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# Answer

This problem sum uses a model called the *Big Box Model* to simplify things. We avoid using the branching diagram as it over-complicates matters. The children in the question takes a fraction of the cookies ‘*and an additional’ *number of it, hence, things are a little complicated. We use the branching diagram usually when there isn’t the ‘*and an additional’ *phrase.

The solution above shows a step-by-step process of how we can draw this simple *Big Box Model* and solve this problem sum much more effectively than other methods.

We visualise the whole B*ig Box* to represent the total number of cookies in the box originally.

At step 1, we can see that 4/7 and an additional 9 cookies were taken away.

At step 2, we can see that 7/9 of the remainder and an additional 6 cookies were taken away.

At step 3, we can see that 75% (which is also 3/4) of the remainder and an additional 4 were taken away.

At step 4, we can see that there are 22 cookies left.

Working backwards and observing the *Big Box *from Step 4 back to Step 1, we sum it back up to find the original number of cookies in the *Big Box* as seen in the solutions provided.

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I see that your child was attempting to use the branching method so will also use that.

From picture attached, I have worked backwards and colour coded each step:

**In orange ink: finding # of cookies before Cheryl took**

Since Cheryl took 3/4 and an additional 4 cookies, this means that what was left was 1/4 minus 4 cookies. We know that 22 cookies were left in the end.

So if we take (22 + 4 = 26), we can find 1/4.

# of cookies before Cheryl took any: 26 × 4 = 104

**In purple ink: finding # of cookies before Benny took**

Since Benny took 7/9 and an additional 6, this means that what was left was 2/9 minus 6 cookies.

104 + 6 = 110 (this is 2/9)

110 ÷ 2 = 55

55 × 9 = 495 (this is (9/9)

**In blue ink: finding # of cookies at first**

Since Adam took 4/7 and an additional 9 cookies, this means that what was left was 3/7 minus an additional 9 cookies.

495 + 9 = 504 (this is 3/7)

504 ÷ 3 = 168

168 × 7 = **1176 cookies **

I see that your child was attempting to use the branching method so will also use that.

From picture attached, I have worked backwards and colour coded each step:

**In orange ink: finding # of cookies before Cheryl took**

Since Cheryl took 3/4 and an additional 4 cookies, this means that what was left was 1/4 minus 4 cookies. We know that 22 cookies were left in the end.

So if we take (22 + 4 = 26), we can find 1/4.

# of cookies before Cheryl took any: 26 × 4 = 104

**In purple ink: finding # of cookies before Benny took**

Since Benny took 7/9 and an additional 6, this means that what was left was 2/9 minus 6 cookies.

104 + 6 = 110 (this is 2/9)

110 ÷ 2 = 55

55 × 9 = 495 (this is (9/9)

**In blue ink: finding # of cookies at first**

Since Adam took 4/7 and an additional 9 cookies, this means that what was left was 3/7 minus an additional 9 cookies.

495 + 9 = 504 (this is 3/7)

504 ÷ 3 = 168

168 × 7 = **1176 cookies **

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