Understanding how to teach addition is critical. Because addition is such a foundational component of our students’ math skills, it’s essential that we know what to teach, when to teach it, how to teach it, and what prerequisite skills are needed for our kids to become successful mathematicians.
The 3 Essential Addition Prerequisites
Before you introduce your students to addition, there are a few basic math skills they need to have mastered. Your young students must have a solid foundation in these areas or they’re going to have a hard time with addition. So let’s take a quick look at what they need to know first!
Developing Number Sense
You may be wondering, “What is number sense?” Well, number sense is basically just the ability to make “sense” of numbers. It’s realizing that numbers are more than mere facts; they can be put together and taken apart in various ways to create new things.
Now, number sense is something that takes a long time to develop, so it’s important to set the stage early for your learners. Helping your kids see themselves as successful mathematicians from the beginning will be pivotal to their budding abilities and confidence.
By mastering each mathematical skill in sequence before learning new skills, your kids will begin using growth mindset language as opposed to the typical, “I’m not good at math.” You will see their confidence increase, and that confidence will translate into better grades and the ability to understand more complex information and tasks.
And of course, it’s important to remember that kids will develop number sense at varying rates. Understanding where each child is in his or her learning journey is the key to helping them be success.
Obviously, you can’t start teaching kids how to add until they understand how to count. If they don’t understand this basic skill, do NOT try to incorporate addition into their math routine. This will just frustrate both of you! If you want some tips and tricks for helping your kids master counting, check out How to Learn Counting the Fun Way.
Before kindergarten students (or even first graders) can begin adding, they also need to have mastered the skills of subitizing, or one-to-one correspondence. This is the knowledge that every object is individual and has an inherent value of one.
So when your child points to the red car, he should understand that this is one red car. If you want to make sure that your kids truly understand this concept, provide them with a tens frame, which is merely a rectangle divided into 10 individual sections.
This simple tool is designed to help kids learn about numbers by providing them with a visual representation of how to isolate individual items in a group as well as how to view the individuals as a whole. Here are some great tens frame resources.
Personally, I like using tens frames to discuss days in school because it’s an excellent way to help your kids visualize an abstract concept in a more concrete way! Plus, the kids love to see how many days they’ve been in school (as well as how many days they still have left).
How to Teach Addition
The basic concept of addition is understanding that individual items can be put together into groups of objects that represent more. Once students understand this premise, we want to give them lots of opportunities to represent these higher numbers.
Students must have the opportunity to first represent numbers and individual numerals with physical objects, and that’s why manipulatives are such important visual cues at this particular level of understanding.
Manipulatives are simply items that can be touched and “manipulated” like counting cubes, bears, discs, cars, etc. You can use any type of manipulatives you want to teach addition, but the key is to have a lot of small items in order to represent the numbers appropriately.
Here are a few examples of helpful manipulatives you need to have in your classroom or homeschool.
A great way to keep your kids interested is by using items they already love. Consider grabbing their favorite characters, action figures, cars, trains, etc. to use during math to keep them engaged. This will be especially important as the skills become more difficult.
Giving your kids the opportunity to “act out” addition problems through physical items first will set them up for success as they transition to the next level of mastery.
Pictures or Images
Students have to be able to move away from concrete figures in order to gain totally mastery over addition. Once they understand how to group and move items by using one-to-one correspondence, you can move them to a slightly more abstract form of math by incorporating pictures or images.
They still have the ability to count each image, but they no longer have the benefit of actually “holding” each one individually. As they show mastery of pictures and images, they are ready for a more abstract form of understanding.
Number Bonds and Number Lines
Once they have mastered pictures or images, they can move on to more advanced practices like working with number bonds and a number line. These different strategies will give them a deeper understanding of the relationship between numbers.
Observing that they can successfully work with numbers in this context will solidify that they are ready for the final and most abstract form of math which is strictly numerals.
The most important thing to note as we discuss how to teach addition is level of understanding. If any of these areas is giving the young children in your classroom pause, pull them into small groups and give them lots of opportunities to work with hands-on materials.
