Slaying the Quantitative Reasoning Dragon


When preparing any battle plan, it’s important to map out all important logistical information.  Let’s look first at the timing and problem types in each level.


ISEE Quantitative Reasoning Section by Level


Total # of questions

Word Problems

Quantitative Comparisons

Total time

Time per question

Lower Level




35 min

55 sec

Middle Level




35 min

56 sec

Upper Level




35 min

56 sec

The only format difference between levels is that that the Lower Level test does not include quantitative comparisons.  Lower Level students will only be tested on multiple-choice word problems.  We’ll get more in depth on the difference between these two problem types soon.

The nature of the beast

So what’s the point of the Quantitative Reasoning section? Unlike more straightforward achievement based tests, this section is meant to test a child’s mathematical thinking rather than ability to calculate.  This is why there are many questions that require little or no calculation.  According to the ERB, the following skills and abilities will be tested in this section:

  • estimate numerical values
  • employ logic to determine what a particular problem is about
  • compare and contrast quantities
  • analyze and interpret data
  • analyze, compare, predict, draw conclusions, and summarize graphs
  • use reason to calculate the probability of events
  • understand concepts and applications of measurements
  • know how to arrive at statistical solutions to problems that are given

As far as actual content, this chart shows the ERB’s objectives and areas of focus.  Take a look.

Screen Shot 2014-03-26 at 10.26.17 AM

Now that we have a general idea of the scope of the section, just for fun, let’s stick with the metaphor of the Quantitative Reasoning section as a monster.  Let’s imagine this monster has two heads, one head representing word problems and the other representing quantitative comparisons.

Word problems: The bigger but less initially scary head

We all know word problems.  The infamous example of calculating the meeting point of Train A moving at 70 miles per hour due south and Train B moving at 80 miles per hour due east will forever haunt most of us.  In Quantitative Reasoning word problems, students will need to pick out relevant information from passages or charts and use that information to solve problems without extensive calculations. The good news is that exposure to word problems throughout their academic life means that most students aren’t too intimidated when approaching them.  However, the danger of this head of the monster is not to be underestimated.  What makes these problems tricky? Problems often combine multiple concepts in ways that students are not used to encountering (coordinate geometry and algebra, for example).  This requires a reasoning ability beyond just memorization of formulas.  Understanding of concepts must be deep and abstract in order to apply knowledge in ways students may not be accustomed to seeing.

Any preparation program will touch on content areas and skills needed to master the Quantitative Reasoning section of the ISEE.  But touching on the content area isn’t enough.  Most preparation books are filled with problems that test single concepts like fractions or exponents without following the format of actual ISEE problems.  At UP, we cover all math content areas, starting with simple drills to build individual skills.  Then we integrate these skills into complex problems in the format that our students will see on the ISEE, helping to bridge the gap between mastery of individual math skills and the reasoning capabilities needed to attack ISEE word problems with ease.

Quantitative comparisons: The seemingly more intimidating but quicker to kill head

Quantitative comparison questions always have the same format.  There are two columns that can contain pictures, equations, numerical values, or references to values in charts or graphs.  The student must compare the columns and choose one of the four answer choices (again, always the same four answer choices).  Let’s give a completely ridiculous example just for fun:

QR example

Looking at this obviously un-solvable question, you see that two quantities are being compared and the objective is to determine which is greater.  These problems generally require only very simple calculations or can even be solved with no calculations at all. I’ve found that most students freak out when they first see the two columns.  The good news about these problems is that once students have learned the format and directions, they quickly get over the initial fear and can even find these problems EASIER than word problems.

At UP, we have a very simple and effective strategy for approaching quantitative comparison problems.  When taught in the right way, this question type, which often starts out as the most anxiety-provoking problem type for students, becomes clear and manageable.

Now that we have examined the two-headed monster, let’s jump into the cave and look at some actual sample problems, shall we?  The samples are a mixture of word problems and quantitative comparison questions.  The latter are notated with an asterisk so that you can pick them out more easily.

 Numbers and Operations

QR Samples Numbers Operations

Algebraic Concepts

QR Samples Algebra     Geometry

QR Samples Geometry 1

QR Samples Geometry 2


QR Samples Measurement 1

QR Samples Measurement 2

QR Samples Measurement 3

Data Analysis and Probability

QR Samples Data Analysis and Probability 1

QR Samples Data Analysis and Probability 2

Now that we’ve sized up Quantitative Reasoning section, we hope you have a clearer picture of what your child is up against.  Our goal is that students are equipped with all the right strategies and skills (their “armor” if you will) to combat this section and come out unscathed.

For more information on our offerings and what kind of training would be best for your child, feel free to set up a free consultation so that we can help guide your child toward victory.

Next week, we will be attempting to comprehend the Reading Comprehension section of the ISEE.  Join us if you dare!

Your noble servants,

Jenni and Erin

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