping me and kids. UGH! Pregnant brain!

Edited by happycc
mistyped.12 for 2 sorry guys
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Singapore 3A in my teachers guide/ standards edition page 70.

Enrichment problem

Ann and Amy have \$42 altogether. Ann has \$12 less than Amy. If Amy gives \$3 to Ann, how much more money does Amy have than Ann?

Now here is the part that stumps me:

They say " A straightforward way to solve this is to find the amount each has, (12 units = 42-12=30; one unit =15.; Ann has 15, Amy has 15+12 =27

Where are these units they are talking about....

I get the pictures.....but the whole units part is stumping me and kids. UGH! Pregnant brain!

In SM's bar chart approach, each bar is a unit. So the bar chart way would be to do the following:

Amy: [XXXXXX][12]

Ann: [XXXXXX]

[XXXXXX][XXXXXX][12]=[42] >>> [XXXXXX][XXXXXX]=[30] >>> [XXXXXX]=[15]

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I'm no expert on SM methods, but since no one's answered you yet I'll give it a try.

It looks to me like they're defining the \$\$ Amy has as one unit, and it was a misprint in the book. It should read 2 units = 42-12. That gives you 2 units = 30. Dividing by 2 gives you 1 unit = 15.

So they're defining Amy's money as one unit. That's pretty much the same thing as saying "Amy has X dollars. Let's solve for X."

If anyone knows more than me about SM, though, please feel free to correct me. :)

ETA: I knew I should have waited longer for someone to jump in. ;)

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Yup, I agree with both of the previous posters....

Anne [---------][12] }

Amy [---------] } 42

So a unit is what Amy has and 2 units equal 42-12=30 so 1 unit is 15.

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why we had to use the unit and the point of doing that. What do I say to her?

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why we had to use the unit and the point of doing that. What do I say to her?

I draw the bar diagram and call the working amount a "unit".

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I draw the bar diagram and call the working amount a "unit".

This non-SMer is curious ..

is the bar (/unit) diagram way of solving a problem a visual .. perhaps less abstract .. version of algebra?

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This non-SMer is curious ..

is the bar (/unit) diagram way of solving a problem a visual .. perhaps less abstract .. version of algebra?

Yup, you got it. :) I'm hoping this helps ME finally understand some algebra better. The kids are already making these jumps...:lol:

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I think that using the word "unit" was just a short way of describing the problem. You don't need to use the word if it confuses you or your child.

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I think that using the word "unit" was just a short way of describing the problem. You don't need to use the word if it confuses you or your child.

You could call it the "base amount". It can be confusing with units such as feet, pounds, grams.

Edited by kalanamak
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I call it "x". :D

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A foot is a unit, right? It's a unit made up of 12 inches. A pound is a unit made up of 16 ounces. A kilometer is a unit made up of 1000 meters (or 100,000 cms, or 3,280 ft, or whatever). Similarly, in upper level algebra we use a unit vector - a vector where the length is 1 'unit'.

Depending on the problem, we pick the unit that makes the most sense and that will make the math easier for us. So instead of measuring the length of a room in inches, we choose to measure it in feet. Saying that the room is 11 feet long is easier than saying that it's 132 inches long.

In the same way, this problem is using a 'unit' made up of however many dollars Amy has. It doesn't matter that we don't know right away how much money she has. By calling it a unit, we can solve the problem much easier. It's algebra with pictures, and it's completely brilliant.

I would have loved to learn algebra this way in elementary school. Not because I hated algebra (it's my favorite math :D), but because it's just so cool.

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This is also one of my favourite things about Singapore. It took a little while to get used to with my elder son coming from public school but now whenever they are stuck on a problem, I ask them to draw the diagram before they ask me. Many times seeing it visually in this way helps a great deal. It is also a great way to introduce algebraic concepts before actually doing "real" algebra.

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How do you decide how big to draw the unit in relation to the known amounts when you don't know it's value? Do you estimate?

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How do you decide how big to draw the unit in relation to the known amounts when you don't know it's value? Do you estimate?

The unit is an unknown quantity. It's not drawn to scale compared to the known values.

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The unit is an unknown quantity. It's not drawn to scale compared to the known values.

Are the known values drawn to scale?

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Are the known values drawn to scale?

We make 12 bigger than 5, but that's about it.

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We make 12 bigger than 5, but that's about it.

Okay. I found some app once for this stuff and I couldn't work with it. Im trying to figure out if I'm not really getting something or if my brain is just wired differently. Sorry if my questions sound silly. :001_smile:

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Okay. I found some app once for this stuff and I couldn't work with it. Im trying to figure out if I'm not really getting something or if my brain is just wired differently. Sorry if my questions sound silly. :001_smile:

Pick up a CWP book... maybe grade 3 would be good? Look through the examples there, and it will teach you how they're used. The challenge problems will show some problems where they're super helpful (sometimes making the problem easier than algebra would).

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why we had to use the unit and the point of doing that. What do I say to her?

"Unit" is just what Singapore math calls any unknown amount --- especially if the same amount is used more than once in the problem. For example, if they said that Amy had three times as much as Ann, then they would draw four units: one for Ann and three for Amy.

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I call it "x". :D

I'm starting to, after we introduced X and Y as angles of unknown degree.

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Are the known values drawn to scale?

By eyeball. When we very, VERY first started I did it on big graph paper, to scale, but now he knows that the biggest bar goes all the way across my Boogie Board (which I use instead of a white board) and we work from there. About all I get is the smaller part of the total is a smaller bar than the bigger part. I sweated about this at the beginning, but kiddo seems to catch on with eyeballing.

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