Maria Guzman
September 22, 2010
Grade Level: Third Grade
Topic: Number Properties: Identity property, zero property, and
commutative property
MA.3.A.1.2 - Solve multiplication and division fact problems by using strategies
that result from applying number properties.
Resources: Go Math Textbook: Chapter 3, Lessons 7 and 8, Chapter 4,
Lessons 3, 5, 6, 9, 11, Chapter 6, lesson 3.
http://www.ixl.com/math/practice/grade-4-properties-of-multiplication
http://www.marion.k12.fl.us/dept/cur/cim/index.cfm#calendars
http://fcat.fldoe.org/fcatis01.asp#specs
Description – Students will work in groups and solve multiplication and division
problems (with Hershey’s candy bars or M&M’s) by applying number
properties.
Objective(s) – Students will be able to differentiate between each number
property. Students will use number properties to solve multiplication and division
problems.
Materials:
Smart Board – The teacher will write problems on the smart board
Hershey’s Milk Chocolate Multiplication Book by J. Pallotta
Hershey’s Milk Chocolate Bars or M&M’s (3 packages of 6 bars or 2 big bags
of M&M’s). Teacher will distribute chocolate bars to students.
Pencils and Paper – Students will already have these materials at their desk.
Graph paper inside of sheet protector – (graphic organizer) pass out to each
group.
Expo markers – pass out to each group.
Erasers/socks – pass out to each group.
Prerequisite knowledge:
MA.1.A.1.3 – Create and use increasingly sophisticated strategies, and use
properties such as Commutative, Associative, and Additive Identity, to add whole
numbers.
Motivational activity: Tell students that they will be able to eat the chocolate
bars/M&M’s when they are done with the activity. If they eat pieces of chocolate
during the activity the candy bar/M&M’s will be taken away. Students will want to
follow directions so they can have the whole candy bar/M&M’s. Students will
also get to use graphic organizers and expo markers to make arrays.
Procedures:
Review – Go to board and ask the following: What is zero times any number
(write 0 × ?). Zero times any number is zero. Have the students say a couple of
zero multiplication problems. Write them on the board. Ok, can any one tell
me what happens when I multiply any number by one (write 1× ?)? The number
stays the same. Have the students say a couple of one times multiplication
problems. Write the on the board. Did you know that you already know the
zero property and identity property? Zero times any number is zero (repetition)
and one times any number is the number. So, what are we going to do when we
see a zero multiplication or division problem? So, what are we going to when we
see a one times multiplication or division problem?
Today I will read The Hershey’s Milk Chocolate Multiplication Book by J. Pallotta.
Read the book to the students. Stop and look for the zero property and identity
property. Start making connections to the book and the properties.
Introduce the commutative property. So we already know about the zero
property and identity property. Now we are going to learn about the commutative
property. I think you already know about the commutative property. Ask
students, “Is 6 × 5 the same as 5 × 6.” Well according to the commutative
property you can flip both numbers and get the same answer. So, 2 × 3 is the
same as 3 × 2 (write problems on the board). Can someone give me another
example? What is another way to say 4 × 5? I can change the order of the
numbers and get the same answer. Add division problems during the lesson (25
÷ 5, 10 ÷ 2). Go over some sample problems.
Sample Problems
We will only cover Identity Property, Zero property, and Commutative Property
today. If the students are able to comprehend the previous properties then the
distributive property and associative property can be added.
• Solve and apply the Identity Property
(any number multiplied by 1 equals the same number)
• Solve and apply the Zero Property
• Solve and apply multiplication and division strategies to real world
problems in mathematical contexts and justify solutions
• Solve and apply the Commutative Property
(3 x 4 is the same as 4 x 3)
If time permits add the distributive property and associative property
• Solve and apply the Distributive Property
(5 x 8 is the same as 5 x 4 + 5 x 4)
• Solve and apply the Associative Property
([3 x 2] x 4 is the same as 2 x [3 x 4])
An array is an arrangement of shapes into rows and columns. Students can also
group shapes together to make arrays (circles and sticks).
1. Raymond has 5 pictures of each of 3 types of ocean dolphins. He
also has 4 pictures of river dolphins. The expression below represents
the total number of dolphin pictures Raymond has.
(3 × 5) + 4
Which expression below also represents the total number of dolphin pictures
Raymond has?
 A. 4 + (5 × 3)
B. 3 × (5 × 4)
C. (3 + 4) × (5 + 4)
D. (3 × 5) + (3 × 4)
2. Four children are playing tennis together. They all brought six balls. How
many balls do they have total? Using the commutative property show your
answers.
4 × 6 or 6 × 4
3. The Jones family orders two pizzas to eat. Each pizza is sliced into four
parts. How many pizza slices do they get? Solve and draw an array.
2 × 4 or 4 × 2
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or
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Pass out materials
or have students help pass out materials. Show
students how to make arrays on their graph paper representing the
problems you have discussed. Students can also use their candy as a
manipulative. Have the students work in groups to make problems with the
properties. The students can use the Candy bars/M&M as a manipulative. They
should also show another way to represent the problem on their graphic
organizer. Students should make arrays on the graphic organizer. Students
should transfer their answers to paper when done.
Closure: Can anyone tell me a zero property problem? How about an identity
property problem? Now, can someone tell me a commutative property problem?
Have the students explain the properties. When you go home you will make up
your own multiplication problems using arrays. Later in the week I will be giving
you a quiz with some of your own problems on the quiz. Make sure your
problems are correct and neat.
The students love to use expo markers. If the students are able to use the
graphic organizer (graph paper) correctly they can continue to use it throughout
the year. The students will have created their own math problems using the
properties discussed. The teacher would have seen what students need help
and what students are excelling. The students that need an intervention will
get it in small group time.
The teacher will assess the students by walking around and taking anecdotal
notes. The students will also write their problems down on paper. The students
should have two different ways of writing multiplication problems as well as an
array.