Basic Properties of Numbers Poster
Congratulations on your purchase of this
Really Good Stuff® Basic Properties of
Numbers Poster—a terrific reference for
students to use throughout the year as they
explore numbers.
This Really Good Stuff® product includes:
• Basic Properties of Numbers Poster,
laminated
• This Really Good Stuff® Activity Guide
Introducing the Basic Properties of
Numbers Poster
Display the poster in an area visible to all
students. This poster can be used as a
reference throughout the year. Explain to
students that the four properties of numbers
that are identified on the Basic Properties of
Numbers Poster are a basis for much of the
mathematics they’ll be exploring throughout
the school year. Tell students that you’re
going to give them hints to help them
remember the names of each of the
properties.
Commutative Property: Ask students what it
means to commute to work. Students will
likely suggest that it means to go to or to
move to work. Tell students that numbers can
commute, too; they can move within an
addition or multiplication problem without
affecting the answer. List some addition and
multiplication examples of the commutative
property on the chalkboard or whiteboard. Ask
student volunteers to come to the board and
add more examples.
Hint: Addends and factors can commute
(move) and switch order without changing the
sum or product.
Associative Property: Ask students what it
means to associate with someone. Students
will likely suggest that it means to talk to or
Commutative
Associative
Changing the order of addends or factors
does not affect the sum or product.
The order in which numbers are grouped
does not affect the sum or product.
a+b=c
b+a=c
axb=c
bxa=c
(a + b) + c = d
a + (b + c) = d
(a x b) x c = d
a x (b x c) = d
12 + 6 = 18
6 + 12 = 18
5 x 7 = 35
7 x 5 = 35
(3 + 5) + 2 = 10
3 + (5 + 2) = 10
(4 x 7) x 3 = 84
4 x (7 x 3) = 84
Distributive
Adding two or more numbers together, then
multiplying the sum by a factor is equal
to multiplying each number alone by the
factor first, and then adding the products.
a (b + c) = (a x b) + (a x c)
4 (1 + 8) = (4 x 1) + (4 x 8)
Identity
The additive identity
is zero. If you add
zero to an addend, the
sum will equal that
addend.
a+0=a
8+0=8
4 x 9 = 4 + 32
The multiplicative
identity is one. If you
multiply a factor by
one, the product will
equal that factor.
ax1=a
25 x 1 = 25
36 = 36
© 2007 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #155819
“hang out” with people. Tell students that
numbers can associate, or group themselves,
with different numbers in an addition or
multiplication problem. Explain that numbers
are grouped by parentheses, and that
groupings of addends or factors can change
without affecting the sum or product. Write
these examples on the whiteboard or
chalkboard:
(2 + 3) + 4 = 2 + (3 + 4)
5+4=2+7
9=9
(3 x 4) x 5 = 3 x (4 x 5)
12 x 5 = 3 x 20
60 = 60
Point out to students that the addends and
factors remained in the same order in each
example. The only change in each side of the
equation is the grouping, or association,
within the set of numbers. List other examples
of the associative property in addition and
multiplication on the chalkboard or
whiteboard. Then ask student volunteers to
come to the board and add more examples.
Hint: Addends and factors can associate
(group) with different numbers within the
problem without changing the sum or product.
Distributive Property: Ask students what it
means to distribute materials. Students will
All activity guides can be found online:
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© 2007 Really Good Stuff
®
1-800-366-1920 www.reallygoodstuff.com #155819
Basic Properties of Numbers Poster
likely suggest that it means to hand out, such
as distributing papers to students in class.
Explain that the distributive property allows
multiplication to be distributed over addition.
Write this example on the whiteboard or
chalkboard:
a (b + c) = (a x b) + (a x c)
Point out that in this example, b and c share a
on the left side. On the right side, a has been
distributed, or handed out, to b and c.
Tell students that the distributive property
can be used to make some problems easier to
solve. Sometimes it is easier to solve
equations by adding the addends inside the
parentheses first, then multiplying. Write this
example on the whiteboard or chalkboard and
ask students which side of the equation will
be easier to solve:
25 (30 + 70) = (25 x 30) + (25 x 70)
Solve each side of the equation:
25 (30 + 70) = (25 x 30) + (25 x 70)
25 (100)
= 750 + 1,750
2,500
= 2,500
Many students will agree that in this example,
the left side of the equation was easier to
solve, since they could mentally add 30 + 70
and then mentally multiply 25 x 100.
