Step 42: Double-Digit Add/sub
Single digit
A gentle introduction to working with two two-digit numbers is to have one of them be a single-digit number. One of the best ways to practice adding or subtracting a single-digit number with a double-digit number is to do skip counting using various skip sizes, going up or down, and starting at any number. The following methods for two two-digit numbers will of course work when one of the numbers is a single-digit number.
Use objects
Grounding your child’s understanding by using physical objects is always a good idea. Start by representing both of the numbers with groups of tens and ones.
Adding
If you are adding the two numbers, put all the groups together and discuss the result. If you are adding two numbers, such as 23 and 45, that is all you need to do. However, if you are adding 23 and 48, the two groups of ones form at least a group of ten. Talk about how that changes the total number of tens you have from 6 to 7. This is called regrouping.
Subtracting
If you are subtracting, start by removing the tens being subtracted from the bigger number and then attempt to remove the appropriate number of ones. For example, if you are subtracting 23 from 45, then there are enough ones and you are done. If there are not enough ones, such as if you are subtracting 28 from 45, then discuss how one of the groups of tens needs to be broken up and included with the ones. The original grouping of 45 as 4 tens and 5 ones becomes a grouping of 3 tens and 15 ones. This is also called regrouping.
Use expanded form
Use objects for double-digit adding and subtracting until your child thoroughly understands the process and why regrouping makes sense when it is needed. At this point, move to representing the adding and subtracting with numbers written in expanded form. When working with numbers in expanded form, the process and the steps are exactly the same as they were when you were working with groups of tens and ones – and that is the point.
Making it automatic
Over time and with lots of practice, your child will stop needing to use groups of tens and ones or expanded form. However, as with so many other things, there is no hurry getting to that point – it will come with practice.