Commutative Property

1
Commutative Property

• Aimee Barse
• EDM 453
• Grade 3

2
Rational

• I will be going over the commutative property.
  This is very important according to the NYS
  standards. Using arrays will help the students
  learn this property much better. I will also
  explain to the students that arrays are used in
  their daily lives, they will realize this when
  they go home and do their homework.

3
Lesson Objective

• Given buttons the learner will make different
  sized arrays according to the multiplication
  equation on a flash card to learn the commutative
  property with 100 accuracy.

4
NYS Standards

• 3.PS.6 Translate from a picture/diagram to
  numeric expression.
• 3.PS.7 Represent problem situations on oral,
  written, concrete, pictorial, and graphical
  forms.
• 3.PS.12 Use physical objects to model problems.
• 3.RP.12 Justify general claims or conjectures,
  using manipulatives, models, and expressions.

5
NYS Standards Cont

• 3.CM.4 Organize and accurately label work.
• 3.CM.5 Share organized mathematical ideas through
  the manipulation of objects, drawings, pictures,
  charts, graphs, tables, diagrams, models,
  symbols, and expressions in written and verbal
  form.
• 3.CN.6 Recognize the presence of mathematics in
  their daily lives.

6
NYS Standards Cont

• 3.R.1 Use verbal and written language, physical
  models, drawing charts, graphs, tables, symbols,
  and equations as representations.
• 3.N.6 Use and explain the commutative property of
  addition and multiplication.
• 3.N.20 Use a variety of strategies to solve
  multiplication problems with factors up to 12 x
  12.

7
NYS Standards Cont

• 3.N.21 Use the area model, tables, patterns,
  arrays, and doubling to provide meaning for
  multiplication.

8
Teacher Materials

• cans
• blank bulletin board
• overhead projector
• buttons
• multiplication flash cards
• clear overhead papers

• grid paper
• dry erase marker
• pen or pencil
• black board
• chalk

9
Student Materials

• buttons
• grid paper
• construction paper
• colored pencils or crayons
• scissors
• glue or tape

10
Anticipatory Set

• I will set an array of cans on a table in the
  front of the room. The array will be a 3 x 5
  array. I will then begin by asking the students
  if they have ever seen anything like this before?
  If so, where? I will then explain to them what
  an array is and that my display is an example of
  an array. I will then ask the students where
  else have they seen an array of items before.

11
Anticipatory Set cont

• I will then have them point out arrays in the
  classroom (I will make sure there are plenty of
  examples around the classroom). Then I will show
  the blank bulletin board to the students and
  explain to them that they will be covering it
  with their work they do today.

12
Providing Information

• 1.) I will again bring the students attention to
  the array of cans in the front of the room. I
  will ask them how many rows across are there of
  cans, then how many cans in each row? I will
  write on the board 3 rows of 5 cans. Then I
  will ask them how many cans total. Then I will
  write 15 next to the sentence. Then I will
  ask if there is another way that I can write the
  sentence? I will then write on the board 3 x 5
  15.

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Providing Information Cont

• 2.) I will then break the students up into pairs
  and pass out a bag of buttons to each group. I
  will tell the class we are going to practice
  making arrays using the buttons.
• 3.) I will use flashcards, that I made, but not
  using any 0 facts, to pick multiplication
  problems. I will use buttons on the overhead to
  show the students.

14
Providing Information Cont

• 4.) I will continue to pick cards from the pile
  of flashcards, while the students continue to
  make arrays using the buttons. I will call on
  volunteers to demonstrate what they have done at
  their desks using the buttons on the overhead. I
  will then ask if any other group did it another
  way. At that point the students would have
  learned the commutative property. If no other
  group did it different then I would turn the
  paper on the overhead so it is sideways and this
  will show the students the other way of doing the
  problem. Then I will ask if this is the same
  problem, why or why not? We will then discuss
  how this problem is written and why it is the
  same.

15
Providing Information Cont

• 5.) We will repeat this activity, but this time I
  will have the groups make the arrays in the two
  different ways that will get them the same
  answer. I will then have volunteers come up and
  demonstrate on the overhead. We will then have a
  short discussion about the commutative property
  so the students know what they just learned.

16
Providing Information Cont

• 6.) After the students have a good handle on the
  subject I will collect the buttons and separate
  the groups.
• 7.) Next, I will use the overhead to show how the
  arrays can be made on a grid. We will practice
  this together. I will make sure to point out
  that a 3 x 5 array takes up the same amount of
  space as a 5 x 3 array, if the students do not
  realize this on their own, I will also be sure to
  label each array appropriately.

17
Guided Practice

• 1.) I will pass out the grid paper to each
  student. I will mix up the flash cards, hold
  them face down, and have each child pick one. I
  will give each student the corresponding card as
  well (if a student picks the card that says 4 x 6
  then I will give them the card that says 6 x 4).

18
Guided Practice Cont

• 2.) I will then tell the students to make the
  arrays on the grid paper, color them in and then
  cut them out.
• 3.) While the students are working on this I will
  pass out construction paper to each student.
  When they are done they will put each array on
  the construction paper. I will show them the
  example I have already made.

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Guided Practice Cont

• 4.) Also while the students are working I will
  walk around to make sure that the students are
  labeling their arrays correctly. If no one has
  done this then I will point out why it is
  important to label the arrays.

20
Closure

• After all of the students have finished making
  and labeling their arrays, I will bring their
  attention to the bulletin board again. I will
  then explain to the them that we are going to
  hang our arrays on there. I will put up the
  title Array For Mathematics! Then I will have
  the students come up one by one to show their
  array to the class, tell us what multiplication
  sentence that each one shows and then I will hang
  them up on the bulletin board.

21
Independent Practice

• I will have the students try to find arrays of
  items in their own home. Then they will have to
  write the multiplication sentence associated with
  the size of the array as well as the answer.
  They will write the multiplication sentence in
  both ways (ex. 3 x 5 15 and 5 x 3 15) for all
  the arrays they find.

22
Extension

• I will try to incorporate the use of arrays
  during another subject, like gym. I would have
  the students get into teams and make 2 teams of
  10 students or 4 teams with 5 students to play a
  game in gym. This would be a way to practice
  making arrays.

23
Student Evaluation

• I will observe the students to make sure they are
  participating in the activity. Also I will make
  sure that they have completed their array
  projects with 100 accuracy.

24
Teacher Evaluation

• 1.) What could I have done to make this lesson
  better?
• 2.) What are some of the things I would change?
• 3.) Did the lesson go as well as I hoped?
• 4.) Did the students really understand the
  commutative property through this lesson?
• 5.) Did the students like the lesson?