Students will illustrate multiplication problems using Unifix cubes.
- The Grapes of Math, by Greg Tang; ISBN 043921033X
- Hershey's Milk Chocolate Multiplication Book, by Jerry Pallotta,
Rob Bolster, illustrator; ISBN 0439254124
http://www.matti.usu.edu (National Library of Virtual Manipulatives)
Background for Teachers
An array is a rectangular arrangement of objects in rows and
columns. Arrays can be used to illustrate multiplication facts. Some
multiplication facts create a square. Their products are called square
numbers. Prime numbers can only be made in a rectangular array with
one row or one column.
Intended Learning Outcomes
3. Reason mathematically.
5. Make mathematical connections.
Invitation to Learn
Show pictures of rows and columns in the real world. Tell the
students that rows and columns combined are called arrays. Ask the
students to look for arrays in the classroom. Where could they find them
at home? How about on the playground?
- Tell the students to imagine they work in a bakery. They have
been asked to bake a dozen cookies. Ask them how many cookies
are in a dozen. Then tell the students the manager of the bakery
wants the cookie dough to be organized on the trays in equal
numbers of rows and columns, or in other words, arrays. How
could the cookie dough be arranged on the cookie sheet? (Find all
- Have the students work in pairs or individually with paper Cookie
Sheet Mats and Unifix cubes (representing cookie
- Ask for the results of their findings to be shared with the class. As
each way is suggested, show the students how to write this as a
multiplication problem. Also, switch the order of the factors. For
example, when three rows of four is suggested (3 x 4) ask the
students if four rows of three (4 x 3) is the same number of
cookies. Rotate the array to show four rows of three. Tell them
that multiplication factors can trade places like this without
changing the total. This is called the commutative property of
- Ask the students, “What if the manager wanted us to bake 16
cookies, what would that look like?”
- For more guided practice as a group or in partners, roll a pair of
dice to give you two factors to work with. Have the students show
the two arrays for those factors on their Cookie Sheets Mats.
Then, have them work individually with the Cookie Sheet
worksheet and dice.
- Have the students write in a learning journal about the
commutative property of multiplication and explain how it works.
- The gradual release structure of this lesson lends itself well to
accommodations for students with special needs. Give more time
for partners to work with the dice and cookie sheet mats when
needed rather than individual practice.
- Have the students look for arrays at home. Draw these and record
the multiplication facts illustrated. Show the corresponding fact
using the commutative property.
- Families can make a batch of cookies at home arranged in arrays.
Or, what else can be cooked in an array? Try something and
report your findings.
Have the students write a paragraph explaining why
multiplication facts can switch the factor’s places and still get the
same answer (commutative property).