Four Models of Multiplication

Learning the four models of multiplication enables children to fully understand multiplication used in problem solving, various operations, and in everyday life.

Sets: within each of some sets, an equal number of objects

Array: an equal number of columns and rows.

Cross Product: every item in one set of objects combining with each item in another set.

Measuring: on a number line of objects, skipping an equal number of times across the line.

After explaining the four models, examples should be presented. It takes a while for children to realize that the numerical answer is not the answer – you want to hear which model it is. The following are some examples, first for a mother with a child or two and then for a teacher with a class:

Mother, for sets: there are 3 bags of candy. There are 6 pieces of candy in each bag. How many pieces of candy are there?

Mother, for array: on our cookie tray, we put cookies in 3 rows and 4 columns. How many cookies are we baking?

Mother, for cross product: if 4 butterflies landed on each of 3 flowers, how many landings were there?

Mother, for measuring: Mary took a walk. On every 3 blocks, she took a drink of water. She drank water 4 times. How far does she walk?

Teacher, for sets: we will listen to 5 children read 2 stories each. How many stories will we hear?

Teacher, for array: we need 3 rows of chairs with 4 chairs in each row. How many chairs do we need?

Teacher, for cross product: Jane has 4 skirts that can go with 3 different blouses. How many outfits does she have?

Teacher, for measuring: on a number line, Susan put a marker on every 3rd number, 4 times. What number did she end with?

Again, it takes practice for children to answer which model it is. But when children are easily able to give the correct model, they will fully understand the use and purpose for multiplication.

Read more about teaching Math in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success.  Included is a web site where programs and activities can be downloaded for use in a classroom. Also, see 7 reviews on

   Teaching Young Children © Peggy Broadbent 2011 - All Rights Reserved