After students master simple subtraction, they will quickly move on to 2-digit subtraction, which often requires students to apply the concept of "borrowing a one" in order to subtract properly without yielding negative numbers.

The best way to demonstrate this concept to young mathematicians is to illustrate the process of subtracting each number of the 2-digit numbers in the equation by separating them into individual columns where the first number of the number being subtracted lines up with the first number of the number it's subtracting from.

Tools called manipulatives such as number lines or counters can also help students grasp the concept of regrouping, which is the technical term for "borrowing a one," wherein they can use the one to avoid a negative number in the process of subtracting 2-digit numbers from one another.

## Explaining Linear Subtraction of 2-Digit Numbers

These simple subtraction worksheets (#1, #2, #3, #4, and #5) help guide students through the process of subtracting 2-digit numbers from one another, which oftentimes requires regrouping if the number being subtracted requires the student to "borrow a one" from a larger decimal point.

The concept of borrowing a one in simple subtraction comes from the process of subtracting each number in a 2-digit number from the one directly above in when laid out like question 13 on worksheet #1:

24

-16

In this case, 6 cannot be subtracted from 4, so the student must "borrow a one" from the 2 in 24 to subtract 6 from 14 instead, making the answer to this problem 8.

None of the problems on these worksheets yield negative numbers, which should be addressed after students grasp the core concepts of subtracting positive numbers from one another, often first illustrated by presenting a sum of an item like apples and asking what happens when *x* *number* of them is taken away.

## Manipulatives and Additional Worksheets

Keep in mind as you challenge your students with worksheets #6, #7, #8, #9, and #10 that some children will require manipulatives such as number lines or counters.

These visual tools help explain the process of regrouping wherein they can use the number line to track the number which is being subtracted from as it "gains a one" and jumps up by 10 then the original number below is subtracted from it.

In another example, *78 - 49*, a student would use a number line to individually examine the 9 in 49 being subtracted from the 8 in 78, regrouping to make it 18 - 9, then the number 4 being subtracted from the remaining 6 after regrouping 78 to be *60 + (18 - 9) - 4*.

Again, this is easier to explain to students when you allow them to cross out the numbers and practice on questions like those in the above worksheets. By already presenting the equations linearly with the decimal places of each 2-digit number aligned with the number below it, students are better able to understand the concept of regrouping.