# Number Sense: Deconstructing Numbers

There are many things involved in developing number sense such as learning about place value, number word, and comparing numbers.  Another aspect of number sense is deconstructing numbers. Deconstructing numbers means being able to see a number in terms of other numbers that can be put together to form that number.  There are several ways to practice this concept.

## Base 10 Frames

A base 10 frame is a simple set of boxes with five spaces on the top and five on the bottom. (Mathwire.com has a blank frame for you to print out and use.)  Give a child several small toys in two colors. You could also use food items in two colors.  Have them use the two colors in different combinations to form the same number. (For example 8 could be 1 and 7, 2 and 6, 3 and 5, or 4 and 4.)  This not only allows children to see addition facts in a less abstract way, but it also teaches them that numbers are made up of other numbers.

## Deconstructing Numbers Without Manipulatives

Once a child becomes skilled at using the 10 frame to deconstruct numbers, they should start practicing without the frame.  Write a number at the top of a piece of paper.  Underneath the number have your child write the different combinations that can form that number.  The answers would be the same as when a ten frame was used, but they would be written out instead of shown with manipulatives.

## Deconstructing Larger Numbers

When working with a larger number, you don’t want to make your child list all the numbers that can be added together to form that number. The list would be really long! Instead focus on taking ten away from the tens place number and adding it to the ones place number to form new combinations. For example 37 can be formed as 30 + 7, 20 + 17, and 10 + 27.  Start by showing this to your child and talking about how you are taking ten away from one place and adding it to the other.  You may then want to have a number with just blanks in some of the combination for your child to fill in.  If you feel like they understand, have them list all of the combinations for the number you give them.

Deconstructing numbers sets a foundation for working with numbers in basic operations later on.  It also gives children a better understanding of how the concepts of borrowing and renaming work in addition and subtraction.  Building your child’s number sense in these ways will help them in every math area.