Quantitative Skills
What does the HSPT Quantitative Skills subtest test?
Quantitative Skills has 52 items in four styles named in STS score reports: sequences, reasoning, geometric comparison and non-geometric comparison. None needs advanced math, and all of them punish careless reading.
The four Quantitative Skills item styles (skill names from the STS Performance Profile; descriptions ours)| Style | What the student does | Typical slip |
|---|
| Sequence (number series) | Find the rule in a list of numbers and give the next term, or a missing one | Seeing one pattern when two alternate |
| Reasoning (number manipulation) | Translate a sentence such as "6 more than one third of 45" into arithmetic | Doing the operations in the order they are read |
| Geometric comparison | Compare lengths, areas or shaded parts in figures | Trusting the picture instead of the numbers |
| Non-geometric comparison | Evaluate three expressions and choose the true statement about them | Stopping after evaluating two of three |
Worked example 1, a series with two rules (ours). What comes next in 4, 9, 7, 12, 10, 15, ...? The differences are +5, −2, +5, −2, +5, so the next step is −2, and the answer is 13. A student who looks only at every other term sees 4, 7, 10 and 9, 12, 15, two counts by 3, which confirms it. Checking a pattern two ways is the habit we drill most for this subtest.
Worked example 2, a comparison (ours). Examine (a) 2 to the power 5, (b) 5 squared and (c) 4 cubed divided by 2. Which is true: a is greater than b, b equals c, or a equals c and both are greater than b? Evaluate all three before reading the choices: (a) 32, (b) 25, (c) 64 / 2 = 32. So a equals c and both exceed b. The trap is treating 2 to the power 5 and 5 squared as the same size because they use the same two digits.
How we teach series
Every series lesson starts with a written difference row under the numbers. If the differences are not constant, the student writes the differences of the differences, then tries ratios, then tries splitting odd and even positions.
Four checks in a fixed order turn a guessing game into a routine. Most series at this level fall to one of the four.
How we teach comparisons
For every comparison item the rule is to write the value of (a), (b) and (c) in the margin first, and only then read the answer choices. Reading the choices first invites the student to test one statement and stop.
For figures, we teach students to label every length they can calculate. A figure that looks half shaded may be three eighths shaded once the numbers are written in.