Determine where the confusion lies for learners whether it is in the transition from manipulatives to images, the transition to number bonds and number lines, or the transition to simply numbers.
When you figure out where the breakdown occurs, you can give your students many opportunities to practice at that level before moving on to the next step.
The Language of Math
When teaching the language of math you have to treat it like any other foreign language. It is essential that you define new words and teach these words in isolation before trying to add them into a sentence.
Words & Symbols
When they are first introduced to addition, they will commonly hear the word “plus” to represent addition. However, it isn’t long before we begin substituting other synonyms like “and, add, another, also, in addition to.”
These other words and phrases need to be clearly explained so that your kids comprehend that they mean the same as the word “plus.”
They also need to understand addition symbols. Obviously these symbols are going to be more abstract. So the easiest way to teach your students is to explain that these pictures or symbols are a quicker way for us to write the word addition.
As a fun little experiment, let your students count while you write the word addition. Then let them count while you draw the “+” symbol. They will quickly come to realize that a plus symbol is much easier to write than the word addition.
Expressions & Equations
For a long time, I didn’t realize there was a difference between addition expressions and addition equations. However, there is a very distinct difference that is important for you, as the teacher, to understand.
Math expressions do NOT have an equal sign. So when we write an addition problem vertically, with one number, a plus sign, and another number, this is an addition expression. An equation, on the other hand, ALWAYS includes an equals sign, and these are the ones that we see written horizontally.
While we understand that expressions and equations symbolize the same thing, it is important to teach each one in isolation so that your kids understand the difference. Then you can show how there are different ways to get to the same outcome.
The most abstract form of math language is the word problem.
Your kids have to be able to integrate what they have learned about math words, use symbols to produce a math expression to represent those words, and then finally create an equation from the language in the word problem. This is definitely a much more complex task!
To help your kids overcome the fear of word problems, explain that it’s like a treasure hunt. They simply need to find the important words to help them solve the mystery. And remind them that it’s much easier to write numbers and symbols than it is to write all of the words associated with the numbers and symbols.
The best way to do this is with the Baking Up Sum Addition Word Problems resource.
This resource contains three levels of complexity, and each level has a math “mat” that is designed for that unique level of understanding. Level 1 has room for manipulatives, Level 2 includes space for drawing pictures, and Level 3 incorporates numerals and equations.
Students are also encouraged to take their correct answer and produce a number sentence.
Allowing students to practice a variety of addition strategies will give them more confidence in their ability to understand numbers and ultimately their ability to move into more complex mathematical skills like two-digit numbers.
The Best Addition Teaching Resources
If you are going to spend money on resources for your classroom or homeschool, you want to make sure they are good quality. So as you’re thinking about what types of products to purchase consider ones that include…
- visual aids
- whole group and small group components
- hands-on addition activities
- an addition game
- story problems
Here are a few great options directly from Teachers Pay Teachers.
Each of these resources gives students opportunities to practice basic addition facts and work through simple addition problems using single-digit numbers and progressing into larger numbers. They even have a chance to work with number bonds and a number line!
In our house, we love to play board games! And without a doubt one of the best ways to give students extra practice in addition is through board games. Whether it’s counting the number of dots on the dice or how many spaces to move forward, here are some excellent beginner options that will be perfect for kindergarten or 1st grade students.
Books That Teach Addition
My absolute favorite way to help kids understand new concepts is with quality children’s books. And yes, I already know what you’re thinking…we are talking about math not reading. But did you know that there are TONS of engaging stories that help kids make meaningful connections with math? It’s true! And here are some excellent selections that will engage your kids and help them think about math more holistically!
Addition is one of the most foundational parts of mathematics and that is why we teach children what numbers are and the value of each number BEFORE we teach them addition. However, the ability to mater addition is an essential prerequisite to more complex skills like multiplication, division, algebra, and geometry.
But that doesn’t mean that teaching (or learning) addition has to be boring! Incorporating engaging resources and books will keep your learners interested and excited about learning math.