Math q for 9 year old: "Susie & Stacie baked an equal amount of cupcakes...."

[Haydn]

Math q for 9 year old: "Susie & Stacie baked an equal amount of cupcakes...."

Sorry. Please help with algebra type formula to solve this:

Susie & Stacie baked an equal amount of cupcakes.
After Susie baked another 36 cupcakes and Stacey baked another 8 cupcakes, Susie had thrice as many cupcakes as Stacey.
How many cupcakes did each of them bake at first?

 

[stapel]

Sorry. Please help with algebra type formula to solve this:

Susie & Stacie baked an equal amount of cupcakes.
After Susie baked another 36 cupcakes and Stacey baked another 8 cupcakes, Susie had thrice as many cupcakes as Stacey.
How many cupcakes did each of them bake at first?

Is the student (a third-grader, I think) supposed to use algebra for this exercise? If so, please reply with the student's efforts, so we can see what is going on.

If not, use more intuitive methods. Such as:

Draw boxes to represent the original amounts made by each:

original:

       *---*
Susie: |   |
       *---*
Stacy: |   |
       *---*

Then add boxes to include the additional amounts made by each:

added:

       *---*-------------*
Susie: |   |36           |
       *---*--*----------*
Stacy: |   | 8|
       *---*--*

Note that the added amounts mean that Susie now has three times as many, so the new situation is equivalent to:

new:

       *-----*-----*-----*
Susie: |     |     |     |
       *-----*-----*-----*
Stacy: |     |
       *-----*

Each of these new boxes is equal to an original box, plus eight more. This tells us that (the original box, plus eight more), when multiplied by three, is equal to (the original box, plus thirty-six more). What is three times (the original box, plus eight more)? If you subtract one box and 24 cupcakes from each total, what does this give you? So how many are in two of the original boxes? Then how many are in one?

 

[Haydn]

Pre-Algebra Q

Is the student (a third-grader, I think) supposed to use algebra for this exercise? If so, please reply with the student's efforts, so we can see what is going on.

If not, use more intuitive methods. Such as:

Draw boxes to represent the original amounts made by each:

original:

       *---*
Susie: |   |
       *---*
Stacy: |   |
       *---*

Then add boxes to include the additional amounts made by each:

added:

       *---*-------------*
Susie: |   |36           |
       *---*--*----------*
Stacy: |   | 8|
       *---*--*

Note that the added amounts mean that Susie now has three times as many, so the new situation is equivalent to:

new:

       *-----*-----*-----*
Susie: |     |     |     |
       *-----*-----*-----*
Stacy: |     |
       *-----*

Each of these new boxes is equal to an original box, plus eight more. This tells us that (the original box, plus eight more), when multiplied by three, is equal to (the original box, plus thirty-six more). What is three times (the original box, plus eight more)? If you subtract one box and 24 cupcakes from each total, what does this give you? So how many are in two of the original boxes? Then how many are in one?

Hi,
Thank-you very much for this.
My daughter is soon 10 and is in Primary 4 level. She has been taught the intuitive idea that you describe...but (I now think wrongly) we have both resisted this and preferred to formulate a problem as an equation or approximation...then eliminate/replace the variables so that only a single variable remains..then it can be solved. This works except when a "modelling" approach is needed.
I studied your boxes intuitive approach and much appreciate this. I was puzzled near the end by your choosing number "24"...and did'nt follow at this point. Anyway, I solved it by getting a greater grasp of the relationship between the 2 tottals at beginning and end, using the boxes as illustration..then i used trial and error i.e. at End: 1. If Stacy = 15; Susie = 45 (starting is then Stacy 7, Susie 9) False Result....another try...THEN, If Stacy = 14; Susie = 42 (solving back to beginning, BOTH = 6....THANKS!! I will now teach this to my daughter.

 

[Haydn]

hint:
E = equal amount initially baked
total baked:
Susie: E + 36
stacie: E + 8

i wanna cupcake!!

helpful, many thanks!

 

[cornopean]

Yes, at this age I would be more inclined to draw some pictures instead of using an equation.

 

[stapel]

Sorry. Please help with algebra type formula to solve this:

Susie & Stacie baked an equal amount of cupcakes.
After Susie baked another 36 cupcakes and Stacey baked another 8 cupcakes, Susie had thrice as many cupcakes as Stacey.
How many cupcakes did each of them bake at first?

Is the student (a third-grader, I think) supposed to use algebra for this exercise? If so, please reply with the student's efforts, so we can see what is going on.

If not, use more intuitive methods. Such as:

Draw boxes to represent the original amounts made by each:

original:

       *---*
Susie: |   |
       *---*
Stacy: |   |
       *---*

Then add boxes to include the additional amounts made by each:

added:

       *---*-------------*
Susie: |   |36           |
       *---*--*----------*
Stacy: |   | 8|
       *---*--*

Note that the added amounts mean that Susie now has three times as many, so the new situation is equivalent to:

new:

       *-----*-----*-----*
Susie: |     |     |     |
       *-----*-----*-----*
Stacy: |     |
       *-----*

Each of these new boxes is equal to an original box, plus eight more. This tells us that (the original box, plus eight more), when multiplied by three, is equal to (the original box, plus thirty-six more). What is three times (the original box, plus eight more)? If you subtract one box and 24 cupcakes from each total, what does this give you? So how many are in two of the original boxes? Then how many are in one? :wink:

...I was puzzled near the end by your choosing number "24"...and did'nt follow at this point....

Start by answering the questions. The first question was:

What is three times (the original box, plus eight more)?

What did you get when you multiplied (one old box, plus eight more) by three? You should have gotten (three old boxes, plus twenty-four).

The next question was:

If you subtract one box and 24 cupcakes from each total, what does this give you?

The other total was given to you as being (one old box, plus thirty-six). So now you have (one old box, plus thirty-six) being equal to (three old boxes, plus twenty-four).

The next question was:

If you subtract one box and 24 cupcakes from each total, what does this give you?

If you had subtracted one box from each amount, you should have ended up with (thirty six) being equal to (two old boxes, plus twenty-four). If you had subtracted twenty-four from each amount, you should have ended up with (twelve) being equal to (two old boxes).

The next questions were:

So how many are in two of the original boxes? Then how many are in one?

If you had divided by two, you would have ended up with (six) being equal to (one old box).

Note for future reference: Don't just look at leading questions. Follow them through, answering as you go, to see where they lead!