Free Guides
UIL Number Sense tips, tricks, and practice help
Free resources for students, parents, and coaches who want to get faster at Number Sense. Start with the basics, build a daily routine, and practice with purpose.
12 free guides
- Multiplication Shortcut
Multiplying by 11: the fast Number Sense trick
A focused guide for multiplying two-digit numbers by 11 quickly, including when to carry. - Multiplication Shortcut
Multiplying by 25: the divide-by-4 trick
A focused Number Sense guide for multiplying by 25 quickly by using 100 divided by 4. - Multiplication Shortcut
Multiplying by 99: the subtract-from-100 trick
A focused Number Sense guide for multiplying by 99, 999, and 101 by using a nearby round number. - Multiplication Shortcut
Multiplying numbers near 100: the deficit trick
A focused Number Sense guide for multiplying two numbers close to 100 by using how far each is from 100. - Squaring Shortcut
Squaring numbers ending in 5: the next-number trick
Square any number ending in 5 in seconds, and use the same idea for pairs like 43 x 47. - Conversions
Fraction and percent conversions to memorize for Number Sense
The fraction, decimal, and percent equivalents that show up again and again, and how to use them to find percents of numbers fast. - Sums and Series
Sum of 1 through n: the pairing trick and its variations
Add long runs of consecutive numbers instantly, plus quick formulas for sums of odd and even numbers. - Conversions
Repeating decimals to fractions: the 9s trick
Convert repeating decimals to fractions quickly by putting the repeating part over 9s. - Number Theory
GCD and LCM shortcuts for Number Sense
Find the greatest common divisor and least common multiple fast, and use one to get the other. - Powers and Exponents
Laws of exponents for Number Sense practice
The exponent rules that let you simplify powers without expanding everything the long way. - Practice Routine
A simple UIL Number Sense practice routine
A repeatable routine for turning tricks into speed: learn one shortcut, drill it, then use it under time pressure. - Test Overview
UIL Number Sense topics by problem number
What shows up on the UIL Number Sense test, grouped by approximate problem number, from fast arithmetic early on to calculus-style questions at the end.
Practice With the App
Turn the tips into timed drills
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