We can't figure these math problems out. Singapore 5A

[Miss Peregrine]

These are word problems from Singapore 5A. I need help to figure out the processes.

 

#1 The total weight of Peter, David and Henry is 123 kg. Peter is 15 kg heavier than David. David is 3 kg lighter than Henry. Find Henry's weight.

 

#2 Peter has twice as many stickers as Joe. Joe has 40 more stickers than Emily. They have 300 stickers altogether. How many stickers does Peter have?

 

DD found the answers with trial and error plugging in of numbers but what are we missing? I am pretty good at math, but for some reason, I just can't figure these out :willy_nilly:

[Mamagistra]

LOL and *snort* Those silly boys with their weight issues AND Joe and Emily and their blasted stickers sent me on a driving journey for the Home Instructor's Guide last week!! That is to say, I am very glad it's not just me! :D

 

What I ended up doing was showing my dd how to model (in the case of the stickers) equal units with the bars...in other words, since E had 40 less, we added 40 to the 300 stickers total, THEN divided that sum (340) into four parts to work up to the answer requested (remembering to subtract that 40 back out).

 

Is this making sense at all? I don't have the problems in front of me...in fact, to help with the weight puzzle, I'll have to go dig out the book.

 

Also, The Essential Parents' Guide to Primary Maths explains many of the solving strategies. It was on my shelf, but I forgot about it until after my joyride for the HIG.

 

I hope this is somewhat helpful. :)

[jesiwins]

Hi!

 

I'm not sure if this is the level of mathematical thinking that the text is trying to get at, but I would rewrite the word problem as an algebraic equation with only one variable.

 

For instance in problem 1,

 

P(peter)+d(david)+h(henry)=123

 

(d+15)+(h-3)+h=123

 

((h-3)+15)+(h-3)+h=123

h-3+15+h-3+h=123

3h+15-6=123

3h=114

h=38

 

Does this make sense?

 

I can try and explain more if you think it would help.

 

-Jesi

[nutmeg]

 

#1 The total weight of Peter, David and Henry is 123 kg. Peter is 15 kg heavier than David. David is 3 kg lighter than Henry. Find Henry's weight.

 

 

So using Dave as the base, Peter weighs 15 more than him, and Henry weighs 3 more than him.

 

xxxxxxxxxxxxxxxxx|15 Peter

xxxxxxxxxxxxxxxxx Dave

xxxxxxxxxxxxxxxxx|3 Henry

 

Take their total weigh of 123 minus the 18 'extra' pounds = 105

 

divide the 105 between the 3 boys.

 

105/3= 35kg

 

Then add Henry's extra 3 back on = 38kg

 

Jesi - you are correct with the algebraic solution, but Singapore, at this point in the series, is teaching how to solve these with bar graphs.

[Antonia]

P l x l 15 l

 

D l x l

 

H l x l 3 l

 

 

David's weight is the basic unit x. If you subtract the 18 extra grams from the total 123, you get 105. Dividing this by three gives you x or the basic unit, which is also David's weight. If you then add back the extra grams, you have Peter at 50g, and Henry at 38g. If you add them all back up, they equal 123.

 

Clear as mud?

[MelissaMinNC]

before looking at the solutions, through trial and error and guessing. It only took a couple tries, but I'm SURE that's not how it's supposed to be done.

 

My poor kids are doomed. I need to start lining up math tutors asap.

 

:eek:

Melissa

[Jackie in AR]

These are word problems from Singapore 5A. I need help to figure out the processes.

 

#1 The total weight of Peter, David and Henry is 123 kg. Peter is 15 kg heavier than David. David is 3 kg lighter than Henry. Find Henry's weight.

 

#2 Peter has twice as many stickers as Joe. Joe has 40 more stickers than Emily. They have 300 stickers altogether. How many stickers does Peter have?

 

DD found the answers with trial and error plugging in of numbers but what are we missing? I am pretty good at math, but for some reason, I just can't figure these out :willy_nilly:

 

#1

 

Your bar for number 1 will look as follows: 1 unit for David, 1 unit for Henry plus 3 *extra*, 1 unit for Peter plus 15 *extra*. The total weight of the bar is 123. Now you need to find out how much 1 of the units is equal to. To do that, take the 123 and subtract both of the *extras* (15 + 3). That leaves you with a bar of 105 which is equal to 3 units. Each unit is worth 35 (105/3).

 

So, David's weight is 35; Henry's weight is 35 + 3 *extra* = 38; Peter's weight is 35 + 15 *extra* = 50.

 

#2

 

Emily's stickers = 1 unit.

Joe's stickers = 1 unit + 40

Peter's stickers = 2 units + 80

 

The total bar is 300. Subtract out the *extras* (40 + 80), leaving a bar of 180. 180 = 4 units, so each unit is worth 45 (180/4).

 

Emily's stickers - 45

Joe's stickers - 85

Peter's stickers - 170

[Myrtle]

I apologize for not being able to get this bar diagram to a manageable size for a message board but here is how you need to represent the second problem:

 

LINK

 

And I don't do three separate steps for my kids, it starts off as the first step and I keep adding to it so it ends up as the last step, if that makes any sense.

