1. Multiplying with Base Ten Blocks

2. Ex. # × 3
Instead of modeling 24 × 3, let’s model 3 x 24.
You may use the commutative property of multiplication when modeling multiplication with base ten blocks.

3. Ex. # 1 Repeated Addition Model (cont.) 3 × 24
3 × 24 means 3 24’s.
24 is 2 longs and 4 units.

4. Ex. # 1 Repeated Addition Model (cont.) 3 × 24
Join together.
I now have 6 longs and 12 units.

5. Ex. # 1 Repeated Addition Model (cont.) 3 × 24
Exchange 10 units for 1 long.
I now have 7 longs and 2 units.
3 × 24 = 72, so
24 × 3 = 72.

6. Ex. # 2 Rectangular Array Model 3 × 24
3 × 24 means 3 24’s.
24 is 2 longs and 4 units.
Place 2 longs and 4 units in a rectangular array 3 times.

7. Ex. # 2 Rectangular Array Model (cont.) 3 × 24
Count the number of blocks used.
There are 6 longs and 12 units. Exchange 10 units for 1 long. There are 7 longs and 2 units.
3 × 24 = 72

8. Ex. # 3 Rectangular Array Model 13 × 12
Use 1 long and 3 units to outline a rectangle whose width is 13.
Use 1 long and 2 units to complete the outline of a rectangle whose length is 12.
Fill in the rectangle, using as few base ten blocks as possible.

9. Ex. # 3 Rectangular Array Model (cont.) 13 × 12
Count the number of blocks used.
There are 1 flat, 5 longs, and 6 units, so the product is or 156.
13 × 12 = 156

10. Ex. # 4 Rectangular Array Model 13 × 22
Use 1 long and 3 units to outline a rectangle whose width is 13.
Use 2 longs and 2 units to complete the outline of a rectangle whose length is 22.
Fill in the rectangle, using as few base ten blocks as possible.

11. Ex. # 4 Rectangular Array Model (cont.) 13 × 22
Count the number of blocks used.
There are 2 flats, 8 longs, and 6 units, so the product is or 286.
13 × 22 = 286