Math 130
Handout #5
Understanding multiplication of whole numbers
Dr. Bergner
Do you work on a separate sheet of paper. Make sure to include diagrams that are to
scale!
The meaning of multiplication
Multiplication of whole numbers is repeated addition or skip counting. When working with
whole numbers, the product a x b literally means adding b to itself a times--- b+b+b+b+…+b.
So 3 x 2 means 2+2+2.
In its broader sense, multiplication is “a groups of b things each”. Hence, 3 x2 means 3
groups of 2 things each.
1. Beginnings: Representing multiplication with chips, Cuisenaire rods,
and skip counting.
Do each of the following products in all 3 ways.
2x8
3x 7
3 x 4
2. Intermediate: Representing multiplication of whole numbers with multibase pieces and using chip model. Works well when a is less than 6.
a. Carry out the following products with base 10 pieces using the
“chip model”.
2 x 134
3 x 56
5 x 24
b. HBB, p 163 #1,2, 3
3. Advanced: Representing multiplication of whole numbers with multibase pieces and using rectangular arrays.
Use base 10 paper and color for these
a. Random regrouping
Spiral activity 3.3 , # 1, 2, 3, 4
b. Regrouping by partial products
Spiral activity 3.3, # 5,6
Products: 132 x 45, 456 x 10, 39 x 47
4. Advanced: Abstract representations
a. Connecting the multi-base pieces to our algorithms
Carry out the partial products algorithm on the following
problems without base 10 pieces:
142 x 35, 345 x 10, 29 x 63
b. Number line model
HBB, p. 180, # 7,8