Number Sense
Number sense for adding 19 is the mental math strategy of rounding 19 up to 20, adding 20 to the number, and then subtracting 1 from the result. In 4th grade math with Saxon Math Intermediate 4, Chapter 1, students learn this technique as a faster alternative to column addition — for example, 36 + 19 becomes 36 + 20 - 1 = 55. This compensating strategy is part of a broader number sense toolkit that builds mental arithmetic fluency, a skill that transfers to estimation and multi-step calculations throughout middle school.
Key Concepts
Property When adding 19 to a number, we may mentally add 20 and then think of the number that is one less than the sum.
Example To solve $36 + 19$, think $36 + 20 = 56$, then subtract one to get $55$. To solve $47 + 19$, think $47 + 20 = 67$, then subtract one to get $66$. To solve $24 + 19$, think $24 + 20 = 44$, then subtract one to get $43$.
Explanation Adding 19 is tricky, but adding 20 is a breeze! Just add 20 to your number and then take one tiny step back to get your answer. It's a clever and super speedy shortcut for your brain.
Common Questions
What is the mental math trick for adding 19?
Round 19 up to 20, add 20 to your number, then subtract 1. For example, 47 + 19: think 47 + 20 = 67, then 67 - 1 = 66. This is faster than column addition.
Why does the add-20-subtract-1 strategy work?
Since 19 = 20 - 1, adding 19 is exactly the same as adding 20 and then subtracting 1. You trade a harder calculation (adding 19) for two easier ones (adding 20, subtracting 1).
What are some examples of the number sense strategy for adding 19?
36 + 19: add 20 to get 56, subtract 1 to get 55. 54 + 19: add 20 to get 74, subtract 1 to get 73. 78 + 19: add 20 to get 98, subtract 1 to get 97.
Can a similar strategy work for adding 29, 39, or 99?
Yes. The same compensation technique works: add the nearest multiple of 10, then subtract the difference. For 29, add 30 and subtract 1. For 99, add 100 and subtract 1.
When do 4th graders learn the number sense strategy for adding 19?
In Saxon Math Intermediate 4, Chapter 1, Lessons 1-10, this mental math strategy is introduced to build flexible arithmetic and reduce reliance on written calculation for simple sums.
Why is mental math number sense important in 4th grade?
Mental math builds number fluency that speeds up multi-step problem solving, supports estimation, and reduces cognitive load when students tackle more complex math. It also improves performance on timed tests.