Solving SAT problems using the model method

David Marain over at MathNotations has been periodically tweeting an SAT problem of the day via @dmarain. A recent series of tweets asked:

A 42 oz mix of nuts is 6 parts peanuts to 1 part cashews. How many ounces of cashews must be added to make a make the mixture 2 parts cashews to 1 part peanuts? Does Singapore (bar) model method work here?

Sure it can! Here’s one solution.

First model the beginning mixture at 6:1.

Singapore Math bar model

Next, we can figure out how many units need to be added to the cashews to make the cashews to peanuts ratio 2:1.

Singapore Math Model diagram - after

Since there are 11 additional units and the value of each unit is 6 oz, we can find the value of the added cashews.

Singapore Math units

66 ounces of cashews must be added to the peanuts to make the mixture 2:1.
Changing Ratios is taught in level 6A in the Primary Mathematics materials (U.S. Edition), typically used in 6th grade classrooms.

About Cassy

Passionate about Singapore Math + Teacher Trainer and Coach + Treasure Hunter + Learner. Answer to the ultimate question? 42.


  1. Thanks, Cassy

    One good model diagram truly is worth a thousand words! My question was rhetorical. I was hoping someone like you would run with it. What do you find is the most difficult obstacle in training? Asking adults to think “different”? Developing an understanding of “unit”? Resistance to change? I would think the proof is in how their students would react…

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