Multiplying with Base Ten
Blocks
Ex. # 1
24 × 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.
Ex. # 1
Repeated Addition Model (cont.)
3 × 24
3 × 24 means 3
24’s.
24 is 2 longs and 4
units.
Ex. # 1
Repeated Addition Model (cont.)
3 × 24
Join together.
I now have 6 longs
and 12 units.
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.
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.
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
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.
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 100 +
50 + 6 or 156.
13 × 12 = 156
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.
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 200 +
80 + 6 or 286.
13 × 22 = 286