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Is there a Singapore Math way to solve this with a bar model?

0

$begingroup$

I have a series of word problems which involve finding two unknowns.

In some problems, the relationship of the two unknowns is stated with a difference and a quotient, or a difference and a sum, or a sum and a quotient. All of these styles lend themselves to a fairly straightforward bar model that leads directly to the solution of finding the two unknowns.

However, some problems state the relationship as a difference and a product, or a sum and a product. For these, I don't see a straightforward bar model way to solve them. I find myself just exhaustively listing the factors of the given product and looking for factor pairs that match the given sum or difference.

Obviously, the unknowns could be found using a quadratic equation. But that is beyond the Primary Year 4 student who has this work.

So, I want to find a more elegant way using bar models and not exhaustively listing the factors, so this solution strategy fits neatly with the other question styles in this group.

Example questions:

1. Two numbers have a difference of $6$ and a product of $187$. What are the numbers?




2. Two numbers have a sum of $18$, and a product of $72$. What are the numbers?

Thank you.

algebra-precalculus

share|cite|improve this question

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Not sure what a "bar model" is, but you can always transform the problem into solving a quadratic equation which has a standard discriminant method.
  $endgroup$
  – Raskolnikov
  Mar 19 at 11:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can't seem to post an image here in a comment, so I guess you could Google for "bar model" and look at the images. A quadratic way is not an option since the student is 9 years old. Thanks.
  $endgroup$
  – user67105
  Mar 19 at 11:20
  

  
  
  
  

add a comment | 

0

$begingroup$

I have a series of word problems which involve finding two unknowns.

In some problems, the relationship of the two unknowns is stated with a difference and a quotient, or a difference and a sum, or a sum and a quotient. All of these styles lend themselves to a fairly straightforward bar model that leads directly to the solution of finding the two unknowns.

However, some problems state the relationship as a difference and a product, or a sum and a product. For these, I don't see a straightforward bar model way to solve them. I find myself just exhaustively listing the factors of the given product and looking for factor pairs that match the given sum or difference.

Obviously, the unknowns could be found using a quadratic equation. But that is beyond the Primary Year 4 student who has this work.

So, I want to find a more elegant way using bar models and not exhaustively listing the factors, so this solution strategy fits neatly with the other question styles in this group.

Example questions:

1. Two numbers have a difference of $6$ and a product of $187$. What are the numbers?




2. Two numbers have a sum of $18$, and a product of $72$. What are the numbers?

Thank you.

algebra-precalculus

share|cite|improve this question

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Not sure what a "bar model" is, but you can always transform the problem into solving a quadratic equation which has a standard discriminant method.
  $endgroup$
  – Raskolnikov
  Mar 19 at 11:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can't seem to post an image here in a comment, so I guess you could Google for "bar model" and look at the images. A quadratic way is not an option since the student is 9 years old. Thanks.
  $endgroup$
  – user67105
  Mar 19 at 11:20
  

  
  
  
  

add a comment | 

$begingroup$

I have a series of word problems which involve finding two unknowns.

In some problems, the relationship of the two unknowns is stated with a difference and a quotient, or a difference and a sum, or a sum and a quotient. All of these styles lend themselves to a fairly straightforward bar model that leads directly to the solution of finding the two unknowns.

However, some problems state the relationship as a difference and a product, or a sum and a product. For these, I don't see a straightforward bar model way to solve them. I find myself just exhaustively listing the factors of the given product and looking for factor pairs that match the given sum or difference.

Obviously, the unknowns could be found using a quadratic equation. But that is beyond the Primary Year 4 student who has this work.

So, I want to find a more elegant way using bar models and not exhaustively listing the factors, so this solution strategy fits neatly with the other question styles in this group.

Example questions:

1. Two numbers have a difference of $6$ and a product of $187$. What are the numbers?




2. Two numbers have a sum of $18$, and a product of $72$. What are the numbers?

Thank you.

algebra-precalculus

share|cite|improve this question

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

$endgroup$

share|cite|improve this question

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

share|cite|improve this question

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

edited Mar 19 at 12:26

YuiTo Cheng

2,1862937

asked Mar 19 at 11:01

user67105user67105

1

asked Mar 19 at 11:01

user67105user67105

1