Ms. Hyman’s Math Newsletter
Students of 3-320 and 3-344
Contexts For Learning Mathematics Curriculum
MUFFLES’ TRUFFLES
​
: MULTIPLICATION
AND DIVISION UNIT WITH THE ARRAY
The focus of this math unit is the development of the open array as a model for
multiplication and division. This unit uses a series of investigations based on the context
of Muffles’ Truffles shop. The questions posed in the first investigation gives students an
opportunity to explore place value, the multiplicative structure of our base-ten system
and quotative division. In the second and third investigations, students build
two-dimensional blueprints and use these arrays to explore some big ideas in
multiplication, including the distributive, associative and commutative properties. In the
fourth and final investigation, students apply their knowledge with open arrays in the
context of labeling and pricing wrapped boxes of truffles. To figure out the dimensions of
the wrapped boxes (open arrays) and the cost, students need to apply a number of big
ideas previously developed in this unit.
STRATEGIES FOR MULTIPLICATION AND DIVISION
This progression shows the most efficient strategies for multiplication and the many entry
points for division.
1. Partial Products
Use a fact you know to make another.
For example, 5 packages of paper towels
(4 rolls in each package) contains 20
rolls, and 3 packages contain 12, then 8
packages contain 32.
8 x 4= ___
/\
5 3
2. Five-times and Ten-times
Once students begin to make use of partial
products, this strategy becomes helpful. Knowing
the ten times can be helpful for nine times (just
subtract one group from the ten-times). 6 ten-times
is 60, take away one group of 6 is 54 ( 6
nine-times).
The same goes for five-times to help with four-times
and six-times.
5 x 4 = 20
3 x 4 = 12
20 + 12 = ​32
3. Doubling and halving
As student’s multiplicative reasoning
becomes stronger, they develop the
ability to group more efficiently. They
begin to realize that if they double the
number of groups and want the total to be
the same, they need to have halve the
amount in each group.
4x6= 8x3
4. Open Array ​Model
Students will manipulate open arrays in order to
group efficiently. Students will use open array
models to further develop their understanding of the
various strategies as well the properties of
multiplication, such as, the associative,
commutative, and distributive properties.
i.e. Students may apply the distributive property to
help them figure out the dimensions of a larger
open array.
​ 5
5
2
(2 x 5) + (2 x 2) = 2 x 7