Quantitative Reasoning: Number Analogies, Number Puzzles, and Number Series
The CogAT Level 8 Quantitative battery assesses arithmetic reasoning with whole numbers, generally within 100, using three subtests: Number Analogies, Number Puzzles, and Number Series. It is not a calculation-speed test; each item is designed so that a second grader can find the underlying rule and apply it.
Core rules
- Number Analogies: Two complete numbers form a pair with a rule. Name the rule ("add 6," "subtract 3," "double"), then apply exactly that rule to the first number of the second pair.
- Number Puzzles: An equation has one missing number, often shown as a box. Treat the two sides as balanced. Use the inverse operation: if the box is added, subtract the known addend from the total.
- Number Series: Compare consecutive terms. Look for a constant step (skip counting by 2, 5, or 10), a repeating step, or a step that increases. Check the pattern on at least three transitions before choosing.
Worked example
A Number Analogy shows 6 → 10 and 11 → 15, then asks 14 → ?. The first pair increases by 4 (10 − 6 = 4). Applying the same rule: 14 + 4 = 18. Check by subtracting: 18 − 14 = 4, so the rule holds. An answer of 10 would come from adding 4 to 6 again, which applies the rule to the wrong pair.
Traps that cost marks
- Assuming every analogy adds. A pair such as 12 → 9 uses subtraction, and the rule must be carried over exactly.
- In Number Puzzles, adding when the box is an addend. For 9 + □ = 16, subtract 9 from 16; the answer is 7, not 25.
- In Number Series, stopping after one difference. The series 2, 4, 8, 10 has steps +2, +4, +2, so the next term is 12, not 16.
- Misreading place value, such as treating 31 as 13.