# Regrouping Whole Numbers Using Base 10 Blocks

Welcome to two examples on regrouping numbers

using base 10 blocks. We are asked to represent the following quantities

using the least amount of base 10 blocks. Write the corresponding number of ones, tens,

and hundreds used. To answer these questions, we will be using

the online base 10 blocks from the National Library of Virtual Manipulatives. For a quick review of the base 10 blocks,

beginning on the right, we have a unit, which equals 1. 10 units equal 1 rod. 1 rod equals 10. 10 rods equal 1 flat. 1 flat equal 100. We can see 1 flat equal 100 units. For the first example, we’re given 8 rods

plus 13 units. Our goal is to represent this quantity using

the least number of base 10 blocks. And because 10 units equals 1 rod, we can

perform an exchange. We can exchange these 10 units for 1 rod and

move the rod to the next column, which shows 8 rods plus 13 units equals 9 rods plus 3

units, giving us the number 93. So going back to our work, to picture the

regrouping we’ll use the notation shown below where a small x equals 1 unit, a small segment

represents 1 rod and a small square represents 1 flat. Because we now know that 8 rods plus 13 units

equals 9 rods plus 3 units, we’ll picture 9 rods and 3 units. For the next column, have 0 flats plus 9 rods

plus 3 units, which is equivalent to 0 100’s plus 9 10’s plus 3 1’s giving us the number

93. Next we have 3 flats plus 9 rods plus 12 units. Again the goal is to represent this quantity

using the least number of base 10 blocks. So looking at the units, we can perform an

exchange. We can exchange these 10 units for 1 rod. Move the rod to the next column. But notice how now we have a total of 1, 2,

3, 4, 5, 6, 7, 8, 9, 10 rods. 10 rods equals 1 flat. So we’ll perform another exchange. We’ll exchange these 10 rods for 1 flat and

move the flat to the next column. We’ve now shown that 3 flats plus 9 rods plus

12 units equals 4 flats plus 2 units, which equals 402. So for the picture, we’ll sketch for flats

and 2 units. So on the right we have 4 flats plus 0 rods

plus 2 units, which is equivalent to 4 100’s plus 0 10’s plus 2 1’s, which equals 402. I hope you found this helpful.