Teaching 3rd grade addition and subtraction can be challenging. Students often make mistakes when adding and subtracting larger multi-digit numbers.

This is usually because they need a **stronger understanding of place value**.

When the standard algorithm is used correctly, it will yield the right answer. However, this strategy focuses heavily on digits and memorizing procedures versus number sense and place value understanding.

Although our students will eventually learn to use the standard algorithm for efficiency, they first need to have a deep understanding of place value and regrouping. If not, it can lead to many misconceptions that will be hard to correct later.

Let’s explore some common misconceptions students have about addition and subtraction within 1,000 and then learn what to do to prevent and fix them.

**Addition and Subtraction Misconceptions**

When solving multi-digit problems, students sometimes focus only on the digits, without considering their value. In the example below, when adding the tens they may view them as “8 + 7” instead of “80 +70”.

In addition, children that don’t have a good understanding of place value will often make errors like subtracting larger digits from smaller digits, no matter the place value like in this example.

These misconceptions get even larger when we use phrases such as “carry the 1” when teaching the standard algorithm because we are stripping place value away from the equation.

The “1” is not really a “1”. It represents one ten, one hundred, one thousand, etc.

When we only use the standard algorithm to teach students who are still struggling with place value concepts, we’re teaching them to memorize a process to get the answer correct, but not understand the math.

So, what should you do instead?

**How to Teach Addition and Subtraction within 1,000**

- Use precise language when discussing the process of adding within each place value. If you’re adding in the tens place say “8 tens plus 7 tens” instead of “8 + 7”

- Be specific when regrouping. Regrouping simply means renaming something. Instead of saying “carry the 1”, say something like “regroup/rename 10 ones as 1 ten”

- Use a variety of models, representations and strategies to teach addition and subtraction problems

- Ask students to show their work and explain their thinking

- Transition students that are ready for the standard algorithm by first using pictorial representations when teaching the process and then move to symbols only

**Top Teaching Tips**

- Use models like
**open****number lines**,**arrow addition charts**and**drawings**to help students visualize addition and subtraction

- Model strategies like
**place value charts**and**expanded form**to reinforce place value

- Use manipulatives like
**base ten blocks**when when introducing strategies and continue to use for students that still need more concrete examples

- Teach the
**standard algorithm**after students have a firm understanding of place value through exposure to the concrete (i.e. using base ten blocks), pictorial (i.e. drawing models & using place value charts) and abstract model (i.e. using only the standard algorithm).

- Provide
**word problem examples**so that students see skills in context

I hope these tips and ideas are helpful to you!

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