Making a Class Array (Meanings of Multiplication)

"What does it mean to multiply?"  I give the students a few minutes to discuss this with their elbow partner (the student to their right or left.)  I call on a few students to share their ideas with the class.  "Today, we will understand the meaning of multiplication.  Will an array help you find the product to a multiplication problem?"  Let's explore to find out."

I begin my lesson by sharing the vocabulary outlined for the lesson.  The vocabulary words for this lesson are array, product, and factor.  Factors are the numbers that you multiply.  A product is the answer to a multiplication problem.   Objects arranged in equal rows form an array. I go over the vocabulary first, because it is very important that the students receive relevant information to help them understand the skill.

To give the students a visual of an array, I use the students as the array.  When students have a visual representation, it gives them more of a conceptual understanding.

 By the end of this activity, the students should have a clear understanding that multiplication is repeated addition, as well as the importance of using arrays to check their multiplication.

Preparation before class for the teacher is to make sure that there are several items in various locations in the classroom that are in multiples.  I placed groups of books, pencils, dry erase markers, scissors, boxes of Kleenex, and rulers around my classroom.  After the whole class lesson, put the students into groups of 3.  Tell the students that they will go on a scavenger hunt.  They must look for things in the classroom that are in multiples.  The students must write the name of the item, make an array (MP4), then write the multiplication and repeated addition sentences for the items(MP1) (MP6).  This will allow the students to interact with others and hear their thinking.  All students should actively participate in the discussion.  The teacher should monitor the groups and ask the students questions to ensure that they reach the goal outlined for the lesson.  Some questions that could lead to the "big idea" are outlined below:

Assessing Questions:

1.  When you multiply, are you putting things together or separating them?

2.  When you add, are you putting things together or separating them?

3.  What does an array show you?

4.  How does counting help you find your answer?

5.  Can you write a multiplication sentence and addition sentence for the same array? Explain why?

6.  Is the "total" the same for the multiplication and addition sentences for the array? Explain.

After the students complete their group assignment, bring the class back together as a whole.  Refer back to the question you asked the students earlier.  "Will an array help me find the product to a multiplication problem?"  Make sure that all students understand that multiplication is repeated addition (MP8), and the array gives a visual of the multiplication problem.  From their array, they can count to find the product.  From the teacher's observation, students can be identified as needing remediation.  Those students will work with me in a small group at the beginning of the next class period on this skill.

 Early finishers can practice on the skill at the following site while the other groups are completing their assignment. 

To assess the students' understanding of the lesson, give the students the handout for the independent activity and collect them when they are completed.  Based upon the results, implement an intervention plan for the students that need it. 

I like to give independent activities after the group activities because I want to get a clear vision of what all of my students know about the skill.  I love group activities, but independent activities are vital.  In groups the students can help each other.  In independent activities, the students must stand on their own.  Both components are instrumental in forming great students.

In this particular lesson, the students used what the learned with their partners to solve the problems.  The students knew that this lesson was on multiplication, so even with giving them word problems, they were able to apply the skill that they learned by decontextualizing the numbers (MP2) and solving the problem.