Math Tip: The Branching Method

The Branching Method is an alternative to the Part-Whole Model. It may not be able to completely replace all variations of the Part-Whole Model, but it is still a very useful strategy to learn. Note that either method, or any method that is mathematically sound, is acceptable. One may not necessarily be better than the other.

The Basic Part-Whole with 3 Variables

Here, Ace has a total of 5u, and she gave 1u to Ben and had 4u left.

She gave 1/2 of 4u, which is 2u, to Carl and had 2u left.

The model and the solution is as follows:

This is a fairly straightforward type of question that can be easily represented with the Part-Whole Model.

Part of a Remainder

Similar to the previous question, if we take the total amount that Andy has as 5u, then he gave 2u to Betty, leaving 3u. The problem here is finding 1/5 of 3u parts.

To solve this, we make the remainder 3u a multiple of 5 by multiplying it and the total by 5.

Hence, we now take the total amount that Andy has as 25u, and he gave 10u to Betty, leaving a remainder of 15u. He then gave 3u (1/5 of the remainder 15u) to Charlie and had 12u left.

The model and the solution is as follows:

Using the Branching Method, we start with Andy’s total of $500.

He then gave 2/5 to Betty and had 3/5 remaining.

Then from the remainder of 3/5, he gave 1/5 of it to Charlie, meaning 3/5 x 1/5 = 3/25,

and had 4/5 of the remainder 3/5 left, meaning 3/5 x 4/5 = 12/25.

The solution would look like this:

In both cases, we end up with the fraction 12/25 or 12u out of 25u as an expression of how much Andy had left. I personally find the Branching Method much more straightforward in this case.

Part of the Remainder and Working Backwards

The Branching Method works for Working Backwards as well.

Here, Abe’s total at first is unknown, but he gave 3/7 to Beth and had 4/7 remaining.

Then from the remainder of 4/7, he gave 2/5 of it to Cindy, meaning 4/7 x 2/5 = 8/35,

and had 3/5 of the remainder 4/7 left, meaning 3/5 x 4/7 = 12/35.

The solution would look like this:

Hence, if a fraction of a remainder yields a whole number, I would suggest sticking to Model Drawing. If it’s a fraction, then the Branching Method would be easier.

Fractions and Non-Fractions

Using the Branching Method, the solution would look like this:

As you can see, in this scenario, we have the same issue of having too much going on, as well as calculations that are not yet taught in Primary School. The Part-Whole Method provides an elegant solution for this kind of question, but that’s for another blog. =)

So, which is better? Model Drawing or the Branching Method? Neither! They both have pros and cons and both work for the question types above. The more mathematical tools your child has, the more scenarios that he or she can deal with. I advise mastering both and learning to apply whichever when needed.

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