Adding with Base 10 and Expanded Notation

In the past few weeks students have been working hard to apply several addition strategies when adding two digit numbers. The first strategy involves using base 10 manipulatives (rods and units) to represent the 10's and the 1's. Once students have either built the numbers with blocks or drawn the pictures of them they combine the blocks together. They can start with the ones (units) and then combine the tens (rods). The part that is most confusing for students is knowing when to regroup their blocks. Students are learning that the highest digit that you can have in any place value is 9- if they have 10 or more then they need to regroup them and move them to the next column (10 units should become a rod).

Here is another picture that represents the process that we have been practicing- it also shows our other strategy which is using expanded notation to break the numbers apart in a very similar way to base 10. When we pull a number apart or break it apart we call it expanded notation. This way requires students to have a more abstract knowledge of numbers and can lead students towards using mental math to solve equations.

This example starts by adding the 10's first but I have been encouraging the students to start with the ones because if there is more than 10 ones they will have to regroup before adding the tens. You can have your child practice adding 2 digit numbers using these strategies at home. Some students require the physical blocks of tens and ones to work with so you could use a variety of creative counter tools that would represent the numbers like legos, beans, really anything that can be separated into piles of 10 and left over ones. Many students are able to draw the pictures of the rods and units and can record the problems symbolically. It is important that students are able to document and explain their thinking so that they can identify if they have made any mistakes and can also prove/back up their answer.