Multiplication

The big idea

If this is the class's first introduction to multiplication arrays, start with a simple definition. Tell students that one number in a multiplication fact is the amount on the side of the array, and the other number is the amount on the top. A 5 by 4 array, for instance, has five on one side and four on the other.

More advanced classes should begin to see how arrays are linked to the idea of multiplication as repeated addition. A 2 by 6 array is six groups of two, which is 2 + 2 + 2 + 2 + 2 + 2.

Learning objectives

By the end of the lesson, students will be able to:

• Build an array for a given multiplication fact.
• Read the two factors from the side and top of any array.
• Explain multiplication as repeated addition.
• Count the squares in an array without double-counting the corner.

Common Core alignment

• CCSS.MATH.CONTENT.2.OA.C.4

  Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

  Reading a small rectangular array as a sum of equal addends is the early multiplication idea this standard introduces.

• CCSS.MATH.CONTENT.3.OA.A.1

  Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

  Saying 'a 5 by 4 array is 5 groups of 4' before earning the glue stick is the product interpretation this standard names.

Materials

• Grid paper, page 103 (2 or more sheets per student)
• Scissors (1 per student)
• Crayons or markers (2 colors per student)
• 12" × 18" construction paper (1 sheet per student)
• Glue sticks (1 per student)
• The completed project, prepared by the teacher before the lesson

The project

Students cut out multiplication arrays with dimensions of their choosing, then glue the arrays into an artistic arrangement. Before gluing, though, each student has to state the multiplication fact each array represents to the teacher or an assisting adult. This makes it impossible for students to create their designs without demonstrating that they can read multiplication arrays. A student gets a glue stick only once the teacher decides they understand the concept. Until then, the teacher and any assistants should be the only people in the room holding glue sticks.

Another way to run the lesson is to give students target products. For instance, tell students they need to find three multiplication facts that each equal 12, 16, 24, 30, 36, and 40. This version is ideal for older students who already understand arrays but need practice memorizing their basic facts.

Common student mistakes

• Counting the corner twice. The single most common error. Prevent it by teaching students to write the numbers along the grid paper before cutting each array.
• Gluing before they can read the fact. Holding back the glue sticks is the whole mechanism. Do not relax it.