# Math Strategies for Teaching Addition and Subtraction – Part 4: Numbers to 1000

This is the final discussion of a 4-part series on teaching Addition and Subtraction. For the previous discussions, please refer to the following links:

Once students learn the foundation for adding and subtracting up to 100, extending to 1000 and beyond is more straightforward than the previous two progressions, i.e. from numbers within 10 to numbers within 20, and to numbers within 100. However, there are still a few new pitfalls and common challenges when first trying to teach addition and subtraction beyond the hundreds. Here we discuss some of our observations and suggestions about how to overcome the challenges faced by teachers and students.

## Skip Counting

One of the first thing we do is to get the kids comfortable counting in this number range. We find that some students have difficulty with skip counting when the numbers exceed a hundred. The problem occurs when counting numbers that cross to the next hundred, e.g.

899->900.

Even more challenging is skip counting by say 5 or 10. For example, some students find it hard to do

898 + 10, or 898 + 5

We find the number line and number pattern questions especially helpful for our students, and of course, it does not hurt to practice these questions over and over again!

## Place Value

Moving into the hundreds, students need to get used to regrouping tens and hundreds.

For example,

16 tens is 1 hundred and 6 tens.

This comes in handy later when adding 3 digit numbers which require regrouping in the tens and hundreds. For example in 184 + 382, students should recognize that 8 tens + 8 tens = 16 tens, which is 1 hundred and 6 tens. Concrete – Pictorial – Abstract representations are very useful at this stage.

### Place Value Strategies

Students usually do not have trouble with addition without regroup. Apart from using the number line, it is helpful to focus on place value strategies at this stage to prepare the students for regrouping, especially in tens and hundreds.

In using place value strategies, the following can be used.

343 + 536

= 3 hundreds 4 tens 3 ones + 5 hundreds 3 tens 6 ones

= 8 hundreds 7 tens 9 ones

= 879

### Standard Algorithm

When dealing with 3-digit addition without regroup in standard algorithm, many students will look at each place value separately and treat the problem as a multi-stage “game” of single digit addition. The mathematically language should focus on place values; for example in 343 + 536, students should say 4 tens plus 3 tens is 7 tens, instead of 4 plus 3 is 7. ### Break-Apart Strategy

When first introducing 3-digit numbers, it is important to get the students familiar with the break-apart strategy through exercises such as this

The ability to break-apart large numbers mentally is especially crucial in later grades, when learning about multiplication and division. Students who can mentally see the numbers in their place value components feel more at ease when they break-apart numbers in other ways, e.g. for problems such as 72 ÷ 3, which can be mentally broken down into

72 ÷ 3 = (60 + 12) ÷ 3 = (60 ÷ 3) + (12 ÷ 3) = 20 + 4 = 24

Adding with regroup can be confusing for some children, especially when dealing with 3-digit addition. Instead of introducing regroup questions randomly, we find that students learn best when the topic is broken into the following:

• addition with regrouping in ones,
• addition with regrouping in tens ,
• addition with regrouping in ones and tens,

In addition and subtraction, we are not only building on procedural fluency but also on number sense and connections. This is to prepare students for Number Theories in higher grades such as Least Common Multiples, Greatest Common Factors, Square and Square roots, Prime Factorization etc.

It is important to let the students work on different approach to the same problem and connect the different methods. For example, a typical addition with regroup problem can be presented using three strategies:

• place value
• standard algorithm
• break-apart

## Subtraction with Regroup

Subtraction is usually much harder to teach than addition. From our experience, the topic of subtraction easily takes twice the time compared to addition.

This is especially true for subtraction with regroup for numbers beyond 100, for two main reasons:

1. Students now have to deal with regrouping in hundreds, tens and ones,
2. Some students have not fully mastered subtraction within 20. For example, if students still have difficulty with 13 – 6, it is hard to get them comfortable with questions such as 413 – 256.

Similar to addition with regroup, we find it useful to  introduce subtraction with regroup in stages. For example,

• regrouping in tens and ones only,
• regrouping in hundreds and tens only,
• regrouping in hundreds, tens and ones,
• regrouping across zeros

### Subtraction across zeros

Perhaps the most challenging of all is subtraction across zeros. We find the place value chart, coupled with concrete-pictorial-abstract approach, to be very helpful in this. This sub-topic can be broken into:

a. Place value regroup, e.g. regroup tens into tens and ones

b. Subtraction across zeros with emphasis on place value.