The Commutative Property

Jennifer Dalke
Subject - Math, Art
Grade Level - 3-5
Standards:
3.2.2.1-Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences.
Lesson 3: The Commutative Property, Using Arrays
Days Three and Four

5.2.2.1-Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.

Performance Objectives
B, D, E

Materials
-- Cans
-- Flashcards
-- Blank bulletin board
-- Small bags of buttons
-- Grid paper
-- Construction paper
-- Crayons
-- Small stickers

Anticipatory Set
I will begin with an array of cans (4 x 6) stacked on the table at the front of the room. I will ask the students if they have ever seen something similar to this. Where? I will explain that this is called an 'array': an arrangement of items in a number of equal-sized rows. I will ask the students where else they have seen arrays of items. I will challenge the students to identify arrays that are in the classroom (I will make sure that there are a number of possibilities before beginning the lesson). Finally, I will point out a blank bulletin board and tell the students that they will be making their own bulletin board with the work they do today.

Guided Practice
1. I will call the students' attention to the array of cans at the front of the room, again. I will ask them how many rows across there are of the cans. How many cans in each row? I will write "4 rows of 6 cans" on the board. How many cans in all? I will write " = 24" next to the existing sentence. Is there another way that I can write this? I will write "4 x 6 = 24."
2. I will have the students get into pairs and I will pass out bags of small buttons to each group. I will tell the class that we are going to practice making arrays with the buttons.
3. I will use a set of flashcards (making sure that the "0" facts are taken out) to pick multiplication problems at random. I will write the problem in large print on the board, and I will ask the students how I could make an array to show this problem. I will use buttons on an overhead to show the students.
4. I will continue to pick cards at random, having the pairs of students make arrays with their buttons. I will call on volunteers to demonstrate what they have done at their desks, using the buttons on the overhead.
5. I will ask if any pair of students has done the problems in a different way. In a perfect situation, the students will have discovered the Commutative Property on their own. If not, I will turn the page on the overhead so that it is sideways. I will ask if this is the same problem. Why or why not? We will discuss how this problem is written and why it is the same.
6. We will repeat this activity, but each group needs to show the two arrays that yield the same answer. Again, students will come up to the overhead to show their work.
7. When I feel that the students have a handle on the subject, I will collect the buttons and separate the pairs of students.
8. Next, I will use an overhead to show how arrays can be drawn on a grid. We will practice doing this together, and I will be sure to point out the fact that a 2 x 3 array yields covers the same space as a 3 x 2 array. I will also be sure to label each array appropriately.

Individual Practice
1. I will pass out grid paper to each student. I will mix up the flashcards, hold them facedown, and have each child pick one. I will give each student the corresponding card as well (i.e. if a student picks 8 x 4, then I will give him/her 4 x 8).
2. I will tell the children that they are to outline and color each array on the grid paper. Then they should cut out each array.
3. While the students are working on this, I will pass out one piece of construction paper to each student. When they are finished, they will need to glue each array onto the construction paper. I will show the students an example that I have already made.
4. As I walk around I will check to see if any students have labeled their arrays, and I will point this out to the other students. If no one has done so, then I will explain to the students why it is important that we do this.
5. Last, I will hand out small stickers that the students can place in each small box of their arrays.

Closure
When all of the students have finished making and labeling their arrays, I will point to the bulletin board and explain that this is where we will be hanging up our arrays. I will put up the title, "Array for Multiplication!" (Kind of like 'hooray!'). Then, I will have the students come up one by one. Each student should show his/her array to the class, tell us what multiplication sentences that each one illustrates, and then I will hang it up on the board.

Assessment
-- I will observe the students to see that they are actively participating in the guided instruction.
-- I will check to see that they have completed the array projects with 100% accuracy. If I see that a child is not doing his/hers correctly, I will have him/her work with an early finisher, who can help the student to understand the concept.

Questions

What introductory information is necessary for children to have prior to starting this activity? Students will need to know their basic multiplication facts prior to this activity. Students will also need to understand how to associate the commutative property and how it relates towards multiplication. I may ask students basic questions during prior knowledge to set them up for the following activity, such as if 3x4=12, how else could this be said and still have the same answer? (4x3=12). I would also make note that this works with addition as well. But if we were to reverse our order for subtraction would we still get the same answer? ect...

What grade level/s is appropriate for this activity? I believe they have mentioned grades 3rd-5th for this activity. I think this is an ideal setting for these age groups. I do not feel you could use this in a younger grade level, as 2nd grade gives a small introductory to multiplication, at least in our district. I always like to include the special education classroom as well. In this case, a special education teacher possibly might be able to use this activity with older students who are having a hard time understanding the commutative property and/or multiplication. I know memorizing multiplication facts for many students is a hardship. So giving them the opportunity to understand that 7x8=56 and 8x7=56 are exactly the same equation is critical towards their understanding.

How will you engage students with different learning styles? I believe while working together in class students will be involved and the teacher is able to guide how fast or slow the process will take. If I see that certain students are struggling I may ask others around him/her to help them out or if I am available I may attend to their needs. And most classrooms have a paraprofessional in the room during math. I will also be sure to call on all students of various abilities to show examples during the process. At the end every student will have the opportunity to explain their array and what they have come up with. I believe this lesson plan is important to helping all students feel successful.

How does this activity connect to the real world for students? In the above mentioned anticipatory set, the teacher is asking for examples of arrays. I believe relating an array to certain real life items gives children a chance to recognize different ways multiplication can be displayed. We may not see it just by looking at it, but when really looking into it you see there are many ways arrays are used in the world. I think this is very crucial to relating this concept to other subject areas. The commutative property can be shown in many different ways. In English you can use it in a sentence form subject+predicate=sentence or predicate+subject=sentence. It doesn't matter what form you have it in, it still creates a sentence.

Why is this activity with its concepts important for student learning? This activity is important because of all of the above stated comments. It is critical towards various learning abilities. It has recollection to real life items. I think the lesson also gives an interactive way towards student understanding. Students are involved and consistently using their hands. The activity also gives the teacher a great idea for a bulletin board! :)

What are your comments on this activity? Would you use it in your classroom? I think any lesson plan picked for these MAR activities is worth trying at some point. I find a lot of various activities that get me excited to teach. I hope to try this one out some day and see what works and what doesn't. The only way to finding out if it is good or not is to test it out. The commutative formula axb=bxa is an important equation for all children to understand. Although, I think I may be tricked by finding different array's around a classroom. If I were using this activity word for word I would definitely need to be creative in finding different items that represent an array. Overall, the activity sounds fun and a great way to display math in your classroom!