The structure of the place value system, and the ways in which numbers can be partitioned, assist students to develop flexibility.

For example, to solve 9 + 7 one can think of building to 10 by splitting the 7 into 6 and 1, and treating it as 9 + 1 + 6.

This is helpful as 10 + 6 is easier to solve than 9 + 7.

To solve 28 + 36 mentally, one easy way is to add 20 and 30, then 8 and 6, knowing that 8 and 6 add to 14.

Use of an empty number line can make students' thinking visible and represent different strategies used.

You can view and download the *Empty Number Line* slide presentation.

Understanding the place value system is necessary when:

- multiplying by powers of 10
- multiplying multi-digit numbers by a single digit using the distributive property.

For example, to multiply 36 by 5, we can split 36 into 30 and 6 and multiply each by 5. Add the partial products together: (30 \(\times\) 5) + (6 \(\times\) 5) so 150 + 30 = 180.