 

Then I would say something like, "What would it take for them to all have the same amount of stickers?" You'd have to subtract some stickers from some folks to make that happen. Okay, and you realize that as you take stickers away from some folks that the total amount of stickers would also decrease by whatever amount you are taking away. In the end you end up with 4 equal groups of stickers and 180 stickers total and 4 equal groups. Divide 180 by 4 and voila.

 

Now, the first problem is handled in a similar manner. Draw three bars of varying lengths then have folks gain and lose weight so that they all weigh the same as Henry. How does that affect the total? Now you have three equal groups totaling to something and then you divide.

[Miss Peregrine]

LOL and *snort* Those silly boys with their weight issues AND Joe and Emily and their blasted stickers sent me on a driving journey for the Home Instructor's Guide last week!! That is to say, I am very glad it's not just me! :D

 

What I ended up doing was showing my dd how to model (in the case of the stickers) equal units with the bars...in other words, since E had 40 less, we added 40 to the 300 stickers total, THEN divided that sum (340) into four parts to work up to the answer requested (remembering to subtract that 40 back out).

 

Is this making sense at all? I don't have the problems in front of me...in fact, to help with the weight puzzle, I'll have to go dig out the book.

 

Also, The Essential Parents' Guide to Primary Maths explains many of the solving strategies. It was on my shelf, but I forgot about it until after my joyride for the HIG.

 

I hope this is somewhat helpful. :)

 

LOL, All of a sudden these type of problems were thrown in and they are nothing like the rest. I might have to buy the HIG, myself :auto:

[Miss Peregrine]

Hi!

 

I'm not sure if this is the level of mathematical thinking that the text is trying to get at, but I would rewrite the word problem as an algebraic equation with only one variable.

 

For instance in problem 1,

 

P(peter)+d(david)+h(henry)=123

 

(d+15)+(h-3)+h=123

 

((h-3)+15)+(h-3)+h=123

h-3+15+h-3+h=123

3h+15-6=123

3h=114

h=38

 

Does this make sense?

 

I can try and explain more if you think it would help.

 

-Jesi

 

I did try to set it up as an algebraic equation but I had 3 variables I was confusing myself. Plus algebraic equations are not introduced yet so DD was more confused than I was, LOL

[Miss Peregrine]

So using Dave as the base, Peter weighs 15 more than him, and Henry weighs 3 more than him.

 

xxxxxxxxxxxxxxxxx|15 Peter

xxxxxxxxxxxxxxxxx Dave

xxxxxxxxxxxxxxxxx|3 Henry

 

Take their total weigh of 123 minus the 18 'extra' pounds = 105

 

divide the 105 between the 3 boys.

 

105/3= 35kg

 

Then add Henry's extra 3 back on = 38kg

 

Jesi - you are correct with the algebraic solution, but Singapore, at this point in the series, is teaching how to solve these with bar graphs.

 

P l x l 15 l

 

D l x l

 

H l x l 3 l

 

 

David's weight is the basic unit x. If you subtract the 18 extra grams from the total 123, you get 105. Dividing this by three gives you x or the basic unit, which is also David's weight. If you then add back the extra grams, you have Peter at 50g, and Henry at 38g. If you add them all back up, they equal 123.

 

Clear as mud?

 

#1

 

Your bar for number 1 will look as follows: 1 unit for David, 1 unit for Henry plus 3 *extra*, 1 unit for Peter plus 15 *extra*. The total weight of the bar is 123. Now you need to find out how much 1 of the units is equal to. To do that, take the 123 and subtract both of the *extras* (15 + 3). That leaves you with a bar of 105 which is equal to 3 units. Each unit is worth 35 (105/3).

 

So, David's weight is 35; Henry's weight is 35 + 3 *extra* = 38; Peter's weight is 35 + 15 *extra* = 50.

 

#2

 

Emily's stickers = 1 unit.

Joe's stickers = 1 unit + 40

Peter's stickers = 2 units + 80

 

The total bar is 300. Subtract out the *extras* (40 + 80), leaving a bar of 180. 180 = 4 units, so each unit is worth 45 (180/4).

 

Emily's stickers - 45

Joe's stickers - 85

Peter's stickers - 170

 

 

 

I apologize for not being able to get this bar diagram to a manageable size for a message board but here is how you need to represent the second problem:

 

LINK

 

And I don't do three separate steps for my kids, it starts off as the first step and I keep adding to it so it ends up as the last step, if that makes any sense.

 

Then I would say something like, "What would it take for them to all have the same amount of stickers?" You'd have to subtract some stickers from some folks to make that happen. Okay, and you realize that as you take stickers away from some folks that the total amount of stickers would also decrease by whatever amount you are taking away. In the end you end up with 4 equal groups of stickers and 180 stickers total and 4 equal groups. Divide 180 by 4 and voila.

 

Now, the first problem is handled in a similar manner. Draw three bars of varying lengths then have folks gain and lose weight so that they all weigh the same as Henry. How does that affect the total? Now you have three equal groups totaling to something and then you divide.

 

 

Thank you all!! I get it now!! :party: