# Number Sense

The MathLeague Number Sense test is 80 questions in 10 minutes. That is about 7.5 seconds each. Mental math, no time for scratchwork. All grades take the same test, how far students get depends on their knowledge, skills, and proficiency. Based on recent local contests, second and third graders should focus on the first 10 and 20 questions. Fourth graders should be mastering through those and working on the 30s. Fifth graders should be working on the 30s and 40s. Sixth graders, everything.

The challenge starts with whether students know the math, then whether they want to be “present” or want to practice to gain proficiency, to learn techniques to do the math quickly.

We have resources available to help students registered for our contests.

Here is a sample test, similar to the resources available to students registered for our contests:

# What Is In The Number Sense Test?

Overall, multiplication is a core challenge. Here is more detailed breakdown:

The first nine questions…

- Basic addition, subtraction, multiplication, and division
- Noting digit placement (e.g., which is the hundreds digit)
- Order of operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)
- Rounding
- The tenth question and every tenth question is an estimation question. These require an estimate within + or – 5% of the actual calculation.

The next set of nine questions… (the teens)

- The numbers get a bit larger for addition, subtraction, multiplication, and division
- Squares
- Roman to Arabic conversion or the reverse
- Fractions (reducing, adding, subtracting)

The next set… (the twenties)

- More of all of the above
- GCD and LCM
- Measures
- Primes
- Exponents

The next set… (the thirties)

- More of all of the above
- Time
- Odd & Even numbers, multiples, sequences
- Shapes, mostly perimeter questions
- Roots, mostly square roots

The next set… (the forties)

- More of all of the above
- Roots, mostly square roots
- Shapes, area and volume questions
- Percents

The next set… (the fifties)

- More of all of the above
- Base conversion
- Simple algebra
- Probability

Then the 60s to 80s. There is currently only one student in the area mastering these and he placed 4th in last year’s national math championship.