Mental Subtraction Facts to 20 - Second Grade Mathematics

Mental subtraction fluency is the ability to determine differences quickly and accurately by understanding the relationships between numbers rather than counting backward one tick at a time. In second grade, developing swift recall of subtraction facts within 20 frees up your working memory, enabling you to focus on multi-digit problems and complex word scenarios. In this chapter, you will master the subtract-zero and subtract-all rules, learn the take-from-ten strategy, explore how doubles unlock subtraction facts, and discover that every subtraction question is secretly an addition question in disguise.

Fundamental Subtraction Rules: Zero and All

Two fundamental rules govern subtraction across all numbers, instantly solving two entire categories of facts.

Subtracting Zero (Identity):
8 - 0 = 8          15 - 0 = 15
(Taking away nothing leaves the original amount untouched!)

Subtracting All (Zero Difference):
8 - 8 = 0          15 - 15 = 0
(Taking away everything leaves an empty set: zero!)

Subtracting One (Predecessor):
9 - 1 = 8          14 - 1 = 13
(Subtracting 1 simply names the number immediately before!)

The Subtracting Zero Rule

When you subtract 0 from any number, the difference is identical to the starting number (the minuend). If you have 14 crayons and give away 0 crayons, you still have 14 crayons: 14 - 0 = 14.

The Subtracting All Rule

When you subtract a number from itself, the difference is always zero. If you have 9 cookies and eat all 9 cookies, you have 0 cookies left: 9 - 9 = 0.

The Minus-One and Minus-Two Patterns

Subtracting 1 simply means stepping backward by one unit to the previous number on the number line. Subtracting 2 means taking two hops backward: 11 - 2 is 10, 9.

The "Think Addition" Mental Superpower

The single most powerful secret to mental subtraction is recognizing that subtraction is the inverse of addition.

Transforming Subtraction into Missing-Addend Addition:

The Problem:     14 - 8 = ?
The Mental Shift: 8 + [ ? ] = 14
Recall Fact:     8 + 6 = 14!
The Answer:      14 - 8 = 6

Why Think Addition Works Faster

Your brain learns addition facts much faster and more securely than subtraction facts. Instead of struggling to count backward 8 steps from 14, flip the question around: "What number do I need to add to 8 to reach 14?" Because you already know that 8 + 6 = 14, the answer 6 appears instantly without any backward counting.

The Take-from-Ten Strategy for Teen Numbers

When subtracting from a teen number (11 through 19), the take-from-ten strategy uses the friendly number 10 as an intermediary.

Solving 13 - 7 using Take-from-Ten:

Step 1: Decompose the teen number 13 into 10 and 3.
        13 = 10 + 3

Step 2: Subtract the 7 from the 10!
        10 - 7 = 3

Step 3: Add the remaining 3 back to the result.
        3 + 3 = 6

Equation Summary:
13 - 7 = (10 - 7) + 3 = 3 + 3 = 6

Visual Ten-Frame Model

Imagine two ten-frames: one completely full (10) and one holding 3 counters (making 13). When asked to remove 7, instead of taking from both frames, take all 7 directly from the full ten-frame! That leaves 3 in the first frame. Combine those 3 with the 3 in the second frame, and you have 6 counters left. This visual trick turns every difficult subtraction into a simple subtraction from 10.

Using Half-Doubles to Subtract

Your doubles addition facts directly unlock subtraction facts where the difference equals half the starting number.

The Doubles-to-Subtraction Bridge:
Addition Double:      6 + 6 = 12
Subtraction Half:    12 - 6 = 6

Addition Double:      8 + 8 = 16
Subtraction Half:    16 - 8 = 8

Addition Double:      9 + 9 = 18
Subtraction Half:    18 - 9 = 9

Near-Doubles in Subtraction

You can also use near-doubles: if you see 15 - 7, think of the double 7 + 7 = 14. Since 15 is 1 more than 14, the answer must be 1 more than 7, which is 8!

Practice Exercises

Exercise 1: Use the think-addition strategy to solve 15 - 9. Write the related addition fact that you used to find the answer.

Exercise 2: Solve 14 - 6 using the take-from-ten strategy. Show how 14 was decomposed into 10 and 4, and write the remaining steps.

Exercise 3: Use a doubles fact to solve 16 - 8, and explain how the addition double relates to this subtraction problem.

Exercise 4: What is the value of 18 - 18, and what general subtraction rule explains this result?

Solutions and Explanations

Solution to Exercise 1: To solve 15 - 9 using think-addition, reframe the question as: 9 + ? = 15. Recalling your addition facts, 9 + 6 = 15. Therefore, 15 - 9 = 6.

Solution to Exercise 2: To solve 14 - 6 using take-from-ten: Decompose 14 into 10 and 4. Subtract 6 from 10: 10 - 6 = 4. Finally, add the remaining 4: 4 + 4 = 8. Therefore, 14 - 6 = 8.

Solution to Exercise 3: The related doubles fact is 8 + 8 = 16. In subtraction, you start with the whole (16) and take away one of the equal parts (8), leaving the other equal part (8). Therefore, 16 - 8 = 8.

Solution to Exercise 4: The value of 18 - 18 is 0. The general rule is the Subtracting All rule: when any quantity is subtracted from itself, all items are removed, leaving an empty set with a difference of zero.