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Cindy had thrice as many stickers as Sonia. After Sonia gave away 12 stickers, Cindy had 5 times as many stickers as Sonia. How many stickers did Sonia have at first?

Please help! TIA 🙂


I thinks P4 kids are taught the concept of units and parts.
They also draw models with block diagram.

Based on the problem description, this is what we get:
This is somewhat hard to solve because the ratios 3:1 and 5:1
are representing different things.

However noticed that Cindy's number of stickers did not change.
So really we are looking for a number that can be divided into
3 and also divided into 5. So we should be using 15u instead.
The teacher probably teach them to use LCM(3,5) = 15.

So let's forget the previous diagram (which is really just to
help us think of a better one) and use this:

Since 1/3 of 15u is 5u, so Sonia had 5u at the start.
After giving away, Sonia had 1/5 of 15u, which is 3u.
That means she gave away 5u - 3u = 2u. So 2u = 12.
That means u = 6.

So Sonia had 5u = 5 x 6 = 30 stickers at first.
(Same answer as Chief's.)

I hope this is easier to explain to your kid if you
want to avoid too much algebraic manipulation.
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Thank you!! This helps plenty. Really appreciate your help 🙂

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Thanks!  I wouldn’t know how to simplify the solution I provided without drawing the model.  So sorry… I only know how to use units u but not parts p🤦‍♂️…

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No prob Chief. Your solution is perfectly fine. If a child is familiar with algebra, your solution is easy to understand.

Units and Parts seem like algebra in another guise. Instead of using x and y or a and b, use u and p. I supposed it is a way of gently guiding younger students into algebra.

When it comes to problem solving, children should be exposed to a variety of solutions. At some point, they will “see” the connections between them and get a deeper understanding.

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Thanks! I’ve only mastered units but not parts 🙂  Will continue to learn from masters like you!

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At first, Sonia has u stickers.
So Cindy has 3u stickers.

Then Sonia gave away 12 stickers, and Cindy has 5 times that of Sonia.

So 5 (u – 12) = 3u
5u – 60 = 3u
2u = 60
u = 30 #


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Thanks for replying! I don’t think a P4 kid can understand this solution though.

Is there another way to solve this that’s suitable for a P4 student? The teacher said something about using units I’m unsure of the method.

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