Addition is one of those math skills that students need throughout their formal education and life beyond school. By mastering addition math facts, students will be able to confidently approach more complex problems in and out of the classroom. As a result, it is imperative for elementary teachers to support their students in building a strong foundation in math. Read below to learn more!

**This blog post will...**

- explain why it's important to teach addition facts to elementary students
- identify the essential understandings of addition in 1st, 2nd, 3rd, 4th, and 5th grade
- provide a list of common misconceptions students have about adding

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

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

Basic addition or single-digit addition is finding the sum of two one-digit addends. In other words, it is combining or adding two one digit-numbers together to find their total. The basic addition facts are all of the combinations of 1-digit numbers. 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 addition include buying a couple of candy bars and calculating the total, adding the different types of stickers in your drawer to find how many total stickers there are in your sticker collection, and adding how many boys and girls are in your camp to find how many kids there are in total. I encourage you to create an addition anchor chart with your students and record these examples and more.

**ESSENTIAL UNDERSTANDINGS of ADDITION**

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 addition lessons and activities.

__FIRST GRADE__

In first grade, students should be able to...

- understand the relationship between addition and subtraction.
- use the counting on strategy to solve addition problems.
- fluently add within 10.
- add within 20 using strategies.
- determine if an addition 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 addition word problems involving numbers within 20.
- solve addition word problems with three addends and a sum within 20.

__SECOND GRADE__

In second grade, students should be able to...

- fluently add within 20.
- fluently add within 100 using strategies.
- add within 1,000 using strategies.
- write an addition equation to express an even number as a sum of two equal addends.
- add up to four two-digit numbers using strategies.
- mentally add 10 or 100 from a given number 100-900.
- use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns and write an equation to express the total as a sum of equal addends.
- explain why addition strategies work.
- solve one and two-step addition word problems within 100.
- solve addition word problems involving length (same units) within 100.
- solve addition word problems involving money.

__THIRD GRADE__

In third grade, students should be able to...

- identify arithmetic patterns on an addition table and explain them using the properties of addition.
- fluently add within 1000 using strategies and algorithms.
- solve addition word problems involving time intervals in minutes.
- solve addition word problems involving mass or volume (same units).
- understand the relationship between area and addition.
- solve real world problems involving addition and area.

__FOURTH GRADE__

In fourth grade, students should be able to...

- fluently add multi-digit whole numbers using the standard algorithm.
- understand addition of fractions as joining parts of a whole.
- add mixed numbers with like denominators.
- add fractions with denominators 10 or 100.
- generate a number or shape pattern that follows a given addition rule.
- solve addition word problems involving fractions with like denominators.
- solve addition problems involving fractions on a line plot.
- solve addition problems involving finding unknown angles on a diagram.

__FIFTH GRADE__

In fifth grade, students should be able to...

- add decimals to the hundredths using strategies.
- add fractions with unlike denominators.
- generate two numerical patterns using two given addition rules.
- solve addition word problems involving fractions with like and unlike denominators.
- understand the relationship between addition and volume.
- solve real world problems involving addition and volume.

**COMMON STUDENT MISCONCEPTIONS ABOUT ADDING**

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

- The student can solve addition 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 addition facts in isolation but cannot apply his or her skills when it is presented in a word problem or real life situation. (Example: A child can tell you 3 + 4 = 7 but cannot solve a word problem with that problem imbedded in it.)
- The student can explain the commutative property of addition, but can not apply it in context. (Example: A child knows 6 + 3 = 9, but struggles to solve 3 + 6 = 9.)
- The student is unable to generalize patterns in addition. (Example: A child knows 5 + 2 = 7, but cannot tell you 5 + 12 = 17 with ease.)
- The student confuses the regrouping procedure for addition with the regrouping procedure for subtraction. (Example: A child regroups a ten from the 2 in the tens place and subtracts 11 - 9 in the problem 321 + 139 = ?)