In other examples, students may find it easier
to perform the operations on the right side of
the equation. Write this example on the
whiteboard or chalkboard and ask students
which side of the equation will be easier to solve:
20 (100 + 4) = (20 x 100) + (20 x 4)
Then solve each side of the equation:
20 (100 + 4) = (20 x 100) + (20 x 4)
20 (104)
= 2,000 + 80
2,080
= 2,080
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Many students will agree that in this example,
the right side of the equation was easier to
solve, since they could mentally multiply 20 x 100
and 20 x 4, then mentally add 2,000 + 80.
Hint: A factor that is multiplied by the sum of
two terms can be “distributed” across those
terms. This means that someone can multiply
the factor by those terms separately, then
add the products.
Identity Property: Ask students what identity
means. Students will likely suggest that it is
who you are. Explain that a factor’s identity
does not change when certain things are done
to it, just as students’ identities do not
change when they put on a sweater. Tell the
class that the additive identity, or the
number that can be added to an addend
without changing the addend’s identity, is
zero. Remind students that adding a zero to
an addend will never change that addend. This
is a property they learned long ago when they
learned their addition facts; now they are
learning the name of that property.
Tell the class that the multiplicative identity,
or the number that can be multiplied by a
factor without changing the factor’s identity,
is one. Remind students that multiplying a
number times one will never change that
factor. They learned this property when they
learned their multiplication facts, and now
they are discovering the name of that
property.
Using the Reproducibles
Make copies of the Properties of Numbers
Reproducible and the Using the Properties of
Numbers Reproducible for your students. Pass
them out to reinforce your lesson on the
properties of numbers.
© 2007 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #155819
Basic Properties of Numbers Reproducible
Identify the property (commutative, associative, distributive, identity) for each problem below:
1. a + b = b + a
__________________________________
2. a (b + c) = (a x b) + (a x c) __________________________________
3. a + 0 = a
__________________________________
4. a x (b x c) = (a x b) x c
__________________________________
5. a x 1 = a
________________________________________
Using the property given, complete the following equations:
6. Associative property:
3 x (2 x 5) = (___ x ___) x ___
7.
Commutative property:
7 + 5 = ___ + ___
8.
Identity property:
8 x 1 = ___
9.
Distributive property:
4 (9 + 7) = (___ x ___) + (___ x ___)
10. Identity property:
15 + 0 = ___
11.
8 x 4 = ___ x ___
Commutative property:
12. Associative property:
(6 + 5) + 4 = ___ + (___ + ___)
13. Distributive property:
7 (6 + 9) = (___ x ___) + (___ x ___)
14. Commutative property:
85 + 22 = ___ + ___
15. Distributive property:
(7 x 4) + (7 x 2) = ___ (___ + ___)
16. Identity property:
58 + ___ = 58
17. Associative property:
9 (___ x 6) = (___ x 8) x ___
18. Commutative property:
195 x 67 = ____ x ____
19. Distributive property:
7 (___ + ___) = (___ x 5) + (___ x 1)
20. Identity property:
____ x ___ = 17
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© 2007 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #155819
Using the Basic Properties of Numbers Reproducible
Solve the following equations to prove that each property is true:
Commutative
Associative
Distributive
Ex: 4 x 9 = 9 x 4
36 = 36
Ex: 4 + (7 + 8) = (4 + 7) + 8
4 + 15 = 11 + 8
19 = 19
Ex: 3(4 + 1) = (3 x 4) + (3 x 1)
3(5) = (12) + (3)
15 = 15
1. 8 x 10 = 10 x 8
2. 7 x (6 x 2) = (7 x 6) x 2
3. 5 (6 + 2) = (5 x 6) + (5 x 2)
4. (9 + 5) + 8 = 9 + (5 + 8)
5. 97 x 2 = 2 x 97
6. (2 x 4) x 5 = 2 x (4 x 5)
7. 6 (3 + 9) = (6 x 3) + (6 x 9)
8. 14 + (7 + 20) = (14 + 7) + 20
9. 8 x 50 = 50 x 8
10. 25 + (10 + 4) = (25 + 10) + 4
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© 2007 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #155819