Not only do elementary students need to have a strong conceptual understanding of subtraction, they also mustbe able to recite subtraction facts by memory, flexibly work with numbers in a subtraction context, and solve real world problems involving subtraction. If this feels overwhelming or you are looking for ideas for teaching subtraction, then you found the right place!

**This blog post will…**

- explain why teaching and learning subtraction facts is important
- identify the essential understandings of subtraction organized by grade level
- describe the common misconceptions surrounding it

**WHY IS LEARNING ABOUT THE BASIC SUBTRACTION FACTS IMPORTANT?**

You should always provide your students with a purpose for learning. This can be done by explaining to them why subtraction fact fluency is important and giving them examples of how we use basic subtraction in the real world.

Basic subtraction, or subtraction within 10 or 20 is finding the difference between two numbers. In other words, it is removing some objects from a group. It is important because mastery of these facts increases a child’s confidence in their math ability, decreases math anxiety, and will help them when they are solving more complex problems. When children are solving complex problems and lack math fact fluency, they will spend so much time and energy calculating each math fact imbedded in the problem that they will lose concentration and will likely not be able to successfully complete the more complex calculations required for solving the problem.

Relating the concept to your students’ own real-life experiences makes their work more interesting and meaningful. Real world examples of basic subtraction include buying candy at the store using your allowance, eating snacks and finding how many are left, cleaning up toys and determining how many more you need to pick up. I encourage you to create a subtraction anchor chart with your students and record these examples and more.

**ESSENTIAL UNDERSTANDINGS of SUBTRACTION**

Essential understandings, also known as enduring understandings, are the big ideas we want our students to master. They help you focus your teaching on what you want your students to know, understand, and do. These “big ideas” derive from standards and serve as the foundation for designing all of your basic subtraction lessons and activities.

__FIRST GRADE__

In first grade, students should be able to…

- understand the relationship between addition and subtraction.
- use the counting back strategy to solve subtraction problems.
- fluently subtract within 10.
- add and subtract within 20 using strategies.
- determine if a subtraction equation is true or false.
- find the missing number in any position of an addition or subtraction problem.
- subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 using strategies.
- solve subtraction word problems involving numbers within 20.

__SECOND GRADE__

In second grade, students should be able to…

- fluently subtract within 20.
- fluently subtract within 100 using strategies.
- subtract within 1,000 using strategies.
- mentally subtract 10 or 100 from a given number 100-900.
- explain why subtraction strategies work.
- solve one and two-step subtraction word problems within 100.
- solve subtraction word problems involving length (same units) within 100.

__THIRD GRADE__

In third grade, students should be able to…

- fluently add and subtract within 1000 using strategies and algorithms.
- solve subtraction word problems involving time intervals in minutes.
- solve subtraction word problems involving mass or volume (same units).

__FOURTH GRADE__

In fourth grade, students should be able to…

- fluently subtract multi-digit whole numbers using the standard algorithm.
- understand subtraction of fractions as separating parts of a whole.
- subtract mixed numbers with like denominators.
- solve subtraction word problems involving fractions with like denominators.
- solve subtraction problems involving fractions on a line plot.
- solve subtraction problems involving finding unknown angles on a diagram.

__FIFTH GRADE__

In fifth grade, students should be able to…

- subtract decimals to the hundredths using strategies.
- subtract fractions with unlike denominators.
- solve subtraction word problems involving fractions with like and unlike denominators.

**COMMON STUDENT MISCONCEPTIONS ABOUT SUBTRACTION**

In order to effectively teach your students about subtraction you must anticipate, identify, and correct and misconceptions or misunderstandings they have developed. To help you, I have listed some of the most common subtraction misconceptions your students are likely to make.

- The student can solve subtraction facts when presented with an equation in a vertical format, but cannot transfer that knowledge to equations in a horizontal format. (Example: A child can solve 8 – 3 = ? when presented in a vertical format but not a horizontal format.)
- The student can solve subtraction facts in isolation but cannot apply his skills when it is presented in a word problem or real life situation. (Example: A child can tell you 8 – 4 = 4 but cannot solve a word problem with that problem imbedded in it.)
- The student does not understand that addition and subtraction are inversely related. (Example: A child knows 9 + 3 = 12, but does not know 12 – 9 = 3.)
- The student thinks that the commutative property applies to subtraction just like addition. (Example: A child thinks 14 – 2 = 2 – 14.)
- The student applies the rule that you subtract the smaller number from the bigger number to the situation where the smaller number is part of the minuend. (Example: A child subtracts 1 from 9 instead of regrouping in 111-39.)