# Essential Guide To Teaching Addition & Subtraction

Teaching Addition and Subtraction and don’t know where to start? You’re not alone.  Our BIG IDEAS in teaching Addition and Subtraction are a must read for teachers serious about teaching it the right way.

By the time kids start formal learning of addition and subtraction they have encountered and performed the process hundreds of times in their everyday lives. So you’d think that teaching addition and subtraction would be simple, right?

Well unfortunately it’s not!

What research tells us, and achievement data shows, especially when solving word problems, is that kids are masters of memorizing mathematical processes and have trouble with understanding the ‘when, what and why’  of computation.

Students are excellent at following a process, or the ‘How To’ do it, but when left to solve things independently or apply what they have been taught in other situations, they fail.

The culprit behind this is teaching programs, activities, printables and worksheets that center on solving algorithms, or ‘sums’.

Yes understanding algorithms is important.  But algorithms are the final piece of the learning jigsaw. In fact  they are actually just a written representation of a very complicated process. Algorithms are  like a math shorthand that should be used by students when deep understanding of the math concept is achieved.

So the solution is simple, for effective teaching and high levels of student achievement in addition and subtraction, ensure that you provide a comprehensive range of opportunities to learn every aspect of the addition and subtraction process.

Finding what you need to include is not so easy. Many curriculum descriptions are vague and contain sweeping explanations rather than a list of things to teach.  So to help we’ve done some research for you and put together a handy list to guide you.

Related Posts: Teaching Numbers 0-20

Before we get to the list it’s important to remember that at the center of all good teaching is understanding what students already know about a topic; their prior knowledge.

Good teachers will identify what students already know and build on it. But identifying what students actually know is only as good as the methods used to find this out. A test that shows a sea of red ticks on a page may not identify understanding. Rather a good memory for a process or a procedure. So it’s important to approach pre-assessment with caution.

Tests can be helpful but they must test the right thing. Do they really test understanding or are they testing memory?

Tests don’t have to be formal they can be a quick informal discussions. Personally I love using brainstorming methods, like creating a graffiti wall, concept attainment tasks or concept maps of everything you know about … activities.

Frayer Model Think boards are also great way to do this as is giving students the answer to a math problem and asking them to prove that it is right or wrong.

Use these ideas alongside other assessment pieces to make sure kids really do understand something. How does the saying go… “If you can’t explain it, you don’t understand it.”

Related Post: Teaching Tricky Teen Numbers

## Teaching Addition & Subtraction - Big Ideas & Essential Understandings

After identifying what kids already know you need to teach them what they don’t know.

Here’s the BIG Ideas and Essential understandings of teaching Addition & Subtraction for you to use as a guide.

Use this list as a guide to what you need to include in your addition and subtraction teaching programs and as a way of differentiating your content.

1. Use materials and models like counters, drawings, ten frames, and number lines to strengthen understanding. These math resources help kids to focus on the addition or subtraction process rather that the answer.
2. Include the Fundamentals of Addition & Subtraction

• The Commutative Property – Numbers can be added in any order and the result will not change. This does not apply to subtraction and needs to be made explicit.
• The Associative Property – Three or more numbers can be added together in any order allowing students to partition difficult numbers to make things easier. e.g. 5 + 8 = 5 + 5 +3
• Inverse Relationship – Every addition calculation can be replaced with an equivalent subtraction calculation and vice versa. The 3 For FREE notion.

For Subtraction

• Subtraction as deduction – If I had 10 cookies and I ate 3 how many are left
• Subtraction as complementing, – e.g. how many more do I need… There are 10 stickers in a set, I have 6 how many more do I need to get a full set?
• Subtraction as difference – e.g. how many more/or less.  I have 12 cookies and you have 6. How many more cookies do I have than you?

Related Post: Teaching Odd Or Even Numbers

## Addition & Subtraction Activities, Printables and Worksheet Ideas

In the classroom select addition and subtraction activities, printables and worksheets that:

• Enable students to recognise and identify a problem as addition or subtraction
• Understand that addition and subtraction can be used to solve problems
• Introduce addition and subtraction through verbal action songs and stories.
• Emphasise the idea of  joining, adding more, or taking away.
• Extend and develop the language of addition and subtraction. Including the idea of part, part, whole.
• Use materials and models to show the action of addition with a 5, 10 or 20 frame, counters, number lines, drawings, and playdough etc. Modeling and linking the words used in  the verbal addition process to a concrete action.
• Use symbolic representations, replacing the ‘and’ with + symbol.
• Develop fluency with addition & subtraction fact knowledge, and mental strategies. Including counting on/back, partitioning into easier numbers, using place value knowledge, doubling and halving.
• Explain the thinking involved
• Practice, Practice and Practice some more!

Click each image below to download our addition and subtraction classroom printables. Check back often or go to the what’s NEW page to keep up to date with our latest resources.