Teachers use base-10 blocks to represent large numbers in addition, subtraction, multiplication and division problems. Students count and move the blocks around to figure out the answers.
Introduce the base-10 blocks by explaining that single cubes represent the number one, the long bars represent 10 and the large squares represent 100. Students experiment with creating numbers using the blocks, such as using a 100 square, three bars and five single cubes to show 135. Practice exchanging smaller blocks for larger ones. Ten long bars turn into a 100 square, and 13 individual cubes turn into a 10 bar and three singles.
To learn addition, students represent two different numbers with the blocks and push them together. They exchange smaller blocks for larger blocks as needed. Students count the total to find the sum of the original numbers.
The opposite works for teaching subtraction. Students represent the large number with blocks and take away the smaller number. They may need to exchange blocks to do the math, such as by trading in a 100 square for 10 long bars.
For multiplication, students build groups of blocks and find the total. For 10 times three, they create either 10 groups of three or three groups of 10 to determine that the answer is 30.
In a division lesson, students start with the large number and determine how may even groups they can make based on the divisor. For 87 divided by nine, they make groups of nine to see how many are left.